ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW473+2 : 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 : n009.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 09:07:56 AM UTC 2026

% Result   : Theorem 59.17s 59.48s
% Output   : Proof 59.31s
% 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__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun949378684l_bool(B_2_1)
     => is_fun949378684l_bool(cOMBB_2140588453a_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool) ).

fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1661590463l_bool(B_2_1)
     => is_fun1661590463l_bool(cOMBB_307249310e_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_) ).

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_COMBK_000tc__HOL__Obool_000tc__Com__Opname,axiom,
    ! [B_1_1] :
      ( is_bool(B_1_1)
     => is_fun_pname_bool(cOMBK_bool_pname(B_1_1)) ),
    file('theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname) ).

fof(gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1] :
      ( is_bool(B_1_1)
     => is_fun949378684l_bool(cOMBK_324466864a_bool(B_1_1)) ),
    file('theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1] :
      ( is_bool(B_1_1)
     => is_fun1661590463l_bool(cOMBK_1857069011e_bool(B_1_1)) ),
    file('theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

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_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_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc,axiom,
    is_fun949378684l_bool(bot_bo1389914601l_bool),
    file('theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc) ).

fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__,axiom,
    is_fun1661590463l_bool(bot_bo1649642514l_bool),
    file('theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__) ).

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__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__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_Set_Oinsert_000t__a,hypothesis,
    ! [B_1_1,B_2_1] :
      ( ( is_fun_a_bool(B_2_1)
        & is_a(B_1_1) )
     => is_fun_a_bool(insert_a(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_Set_Oinsert_000t__a) ).

fof(gsy_c_Set_Oinsert_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2_1] :
      ( ( is_fun_pname_bool(B_2_1)
        & is_pname(B_1_1) )
     => is_fun_pname_bool(insert_pname(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_Set_Oinsert_000tc__Com__Opname) ).

fof(gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2_1] :
      ( ( is_fun949378684l_bool(B_2_1)
        & is_fun_a_bool(B_1_1) )
     => is_fun949378684l_bool(insert_fun_a_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2_1] :
      ( ( is_fun1661590463l_bool(B_2_1)
        & is_fun_pname_bool(B_1_1) )
     => is_fun1661590463l_bool(insert1325755072e_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

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__Com__Opname,axiom,
    ! [B_1_1,B_2_1] :
      ( is_a(B_2_1)
     => is_pname(hAPP_a_pname(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000t__a_000tc__Com__Opname) ).

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_000t__a_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H,axiom,
    ! [B_1_1,B_2_1] :
      ( is_a(B_2_1)
     => is_fun1661590463l_bool(hAPP_a217006258l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H) ).

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_It__a_Mtc__HOL__Obool_J_Mtc__H,axiom,
    ! [B_1_1,B_2_1] :
      ( is_pname(B_2_1)
     => is_fun949378684l_bool(hAPP_p1824510254l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) ).

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__Nat__Onat_000t__a,axiom,
    ! [B_1_1,B_2_1] : is_a(hAPP_nat_a(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000t__a) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2_1] : is_pname(hAPP_nat_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Com__Opname) ).

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_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(B_2_1)
     => is_pname(hAPP_f1128469712_pname(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) ).

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,axiom,
    ! [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__Com__Opname_Mtc__H,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(B_2_1)
     => is_fun_pname_bool(hAPP_f1794073134e_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opname_Mtc__H) ).

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_It__a_Mtc__H,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(B_2_1)
     => is_fun_a_bool(hAPP_f1051908748a_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__H) ).

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__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2_1] : is_pname(hAPP_f1291551745_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) ).

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__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL,axiom,
    ! [B_1_1,B_2_1] : is_fun_a_bool(hAPP_f1549043526a_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opna,axiom,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f654413245e_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opna) ).

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__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__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_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
     => hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),A_1)))) ),
    file('theBenchmark.p',fact_1_finite__Collect__subsets) ).

fof(fact_2_finite__Collect__subsets,axiom,
    ! [A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A_1)))) ),
    file('theBenchmark.p',fact_2_finite__Collect__subsets) ).

fof(fact_3_finite__Collect__subsets,axiom,
    ! [A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
     => hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),A_1)))) ),
    file('theBenchmark.p',fact_3_finite__Collect__subsets) ).

fof(fact_4_finite__Collect__subsets,axiom,
    ! [A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),A_1)))) ),
    file('theBenchmark.p',fact_4_finite__Collect__subsets) ).

fof(fact_5_finite__Collect__subsets,axiom,
    ! [A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A_1)))) ),
    file('theBenchmark.p',fact_5_finite__Collect__subsets) ).

fof(fact_6_finite__Collect__subsets,axiom,
    ! [A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),A_1)))) ),
    file('theBenchmark.p',fact_6_finite__Collect__subsets) ).

fof(fact_7_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_7_finite__imageI) ).

fof(fact_8_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_8_finite__imageI) ).

fof(fact_9_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_9_finite__imageI) ).

fof(fact_10_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_10_finite__imageI) ).

fof(fact_11_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_11_finite__imageI) ).

fof(fact_12_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_12_finite__imageI) ).

fof(fact_13_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_13_finite__imageI) ).

fof(fact_14_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_14_finite__imageI) ).

fof(fact_15_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_15_finite__imageI) ).

fof(fact_16_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_16_finite__imageI) ).

fof(fact_17_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_17_finite__imageI) ).

fof(fact_18_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_18_finite__imageI) ).

fof(fact_19_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_19_finite__imageI) ).

fof(fact_20_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_20_finite__imageI) ).

fof(fact_21_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_21_finite__imageI) ).

fof(fact_22_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_22_finite__imageI) ).

fof(fact_23_finite_OinsertI,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_3,A_1))) ),
    file('theBenchmark.p',fact_23_finite_OinsertI) ).

fof(fact_24_finite_OinsertI,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_3,A_1))) ),
    file('theBenchmark.p',fact_24_finite_OinsertI) ).

fof(fact_25_finite_OinsertI,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_3,A_1))) ),
    file('theBenchmark.p',fact_25_finite_OinsertI) ).

fof(fact_26_finite_OinsertI,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_3,A_1))) ),
    file('theBenchmark.p',fact_26_finite_OinsertI) ).

fof(fact_27_finite_OinsertI,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_3,A_1))) ),
    file('theBenchmark.p',fact_27_finite_OinsertI) ).

fof(fact_28_finite_OinsertI,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_3,A_1))) ),
    file('theBenchmark.p',fact_28_finite_OinsertI) ).

fof(fact_29_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(F,A_1))),hAPP_f921600141ol_nat(finite_card_pname,A_1))) ),
    file('theBenchmark.p',fact_29_card__image__le) ).

fof(fact_30_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(F,A_1))),hAPP_fun_a_bool_nat(finite_card_a,A_1))) ),
    file('theBenchmark.p',fact_30_card__image__le) ).

fof(fact_31_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
     => 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_1))),hAPP_f696928925ol_nat(finite346522414t_bool,A_1))) ),
    file('theBenchmark.p',fact_31_card__image__le) ).

fof(fact_32_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(F,A_1))),hAPP_f55526627ol_nat(finite1340463720e_bool,A_1))) ),
    file('theBenchmark.p',fact_32_card__image__le) ).

fof(fact_33_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
     => 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_1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1))) ),
    file('theBenchmark.p',fact_33_card__image__le) ).

fof(fact_34_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(F,A_1))),hAPP_f921600141ol_nat(finite_card_pname,A_1))) ),
    file('theBenchmark.p',fact_34_card__image__le) ).

fof(fact_35_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(F,A_1))),hAPP_fun_a_bool_nat(finite_card_a,A_1))) ),
    file('theBenchmark.p',fact_35_card__image__le) ).

fof(fact_36_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(F,A_1))),hAPP_f696928925ol_nat(finite346522414t_bool,A_1))) ),
    file('theBenchmark.p',fact_36_card__image__le) ).

fof(fact_37_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(F,A_1))),hAPP_f55526627ol_nat(finite1340463720e_bool,A_1))) ),
    file('theBenchmark.p',fact_37_card__image__le) ).

fof(fact_38_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(F,A_1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1))) ),
    file('theBenchmark.p',fact_38_card__image__le) ).

fof(fact_39_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(F,A_1))),hAPP_fun_a_bool_nat(finite_card_a,A_1))) ),
    file('theBenchmark.p',fact_39_card__image__le) ).

fof(fact_40_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(F,A_1))),hAPP_f22106695ol_nat(finite_card_nat,A_1))) ),
    file('theBenchmark.p',fact_40_card__image__le) ).

fof(fact_41_card__image__le,axiom,
    ! [F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(F,A_1))),hAPP_f921600141ol_nat(finite_card_pname,A_1))) ),
    file('theBenchmark.p',fact_41_card__image__le) ).

fof(fact_42_card__mono,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A_1)),hAPP_f696928925ol_nat(finite346522414t_bool,B_6))) ) ),
    file('theBenchmark.p',fact_42_card__mono) ).

fof(fact_43_card__mono,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)),hAPP_f55526627ol_nat(finite1340463720e_bool,B_6))) ) ),
    file('theBenchmark.p',fact_43_card__mono) ).

fof(fact_44_card__mono,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,B_6))) ) ),
    file('theBenchmark.p',fact_44_card__mono) ).

fof(fact_45_card__mono,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A_1)),hAPP_f921600141ol_nat(finite_card_pname,B_6))) ) ),
    file('theBenchmark.p',fact_45_card__mono) ).

fof(fact_46_card__mono,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A_1)),hAPP_fun_a_bool_nat(finite_card_a,B_6))) ) ),
    file('theBenchmark.p',fact_46_card__mono) ).

fof(fact_47_card__mono,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A_1)),hAPP_f22106695ol_nat(finite_card_nat,B_6))) ) ),
    file('theBenchmark.p',fact_47_card__mono) ).

fof(fact_48_card__seteq,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,B_6)),hAPP_f696928925ol_nat(finite346522414t_bool,A_1)))
         => A_1 = B_6 ) ) ),
    file('theBenchmark.p',fact_48_card__seteq) ).

fof(fact_49_card__seteq,axiom,
    ! [A_1,B_6] :
      ( ( is_fun1661590463l_bool(B_6)
        & is_fun1661590463l_bool(A_1) )
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6))
         => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,B_6)),hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)))
           => A_1 = B_6 ) ) ) ),
    file('theBenchmark.p',fact_49_card__seteq) ).

fof(fact_50_card__seteq,axiom,
    ! [A_1,B_6] :
      ( ( is_fun949378684l_bool(B_6)
        & is_fun949378684l_bool(A_1) )
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
       => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6))
         => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,B_6)),hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)))
           => A_1 = B_6 ) ) ) ),
    file('theBenchmark.p',fact_50_card__seteq) ).

fof(fact_51_card__seteq,axiom,
    ! [A_1,B_6] :
      ( ( is_fun_pname_bool(B_6)
        & is_fun_pname_bool(A_1) )
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
         => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,B_6)),hAPP_f921600141ol_nat(finite_card_pname,A_1)))
           => A_1 = B_6 ) ) ) ),
    file('theBenchmark.p',fact_51_card__seteq) ).

fof(fact_52_card__seteq,axiom,
    ! [A_1,B_6] :
      ( ( is_fun_a_bool(B_6)
        & is_fun_a_bool(A_1) )
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
         => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,B_6)),hAPP_fun_a_bool_nat(finite_card_a,A_1)))
           => A_1 = B_6 ) ) ) ),
    file('theBenchmark.p',fact_52_card__seteq) ).

fof(fact_53_card__seteq,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,B_6)),hAPP_f22106695ol_nat(finite_card_nat,A_1)))
         => A_1 = B_6 ) ) ),
    file('theBenchmark.p',fact_53_card__seteq) ).

fof(fact_54_card__insert__le,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A_1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)))) ),
    file('theBenchmark.p',fact_54_card__insert__le) ).

fof(fact_55_card__insert__le,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)))) ),
    file('theBenchmark.p',fact_55_card__insert__le) ).

fof(fact_56_card__insert__le,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)))) ),
    file('theBenchmark.p',fact_56_card__insert__le) ).

fof(fact_57_card__insert__le,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A_1)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)))) ),
    file('theBenchmark.p',fact_57_card__insert__le) ).

fof(fact_58_card__insert__le,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A_1)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)))) ),
    file('theBenchmark.p',fact_58_card__insert__le) ).

fof(fact_59_card__insert__le,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A_1)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)))) ),
    file('theBenchmark.p',fact_59_card__insert__le) ).

fof(fact_60_card__insert__if,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
     => ( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_3),A_1))
         => hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A_1)) )
        & ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_3),A_1))
         => hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)) = hAPP_f696928925ol_nat(finite346522414t_bool,A_1) ) ) ),
    file('theBenchmark.p',fact_60_card__insert__if) ).

fof(fact_61_card__insert__if,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => ( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_3),A_1))
         => hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)) )
        & ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_3),A_1))
         => hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)) = hAPP_f55526627ol_nat(finite1340463720e_bool,A_1) ) ) ),
    file('theBenchmark.p',fact_61_card__insert__if) ).

fof(fact_62_card__insert__if,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
     => ( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_3),A_1))
         => hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)) )
        & ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_3),A_1))
         => hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1) ) ) ),
    file('theBenchmark.p',fact_62_card__insert__if) ).

fof(fact_63_card__insert__if,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
         => hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A_1)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
         => hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)) = hAPP_f22106695ol_nat(finite_card_nat,A_1) ) ) ),
    file('theBenchmark.p',fact_63_card__insert__if) ).

fof(fact_64_card__insert__if,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
         => hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A_1)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
         => hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)) = hAPP_f921600141ol_nat(finite_card_pname,A_1) ) ) ),
    file('theBenchmark.p',fact_64_card__insert__if) ).

fof(fact_65_card__insert__if,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
         => hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A_1)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
         => hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)) = hAPP_fun_a_bool_nat(finite_card_a,A_1) ) ) ),
    file('theBenchmark.p',fact_65_card__insert__if) ).

fof(fact_66_card__insert__disjoint,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
     => ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_3),A_1))
       => hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A_1)) ) ),
    file('theBenchmark.p',fact_66_card__insert__disjoint) ).

fof(fact_67_card__insert__disjoint,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_3),A_1))
       => hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)) ) ),
    file('theBenchmark.p',fact_67_card__insert__disjoint) ).

fof(fact_68_card__insert__disjoint,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
     => ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_3),A_1))
       => hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)) ) ),
    file('theBenchmark.p',fact_68_card__insert__disjoint) ).

fof(fact_69_card__insert__disjoint,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
       => hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A_1)) ) ),
    file('theBenchmark.p',fact_69_card__insert__disjoint) ).

fof(fact_70_card__insert__disjoint,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
       => hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A_1)) ) ),
    file('theBenchmark.p',fact_70_card__insert__disjoint) ).

fof(fact_71_card__insert__disjoint,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
       => hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A_1)) ) ),
    file('theBenchmark.p',fact_71_card__insert__disjoint) ).

fof(fact_72_finite__Collect__conjI,axiom,
    ! [Q_1,Pa] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1)))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) )
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,Pa),Q_1)))) ),
    file('theBenchmark.p',fact_72_finite__Collect__conjI) ).

fof(fact_73_finite__Collect__conjI,axiom,
    ! [Q_1,Pa] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1)))
        | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) )
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,Pa),Q_1)))) ),
    file('theBenchmark.p',fact_73_finite__Collect__conjI) ).

fof(fact_74_finite__Collect__conjI,axiom,
    ! [Q_1,Pa] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
        | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) )
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,Pa),Q_1)))) ),
    file('theBenchmark.p',fact_74_finite__Collect__conjI) ).

fof(fact_75_finite__Collect__conjI,axiom,
    ! [Q_1,Pa] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1)))
        | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) )
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,Pa),Q_1)))) ),
    file('theBenchmark.p',fact_75_finite__Collect__conjI) ).

fof(fact_76_finite__Collect__conjI,axiom,
    ! [Q_1,Pa] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) )
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,Pa),Q_1)))) ),
    file('theBenchmark.p',fact_76_finite__Collect__conjI) ).

fof(fact_77_finite__Collect__conjI,axiom,
    ! [Q_1,Pa] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) )
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),Q_1)))) ),
    file('theBenchmark.p',fact_77_finite__Collect__conjI) ).

fof(fact_78_Suc__diff__le,axiom,
    ! [N,M] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M))
     => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(M),N)) ),
    file('theBenchmark.p',fact_78_Suc__diff__le) ).

fof(fact_79_finite__Collect__le__nat,axiom,
    ! [K_2] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),K_2)))),
    file('theBenchmark.p',fact_79_finite__Collect__le__nat) ).

fof(fact_80_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_80_card__Collect__le__nat) ).

fof(fact_81_Suc__inject,axiom,
    ! [X,Y] :
      ( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y)
     => X = Y ),
    file('theBenchmark.p',fact_81_Suc__inject) ).

fof(fact_82_nat_Oinject,axiom,
    ! [Nat_3,Nat_2] :
      ( hAPP_nat_nat(suc,Nat_3) = hAPP_nat_nat(suc,Nat_2)
    <=> Nat_3 = Nat_2 ),
    file('theBenchmark.p',fact_82_nat_Oinject) ).

fof(fact_83_Suc__n__not__n,axiom,
    ! [N] : hAPP_nat_nat(suc,N) != N,
    file('theBenchmark.p',fact_83_Suc__n__not__n) ).

fof(fact_84_n__not__Suc__n,axiom,
    ! [N] : N != hAPP_nat_nat(suc,N),
    file('theBenchmark.p',fact_84_n__not__Suc__n) ).

fof(fact_85_le__antisym,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M))
       => M = N ) ),
    file('theBenchmark.p',fact_85_le__antisym) ).

fof(fact_86_le__trans,axiom,
    ! [K,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),K))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K)) ) ),
    file('theBenchmark.p',fact_86_le__trans) ).

fof(fact_87_eq__imp__le,axiom,
    ! [M,N] :
      ( M = N
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    file('theBenchmark.p',fact_87_eq__imp__le) ).

fof(fact_88_nat__le__linear,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    file('theBenchmark.p',fact_88_nat__le__linear) ).

fof(fact_89_le__refl,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N)),
    file('theBenchmark.p',fact_89_le__refl) ).

fof(fact_90_diff__commute,axiom,
    ! [I,J_2,K] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J_2)),K) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),K)),J_2),
    file('theBenchmark.p',fact_90_diff__commute) ).

fof(fact_91_finite__Collect__disjI,axiom,
    ! [Pa,Q_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,Pa),Q_1))))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1)))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) ) ),
    file('theBenchmark.p',fact_91_finite__Collect__disjI) ).

fof(fact_92_finite__Collect__disjI,axiom,
    ! [Pa,Q_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,Pa),Q_1))))
    <=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1)))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) ) ),
    file('theBenchmark.p',fact_92_finite__Collect__disjI) ).

fof(fact_93_finite__Collect__disjI,axiom,
    ! [Pa,Q_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,Pa),Q_1))))
    <=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) ) ),
    file('theBenchmark.p',fact_93_finite__Collect__disjI) ).

fof(fact_94_finite__Collect__disjI,axiom,
    ! [Pa,Q_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,Pa),Q_1))))
    <=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1)))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) ) ),
    file('theBenchmark.p',fact_94_finite__Collect__disjI) ).

fof(fact_95_finite__Collect__disjI,axiom,
    ! [Pa,Q_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Q_1))))
    <=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) ) ),
    file('theBenchmark.p',fact_95_finite__Collect__disjI) ).

fof(fact_96_finite__Collect__disjI,axiom,
    ! [Pa,Q_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,Pa),Q_1))))
    <=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1)))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) ) ),
    file('theBenchmark.p',fact_96_finite__Collect__disjI) ).

fof(fact_97_finite__insert,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_3,A_1)))
    <=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    file('theBenchmark.p',fact_97_finite__insert) ).

fof(fact_98_finite__insert,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_3,A_1)))
    <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    file('theBenchmark.p',fact_98_finite__insert) ).

fof(fact_99_finite__insert,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_3,A_1)))
    <=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    file('theBenchmark.p',fact_99_finite__insert) ).

fof(fact_100_finite__insert,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_3,A_1)))
    <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    file('theBenchmark.p',fact_100_finite__insert) ).

fof(fact_101_finite__insert,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_3,A_1)))
    <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    file('theBenchmark.p',fact_101_finite__insert) ).

fof(fact_102_finite__insert,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_3,A_1)))
    <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    file('theBenchmark.p',fact_102_finite__insert) ).

fof(fact_103_finite__subset,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6))
     => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ) ),
    file('theBenchmark.p',fact_103_finite__subset) ).

fof(fact_104_finite__subset,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ),
    file('theBenchmark.p',fact_104_finite__subset) ).

fof(fact_105_finite__subset,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6))
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ) ),
    file('theBenchmark.p',fact_105_finite__subset) ).

fof(fact_106_finite__subset,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ) ),
    file('theBenchmark.p',fact_106_finite__subset) ).

fof(fact_107_finite__subset,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ),
    file('theBenchmark.p',fact_107_finite__subset) ).

fof(fact_108_finite__subset,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ) ),
    file('theBenchmark.p',fact_108_finite__subset) ).

fof(fact_109_rev__finite__subset,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ) ),
    file('theBenchmark.p',fact_109_rev__finite__subset) ).

fof(fact_110_rev__finite__subset,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ) ),
    file('theBenchmark.p',fact_110_rev__finite__subset) ).

fof(fact_111_rev__finite__subset,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ) ),
    file('theBenchmark.p',fact_111_rev__finite__subset) ).

fof(fact_112_rev__finite__subset,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ) ),
    file('theBenchmark.p',fact_112_rev__finite__subset) ).

fof(fact_113_rev__finite__subset,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ) ),
    file('theBenchmark.p',fact_113_rev__finite__subset) ).

fof(fact_114_rev__finite__subset,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ) ),
    file('theBenchmark.p',fact_114_rev__finite__subset) ).

fof(fact_115_Suc__leD,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    file('theBenchmark.p',fact_115_Suc__leD) ).

fof(fact_116_le__SucE,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
       => M = hAPP_nat_nat(suc,N) ) ),
    file('theBenchmark.p',fact_116_le__SucE) ).

fof(fact_117_le__SucI,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))) ),
    file('theBenchmark.p',fact_117_le__SucI) ).

fof(fact_118_Suc__le__mono,axiom,
    ! [Na,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_1)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_1)) ),
    file('theBenchmark.p',fact_118_Suc__le__mono) ).

fof(fact_119_le__Suc__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,Na)))
    <=> ( M_1 = hAPP_nat_nat(suc,Na)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_119_le__Suc__eq) ).

fof(fact_120_not__less__eq__eq,axiom,
    ! [M_1,Na] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) ),
    file('theBenchmark.p',fact_120_not__less__eq__eq) ).

fof(fact_121_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_121_Suc__n__not__le__n) ).

fof(fact_122_Suc__diff__diff,axiom,
    ! [M,N,K] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N)),hAPP_nat_nat(suc,K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),N)),K),
    file('theBenchmark.p',fact_122_Suc__diff__diff) ).

fof(fact_123_diff__Suc__Suc,axiom,
    ! [M,N] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(minus_minus_nat(M),N),
    file('theBenchmark.p',fact_123_diff__Suc__Suc) ).

fof(fact_124_le__diff__iff,axiom,
    ! [Na,K_2,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_1),K_2)),hAPP_nat_nat(minus_minus_nat(Na),K_2)))
        <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ) ),
    file('theBenchmark.p',fact_124_le__diff__iff) ).

fof(fact_125_Nat_Odiff__diff__eq,axiom,
    ! [N,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),N))
       => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),K)),hAPP_nat_nat(minus_minus_nat(N),K)) = hAPP_nat_nat(minus_minus_nat(M),N) ) ),
    file('theBenchmark.p',fact_125_Nat_Odiff__diff__eq) ).

fof(fact_126_eq__diff__iff,axiom,
    ! [Na,K_2,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na))
       => ( hAPP_nat_nat(minus_minus_nat(M_1),K_2) = hAPP_nat_nat(minus_minus_nat(Na),K_2)
        <=> M_1 = Na ) ) ),
    file('theBenchmark.p',fact_126_eq__diff__iff) ).

fof(fact_127_diff__diff__cancel,axiom,
    ! [I,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N))
     => hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(minus_minus_nat(N),I)) = I ),
    file('theBenchmark.p',fact_127_diff__diff__cancel) ).

fof(fact_128_diff__le__mono,axiom,
    ! [L,M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),L)),hAPP_nat_nat(minus_minus_nat(N),L))) ),
    file('theBenchmark.p',fact_128_diff__le__mono) ).

fof(fact_129_diff__le__mono2,axiom,
    ! [L,M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L),N)),hAPP_nat_nat(minus_minus_nat(L),M))) ),
    file('theBenchmark.p',fact_129_diff__le__mono2) ).

fof(fact_130_diff__le__self,axiom,
    ! [M,N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),N)),M)),
    file('theBenchmark.p',fact_130_diff__le__self) ).

fof(fact_131_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_a_a(F,A_1)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) ),
    file('theBenchmark.p',fact_131_finite__surj) ).

fof(fact_132_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_nat_bool_a(F,A_1)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) ),
    file('theBenchmark.p',fact_132_finite__surj) ).

fof(fact_133_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_876012084bool_a(F,A_1)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) ),
    file('theBenchmark.p',fact_133_finite__surj) ).

fof(fact_134_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_a_bool_a(F,A_1)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) ),
    file('theBenchmark.p',fact_134_finite__surj) ).

fof(fact_135_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_2129980159t_bool(F,A_1)))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) ) ),
    file('theBenchmark.p',fact_135_finite__surj) ).

fof(fact_136_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_47868345e_bool(F,A_1)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) ) ),
    file('theBenchmark.p',fact_136_finite__surj) ).

fof(fact_137_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_112932426a_bool(F,A_1)))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) ) ),
    file('theBenchmark.p',fact_137_finite__surj) ).

fof(fact_138_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_pname_pname(F,A_1)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) ),
    file('theBenchmark.p',fact_138_finite__surj) ).

fof(fact_139_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_pname_nat(F,A_1)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ),
    file('theBenchmark.p',fact_139_finite__surj) ).

fof(fact_140_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) ),
    file('theBenchmark.p',fact_140_finite__surj) ).

fof(fact_141_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_26036933t_bool(F,A_1)))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) ) ),
    file('theBenchmark.p',fact_141_finite__surj) ).

fof(fact_142_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_1655916159e_bool(F,A_1)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) ) ),
    file('theBenchmark.p',fact_142_finite__surj) ).

fof(fact_143_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_nat_fun_a_bool(F,A_1)))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) ) ),
    file('theBenchmark.p',fact_143_finite__surj) ).

fof(fact_144_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_nat_pname(F,A_1)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) ),
    file('theBenchmark.p',fact_144_finite__surj) ).

fof(fact_145_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_nat_nat(F,A_1)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ),
    file('theBenchmark.p',fact_145_finite__surj) ).

fof(fact_146_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) ),
    file('theBenchmark.p',fact_146_finite__surj) ).

fof(fact_147_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1921560913_pname(F,A_1)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) ),
    file('theBenchmark.p',fact_147_finite__surj) ).

fof(fact_148_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1283814551_pname(F,A_1)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) ),
    file('theBenchmark.p',fact_148_finite__surj) ).

fof(fact_149_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1854862208_pname(F,A_1)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ) ),
    file('theBenchmark.p',fact_149_finite__surj) ).

fof(fact_150_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ),
    file('theBenchmark.p',fact_150_finite__surj) ).

fof(fact_151_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_496248727ol_nat(F,A_1)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ),
    file('theBenchmark.p',fact_151_finite__surj) ).

fof(fact_152_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_1551609309ol_nat(F,A_1)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ),
    file('theBenchmark.p',fact_152_finite__surj) ).

fof(fact_153_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_fun_a_bool_nat(F,A_1)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ) ),
    file('theBenchmark.p',fact_153_finite__surj) ).

fof(fact_154_finite__surj,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ) ),
    file('theBenchmark.p',fact_154_finite__surj) ).

fof(fact_155_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun_a_bool(B_6)
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_nat_bool_a(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_fun_nat_bool_a(F,C_7)
              & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_7))
              & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_7),A_1)) ) ) ) ),
    file('theBenchmark.p',fact_155_finite__subset__image) ).

fof(fact_156_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun_a_bool(B_6)
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_876012084bool_a(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_876012084bool_a(F,C_7)
              & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_7))
              & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_7),A_1))
              & is_fun1661590463l_bool(C_7) ) ) ) ),
    file('theBenchmark.p',fact_156_finite__subset__image) ).

fof(fact_157_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun_a_bool(B_6)
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_a_bool_a(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_fun_a_bool_a(F,C_7)
              & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_7))
              & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_7),A_1))
              & is_fun949378684l_bool(C_7) ) ) ) ),
    file('theBenchmark.p',fact_157_finite__subset__image) ).

fof(fact_158_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun_a_bool(B_6)
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_a_a(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_a_a(F,C_7)
              & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7))
              & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1))
              & is_fun_a_bool(C_7) ) ) ) ),
    file('theBenchmark.p',fact_158_finite__subset__image) ).

fof(fact_159_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_a_fun_nat_bool(F,A_1)))
       => ? [C_7] :
            ( B_6 = image_a_fun_nat_bool(F,C_7)
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1))
            & is_fun_a_bool(C_7) ) ) ),
    file('theBenchmark.p',fact_159_finite__subset__image) ).

fof(fact_160_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun1661590463l_bool(B_6)
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_819518260e_bool(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_819518260e_bool(F,C_7)
              & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7))
              & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1))
              & is_fun_a_bool(C_7) ) ) ) ),
    file('theBenchmark.p',fact_160_finite__subset__image) ).

fof(fact_161_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun949378684l_bool(B_6)
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
       => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_a_fun_a_bool(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_a_fun_a_bool(F,C_7)
              & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7))
              & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1))
              & is_fun_a_bool(C_7) ) ) ) ),
    file('theBenchmark.p',fact_161_finite__subset__image) ).

fof(fact_162_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun_pname_bool(B_6)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_a_pname(F,C_7)
              & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7))
              & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1))
              & is_fun_a_bool(C_7) ) ) ) ),
    file('theBenchmark.p',fact_162_finite__subset__image) ).

fof(fact_163_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun_pname_bool(B_6)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1921560913_pname(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_1921560913_pname(F,C_7)
              & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_7))
              & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_7),A_1)) ) ) ) ),
    file('theBenchmark.p',fact_163_finite__subset__image) ).

fof(fact_164_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun_pname_bool(B_6)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1283814551_pname(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_1283814551_pname(F,C_7)
              & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_7))
              & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_7),A_1))
              & is_fun1661590463l_bool(C_7) ) ) ) ),
    file('theBenchmark.p',fact_164_finite__subset__image) ).

fof(fact_165_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun_pname_bool(B_6)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1854862208_pname(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_1854862208_pname(F,C_7)
              & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_7))
              & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_7),A_1))
              & is_fun949378684l_bool(C_7) ) ) ) ),
    file('theBenchmark.p',fact_165_finite__subset__image) ).

fof(fact_166_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1)))
       => ? [C_7] :
            ( B_6 = image_a_nat(F,C_7)
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1))
            & is_fun_a_bool(C_7) ) ) ),
    file('theBenchmark.p',fact_166_finite__subset__image) ).

fof(fact_167_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_496248727ol_nat(F,A_1)))
       => ? [C_7] :
            ( B_6 = image_496248727ol_nat(F,C_7)
            & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_7))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_7),A_1)) ) ) ),
    file('theBenchmark.p',fact_167_finite__subset__image) ).

fof(fact_168_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_1551609309ol_nat(F,A_1)))
       => ? [C_7] :
            ( B_6 = image_1551609309ol_nat(F,C_7)
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_7))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_7),A_1))
            & is_fun1661590463l_bool(C_7) ) ) ),
    file('theBenchmark.p',fact_168_finite__subset__image) ).

fof(fact_169_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_fun_a_bool_nat(F,A_1)))
       => ? [C_7] :
            ( B_6 = image_fun_a_bool_nat(F,C_7)
            & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_7))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_7),A_1))
            & is_fun949378684l_bool(C_7) ) ) ),
    file('theBenchmark.p',fact_169_finite__subset__image) ).

fof(fact_170_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_2129980159t_bool(F,A_1)))
       => ? [C_7] :
            ( B_6 = image_2129980159t_bool(F,C_7)
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1))
            & is_fun_pname_bool(C_7) ) ) ),
    file('theBenchmark.p',fact_170_finite__subset__image) ).

fof(fact_171_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun1661590463l_bool(B_6)
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_47868345e_bool(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_47868345e_bool(F,C_7)
              & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1))
              & is_fun_pname_bool(C_7) ) ) ) ),
    file('theBenchmark.p',fact_171_finite__subset__image) ).

fof(fact_172_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun949378684l_bool(B_6)
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
       => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_112932426a_bool(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_112932426a_bool(F,C_7)
              & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1))
              & is_fun_pname_bool(C_7) ) ) ) ),
    file('theBenchmark.p',fact_172_finite__subset__image) ).

fof(fact_173_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun_pname_bool(B_6)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_pname_pname(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_pname_pname(F,C_7)
              & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1))
              & is_fun_pname_bool(C_7) ) ) ) ),
    file('theBenchmark.p',fact_173_finite__subset__image) ).

fof(fact_174_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_pname_nat(F,A_1)))
       => ? [C_7] :
            ( B_6 = image_pname_nat(F,C_7)
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1))
            & is_fun_pname_bool(C_7) ) ) ),
    file('theBenchmark.p',fact_174_finite__subset__image) ).

fof(fact_175_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun_a_bool(B_6)
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_nat_a(F,C_7)
              & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7))
              & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) ) ) ) ),
    file('theBenchmark.p',fact_175_finite__subset__image) ).

fof(fact_176_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_26036933t_bool(F,A_1)))
       => ? [C_7] :
            ( B_6 = image_26036933t_bool(F,C_7)
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) ) ) ),
    file('theBenchmark.p',fact_176_finite__subset__image) ).

fof(fact_177_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun1661590463l_bool(B_6)
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_1655916159e_bool(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_1655916159e_bool(F,C_7)
              & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7))
              & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) ) ) ) ),
    file('theBenchmark.p',fact_177_finite__subset__image) ).

fof(fact_178_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun949378684l_bool(B_6)
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
       => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_nat_fun_a_bool(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_nat_fun_a_bool(F,C_7)
              & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7))
              & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) ) ) ) ),
    file('theBenchmark.p',fact_178_finite__subset__image) ).

fof(fact_179_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun_pname_bool(B_6)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_nat_pname(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_nat_pname(F,C_7)
              & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7))
              & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) ) ) ) ),
    file('theBenchmark.p',fact_179_finite__subset__image) ).

fof(fact_180_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_nat_nat(F,A_1)))
       => ? [C_7] :
            ( B_6 = image_nat_nat(F,C_7)
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) ) ) ),
    file('theBenchmark.p',fact_180_finite__subset__image) ).

fof(fact_181_finite__subset__image,axiom,
    ! [F,A_1,B_6] :
      ( is_fun_a_bool(B_6)
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1)))
         => ? [C_7] :
              ( B_6 = image_pname_a(F,C_7)
              & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1))
              & is_fun_pname_bool(C_7) ) ) ) ),
    file('theBenchmark.p',fact_181_finite__subset__image) ).

fof(fact_182_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,N_2)),hAPP_nat_bool(F,hAPP_nat_nat(suc,N_2))))
     => ( 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_182_lift__Suc__mono__le) ).

fof(fact_183_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,N_2)),hAPP_n1025906991e_bool(F,hAPP_nat_nat(suc,N_2))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,Na)),hAPP_n1025906991e_bool(F,N_3))) ) ),
    file('theBenchmark.p',fact_183_lift__Suc__mono__le) ).

fof(fact_184_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,N_2)),hAPP_n1699378549t_bool(F,hAPP_nat_nat(suc,N_2))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Na)),hAPP_n1699378549t_bool(F,N_3))) ) ),
    file('theBenchmark.p',fact_184_lift__Suc__mono__le) ).

fof(fact_185_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_2] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,N_2)),hAPP_nat_fun_a_bool(F,hAPP_nat_nat(suc,N_2))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,Na)),hAPP_nat_fun_a_bool(F,N_3))) ) ),
    file('theBenchmark.p',fact_185_lift__Suc__mono__le) ).

fof(fact_186_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,N_2)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_2))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Na)),hAPP_nat_nat(F,N_3))) ) ),
    file('theBenchmark.p',fact_186_lift__Suc__mono__le) ).

fof(fact_187_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(F,A_1)))
       => ? [X_1] :
            ( ~ 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_1)),hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,F)),hAPP_nat_pname(F,X_1))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_187_pigeonhole__infinite) ).

fof(fact_188_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_p1534023578a_bool(cOMBC_a_pname_bool(cOMBB_610033911bool_a(fequal_pname,F)),hAPP_a_pname(F,X_1))))))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
            & is_a(X_1) ) ) ),
    file('theBenchmark.p',fact_188_pigeonhole__infinite) ).

fof(fact_189_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_p61793385e_bool(cOMBC_1149511130e_bool(cOMBB_542850580_pname(fequal_pname,F)),hAPP_pname_pname(F,X_1))))))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
            & is_pname(X_1) ) ) ),
    file('theBenchmark.p',fact_189_pigeonhole__infinite) ).

fof(fact_190_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),A_1)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,F)),hAPP_f1291551745_pname(F,X_1))))))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_190_pigeonhole__infinite) ).

fof(fact_191_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),A_1)),hAPP_p338031245l_bool(cOMBC_1004116266e_bool(cOMBB_598082538e_bool(fequal_pname,F)),hAPP_f1297739591_pname(F,X_1))))))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1))
            & is_fun_pname_bool(X_1) ) ) ),
    file('theBenchmark.p',fact_191_pigeonhole__infinite) ).

fof(fact_192_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),A_1)),hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(cOMBB_1693087065a_bool(fequal_pname,F)),hAPP_f1128469712_pname(F,X_1))))))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A_1))
            & is_fun_a_bool(X_1) ) ) ),
    file('theBenchmark.p',fact_192_pigeonhole__infinite) ).

fof(fact_193_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(F,A_1)))
       => ? [X_1] :
            ( ~ 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_1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,F)),hAPP_nat_nat(F,X_1))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_193_pigeonhole__infinite) ).

fof(fact_194_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(cOMBB_1321347587bool_a(fequal_nat,F)),hAPP_a_nat(F,X_1))))))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
            & is_a(X_1) ) ) ),
    file('theBenchmark.p',fact_194_pigeonhole__infinite) ).

fof(fact_195_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(cOMBB_523834888_pname(fequal_nat,F)),hAPP_pname_nat(F,X_1))))))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
            & is_pname(X_1) ) ) ),
    file('theBenchmark.p',fact_195_pigeonhole__infinite) ).

fof(fact_196_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),A_1)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,F)),hAPP_f22106695ol_nat(F,X_1))))))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_196_pigeonhole__infinite) ).

fof(fact_197_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),A_1)),hAPP_n850744903l_bool(cOMBC_1666426608t_bool(cOMBB_1896684278e_bool(fequal_nat,F)),hAPP_f921600141ol_nat(F,X_1))))))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1))
            & is_fun_pname_bool(X_1) ) ) ),
    file('theBenchmark.p',fact_197_pigeonhole__infinite) ).

fof(fact_198_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),A_1)),hAPP_n1414589940l_bool(cOMBC_619334683t_bool(cOMBB_164527437a_bool(fequal_nat,F)),hAPP_fun_a_bool_nat(F,X_1))))))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A_1))
            & is_fun_a_bool(X_1) ) ) ),
    file('theBenchmark.p',fact_198_pigeonhole__infinite) ).

fof(fact_199_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(F,A_1)))
       => ? [X_1] :
            ( ~ 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_1)),hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,F)),hAPP_nat_a(F,X_1))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_199_pigeonhole__infinite) ).

fof(fact_200_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(F,A_1)))
       => ? [X_1] :
            ( ~ 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_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,F)),hAPP_n1699378549t_bool(F,X_1))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_200_pigeonhole__infinite) ).

fof(fact_201_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(F,A_1)))
       => ? [X_1] :
            ( ~ 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_1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,F)),hAPP_n1025906991e_bool(F,X_1))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_201_pigeonhole__infinite) ).

fof(fact_202_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(F,A_1)))
       => ? [X_1] :
            ( ~ 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_1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,F)),hAPP_nat_fun_a_bool(F,X_1))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_202_pigeonhole__infinite) ).

fof(fact_203_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_f654413245e_bool(cOMBC_267053842l_bool(cOMBB_928955006_pname(fequal_fun_nat_bool,F)),hAPP_p1499970991t_bool(F,X_1))))))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
            & is_pname(X_1) ) ) ),
    file('theBenchmark.p',fact_203_pigeonhole__infinite) ).

fof(fact_204_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(cOMBB_408569982_pname(fequal533582459e_bool,F)),hAPP_p61793385e_bool(F,X_1))))))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
            & is_pname(X_1) ) ) ),
    file('theBenchmark.p',fact_204_pigeonhole__infinite) ).

fof(fact_205_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_f1794073134e_bool(cOMBC_445755039l_bool(cOMBB_392435466_pname(fequal_fun_a_bool,F)),hAPP_p1534023578a_bool(F,X_1))))))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
            & is_pname(X_1) ) ) ),
    file('theBenchmark.p',fact_205_pigeonhole__infinite) ).

fof(fact_206_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_a_fun_a_bool(cOMBC_a_a_bool(cOMBB_a_fun_a_bool_a(fequal_a,F)),hAPP_a_a(F,X_1))))))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
            & is_a(X_1) ) ) ),
    file('theBenchmark.p',fact_206_pigeonhole__infinite) ).

fof(fact_207_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_f1549043526a_bool(cOMBC_777206479l_bool(cOMBB_743407885bool_a(fequal_fun_nat_bool,F)),hAPP_a_fun_nat_bool(F,X_1))))))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
            & is_a(X_1) ) ) ),
    file('theBenchmark.p',fact_207_pigeonhole__infinite) ).

fof(fact_208_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(cOMBB_1137537805bool_a(fequal533582459e_bool,F)),hAPP_a93125764e_bool(F,X_1))))))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
            & is_a(X_1) ) ) ),
    file('theBenchmark.p',fact_208_pigeonhole__infinite) ).

fof(fact_209_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(cOMBB_472261505bool_a(fequal_fun_a_bool,F)),hAPP_a_fun_a_bool(F,X_1))))))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
            & is_a(X_1) ) ) ),
    file('theBenchmark.p',fact_209_pigeonhole__infinite) ).

fof(fact_210_pigeonhole__infinite,axiom,
    ! [F,A_1] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(F,A_1)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,F)),hAPP_pname_a(F,X_1))))))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
            & is_pname(X_1) ) ) ),
    file('theBenchmark.p',fact_210_pigeonhole__infinite) ).

fof(fact_211_image__eqI,axiom,
    ! [A_1,B_1,F,X_3] :
      ( B_1 = hAPP_pname_nat(F,X_3)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_pname_nat(F,A_1))) ) ),
    file('theBenchmark.p',fact_211_image__eqI) ).

fof(fact_212_image__eqI,axiom,
    ! [A_1,B_1,F,X_3] :
      ( B_1 = hAPP_a_nat(F,X_3)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_a_nat(F,A_1))) ) ),
    file('theBenchmark.p',fact_212_image__eqI) ).

fof(fact_213_image__eqI,axiom,
    ! [A_1,B_1,F,X_3] :
      ( B_1 = hAPP_nat_pname(F,X_3)
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_nat_pname(F,A_1))) ) ),
    file('theBenchmark.p',fact_213_image__eqI) ).

fof(fact_214_image__eqI,axiom,
    ! [A_1,B_1,F,X_3] :
      ( B_1 = hAPP_nat_a(F,X_3)
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_nat_a(F,A_1))) ) ),
    file('theBenchmark.p',fact_214_image__eqI) ).

fof(fact_215_image__eqI,axiom,
    ! [A_1,B_1,F,X_3] :
      ( B_1 = hAPP_pname_a(F,X_3)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1))) ) ),
    file('theBenchmark.p',fact_215_image__eqI) ).

fof(fact_216_equalityI,axiom,
    ! [A_1,B_6] :
      ( ( is_fun_pname_bool(B_6)
        & is_fun_pname_bool(A_1) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1))
         => A_1 = B_6 ) ) ),
    file('theBenchmark.p',fact_216_equalityI) ).

fof(fact_217_equalityI,axiom,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1))
       => A_1 = B_6 ) ),
    file('theBenchmark.p',fact_217_equalityI) ).

fof(fact_218_equalityI,axiom,
    ! [A_1,B_6] :
      ( ( is_fun_a_bool(B_6)
        & is_fun_a_bool(A_1) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1))
         => A_1 = B_6 ) ) ),
    file('theBenchmark.p',fact_218_equalityI) ).

fof(fact_219_subsetD,axiom,
    ! [C_1,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B_6)) ) ),
    file('theBenchmark.p',fact_219_subsetD) ).

fof(fact_220_subsetD,axiom,
    ! [C_1,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),A_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),B_6)) ) ),
    file('theBenchmark.p',fact_220_subsetD) ).

fof(fact_221_subsetD,axiom,
    ! [C_1,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),A_1))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),B_6)) ) ),
    file('theBenchmark.p',fact_221_subsetD) ).

fof(fact_222_insertCI,axiom,
    ! [B_1,A_3,B_6] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),B_6))
       => A_3 = B_1 )
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,B_6))) ),
    file('theBenchmark.p',fact_222_insertCI) ).

fof(fact_223_insertCI,axiom,
    ! [B_1,A_3,B_6] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),B_6))
       => A_3 = B_1 )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,B_6))) ),
    file('theBenchmark.p',fact_223_insertCI) ).

fof(fact_224_insertCI,axiom,
    ! [B_1,A_3,B_6] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),B_6))
       => A_3 = B_1 )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,B_6))) ),
    file('theBenchmark.p',fact_224_insertCI) ).

fof(fact_225_insertE,axiom,
    ! [A_3,B_1,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,A_1)))
     => ( A_3 != B_1
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1)) ) ),
    file('theBenchmark.p',fact_225_insertE) ).

fof(fact_226_insertE,axiom,
    ! [A_3,B_1,A_1] :
      ( ( is_pname(B_1)
        & is_pname(A_3) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,A_1)))
       => ( A_3 != B_1
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1)) ) ) ),
    file('theBenchmark.p',fact_226_insertE) ).

fof(fact_227_insertE,axiom,
    ! [A_3,B_1,A_1] :
      ( ( is_a(B_1)
        & is_a(A_3) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
       => ( A_3 != B_1
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)) ) ) ),
    file('theBenchmark.p',fact_227_insertE) ).

fof(fact_228_zero__induct__lemma,axiom,
    ! [I_1,Pa,K_2] :
      ( hBOOL(hAPP_nat_bool(Pa,K_2))
     => ( ! [N_2] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2)))
           => hBOOL(hAPP_nat_bool(Pa,N_2)) )
       => hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(K_2),I_1))) ) ),
    file('theBenchmark.p',fact_228_zero__induct__lemma) ).

fof(fact_229_Suc__le__D,axiom,
    ! [N,M_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_3))
     => ? [M_2] : M_3 = hAPP_nat_nat(suc,M_2) ),
    file('theBenchmark.p',fact_229_Suc__le__D) ).

fof(fact_230_insertI1,axiom,
    ! [A_3,B_6] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(A_3,B_6))),
    file('theBenchmark.p',fact_230_insertI1) ).

fof(fact_231_insertI1,axiom,
    ! [A_3,B_6] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(A_3,B_6))),
    file('theBenchmark.p',fact_231_insertI1) ).

fof(fact_232_insertI1,axiom,
    ! [A_3,B_6] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(A_3,B_6))),
    file('theBenchmark.p',fact_232_insertI1) ).

fof(fact_233_insert__compr,axiom,
    ! [A_3,B_6] : insert_fun_nat_bool(A_3,B_6) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),B_6))),
    file('theBenchmark.p',fact_233_insert__compr) ).

fof(fact_234_insert__compr,axiom,
    ! [A_3,B_6] : insert1325755072e_bool(A_3,B_6) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),B_6))),
    file('theBenchmark.p',fact_234_insert__compr) ).

fof(fact_235_insert__compr,axiom,
    ! [A_3,B_6] : insert_fun_a_bool(A_3,B_6) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),B_6))),
    file('theBenchmark.p',fact_235_insert__compr) ).

fof(fact_236_insert__compr,axiom,
    ! [A_3,B_6] : insert_nat(A_3,B_6) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B_6))),
    file('theBenchmark.p',fact_236_insert__compr) ).

fof(fact_237_insert__compr,axiom,
    ! [A_3,B_6] : insert_pname(A_3,B_6) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B_6))),
    file('theBenchmark.p',fact_237_insert__compr) ).

fof(fact_238_insert__compr,axiom,
    ! [A_3,B_6] : insert_a(A_3,B_6) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B_6))),
    file('theBenchmark.p',fact_238_insert__compr) ).

fof(fact_239_insert__Collect,axiom,
    ! [A_3,Pa] : insert_pname(A_3,collect_pname(Pa)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3))),Pa)),
    file('theBenchmark.p',fact_239_insert__Collect) ).

fof(fact_240_insert__Collect,axiom,
    ! [A_3,Pa] : insert_fun_nat_bool(A_3,collect_fun_nat_bool(Pa)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3))),Pa)),
    file('theBenchmark.p',fact_240_insert__Collect) ).

fof(fact_241_insert__Collect,axiom,
    ! [A_3,Pa] : insert1325755072e_bool(A_3,collec1974731493e_bool(Pa)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3))),Pa)),
    file('theBenchmark.p',fact_241_insert__Collect) ).

fof(fact_242_insert__Collect,axiom,
    ! [A_3,Pa] : insert_fun_a_bool(A_3,collect_fun_a_bool(Pa)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3))),Pa)),
    file('theBenchmark.p',fact_242_insert__Collect) ).

fof(fact_243_insert__Collect,axiom,
    ! [A_3,Pa] : insert_nat(A_3,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_3))),Pa)),
    file('theBenchmark.p',fact_243_insert__Collect) ).

fof(fact_244_insert__Collect,axiom,
    ! [A_3,Pa] : insert_a(A_3,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_3))),Pa)),
    file('theBenchmark.p',fact_244_insert__Collect) ).

fof(fact_245_insert__absorb2,axiom,
    ! [X_3,A_1] : insert_pname(X_3,insert_pname(X_3,A_1)) = insert_pname(X_3,A_1),
    file('theBenchmark.p',fact_245_insert__absorb2) ).

fof(fact_246_insert__absorb2,axiom,
    ! [X_3,A_1] : insert_nat(X_3,insert_nat(X_3,A_1)) = insert_nat(X_3,A_1),
    file('theBenchmark.p',fact_246_insert__absorb2) ).

fof(fact_247_insert__absorb2,axiom,
    ! [X_3,A_1] : insert_a(X_3,insert_a(X_3,A_1)) = insert_a(X_3,A_1),
    file('theBenchmark.p',fact_247_insert__absorb2) ).

fof(fact_248_insert__commute,axiom,
    ! [X_3,Y_2,A_1] : insert_pname(X_3,insert_pname(Y_2,A_1)) = insert_pname(Y_2,insert_pname(X_3,A_1)),
    file('theBenchmark.p',fact_248_insert__commute) ).

fof(fact_249_insert__commute,axiom,
    ! [X_3,Y_2,A_1] : insert_nat(X_3,insert_nat(Y_2,A_1)) = insert_nat(Y_2,insert_nat(X_3,A_1)),
    file('theBenchmark.p',fact_249_insert__commute) ).

fof(fact_250_insert__commute,axiom,
    ! [X_3,Y_2,A_1] : insert_a(X_3,insert_a(Y_2,A_1)) = insert_a(Y_2,insert_a(X_3,A_1)),
    file('theBenchmark.p',fact_250_insert__commute) ).

fof(fact_251_insert__iff,axiom,
    ! [A_3,B_1,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,A_1)))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1))
        | A_3 = B_1 ) ),
    file('theBenchmark.p',fact_251_insert__iff) ).

fof(fact_252_insert__iff,axiom,
    ! [A_3,B_1,A_1] :
      ( ( is_pname(B_1)
        & is_pname(A_3) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,A_1)))
      <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1))
          | A_3 = B_1 ) ) ),
    file('theBenchmark.p',fact_252_insert__iff) ).

fof(fact_253_insert__iff,axiom,
    ! [A_3,B_1,A_1] :
      ( ( is_a(B_1)
        & is_a(A_3) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
      <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
          | A_3 = B_1 ) ) ),
    file('theBenchmark.p',fact_253_insert__iff) ).

fof(fact_254_insert__code,axiom,
    ! [Y_2,A_1,X_3] :
      ( ( is_pname(X_3)
        & is_pname(Y_2) )
     => ( hBOOL(hAPP_pname_bool(insert_pname(Y_2,A_1),X_3))
      <=> ( hBOOL(hAPP_pname_bool(A_1,X_3))
          | Y_2 = X_3 ) ) ),
    file('theBenchmark.p',fact_254_insert__code) ).

fof(fact_255_insert__code,axiom,
    ! [Y_2,A_1,X_3] :
      ( hBOOL(hAPP_nat_bool(insert_nat(Y_2,A_1),X_3))
    <=> ( hBOOL(hAPP_nat_bool(A_1,X_3))
        | Y_2 = X_3 ) ),
    file('theBenchmark.p',fact_255_insert__code) ).

fof(fact_256_insert__code,axiom,
    ! [Y_2,A_1,X_3] :
      ( ( is_a(X_3)
        & is_a(Y_2) )
     => ( hBOOL(hAPP_a_bool(insert_a(Y_2,A_1),X_3))
      <=> ( hBOOL(hAPP_a_bool(A_1,X_3))
          | Y_2 = X_3 ) ) ),
    file('theBenchmark.p',fact_256_insert__code) ).

fof(fact_257_insert__ident,axiom,
    ! [B_6,X_3,A_1] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6))
       => ( insert_nat(X_3,A_1) = insert_nat(X_3,B_6)
        <=> A_1 = B_6 ) ) ),
    file('theBenchmark.p',fact_257_insert__ident) ).

fof(fact_258_insert__ident,axiom,
    ! [B_6,X_3,A_1] :
      ( ( is_fun_pname_bool(A_1)
        & is_fun_pname_bool(B_6) )
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
       => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6))
         => ( insert_pname(X_3,A_1) = insert_pname(X_3,B_6)
          <=> A_1 = B_6 ) ) ) ),
    file('theBenchmark.p',fact_258_insert__ident) ).

fof(fact_259_insert__ident,axiom,
    ! [B_6,X_3,A_1] :
      ( ( is_fun_a_bool(A_1)
        & is_fun_a_bool(B_6) )
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
       => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
         => ( insert_a(X_3,A_1) = insert_a(X_3,B_6)
          <=> A_1 = B_6 ) ) ) ),
    file('theBenchmark.p',fact_259_insert__ident) ).

fof(fact_260_insertI2,axiom,
    ! [B_1,A_3,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),B_6))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,B_6))) ),
    file('theBenchmark.p',fact_260_insertI2) ).

fof(fact_261_insertI2,axiom,
    ! [B_1,A_3,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),B_6))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,B_6))) ),
    file('theBenchmark.p',fact_261_insertI2) ).

fof(fact_262_insertI2,axiom,
    ! [B_1,A_3,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),B_6))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,B_6))) ),
    file('theBenchmark.p',fact_262_insertI2) ).

fof(fact_263_insert__absorb,axiom,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1))
     => insert_nat(A_3,A_1) = A_1 ),
    file('theBenchmark.p',fact_263_insert__absorb) ).

fof(fact_264_insert__absorb,axiom,
    ! [A_3,A_1] :
      ( is_fun_pname_bool(A_1)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1))
       => insert_pname(A_3,A_1) = A_1 ) ),
    file('theBenchmark.p',fact_264_insert__absorb) ).

fof(fact_265_insert__absorb,axiom,
    ! [A_3,A_1] :
      ( is_fun_a_bool(A_1)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
       => insert_a(A_3,A_1) = A_1 ) ),
    file('theBenchmark.p',fact_265_insert__absorb) ).

fof(fact_266_subset__refl,axiom,
    ! [A_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),A_1)),
    file('theBenchmark.p',fact_266_subset__refl) ).

fof(fact_267_subset__refl,axiom,
    ! [A_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),A_1)),
    file('theBenchmark.p',fact_267_subset__refl) ).

fof(fact_268_subset__refl,axiom,
    ! [A_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),A_1)),
    file('theBenchmark.p',fact_268_subset__refl) ).

fof(fact_269_set__eq__subset,axiom,
    ! [A_1,B_6] :
      ( ( is_fun_pname_bool(B_6)
        & is_fun_pname_bool(A_1) )
     => ( A_1 = B_6
      <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ) ) ),
    file('theBenchmark.p',fact_269_set__eq__subset) ).

fof(fact_270_set__eq__subset,axiom,
    ! [A_1,B_6] :
      ( A_1 = B_6
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ) ),
    file('theBenchmark.p',fact_270_set__eq__subset) ).

fof(fact_271_set__eq__subset,axiom,
    ! [A_1,B_6] :
      ( ( is_fun_a_bool(B_6)
        & is_fun_a_bool(A_1) )
     => ( A_1 = B_6
      <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) ) ),
    file('theBenchmark.p',fact_271_set__eq__subset) ).

fof(fact_272_equalityD1,axiom,
    ! [A_1,B_6] :
      ( A_1 = B_6
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ),
    file('theBenchmark.p',fact_272_equalityD1) ).

fof(fact_273_equalityD1,axiom,
    ! [A_1,B_6] :
      ( A_1 = B_6
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ),
    file('theBenchmark.p',fact_273_equalityD1) ).

fof(fact_274_equalityD1,axiom,
    ! [A_1,B_6] :
      ( A_1 = B_6
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
    file('theBenchmark.p',fact_274_equalityD1) ).

fof(fact_275_equalityD2,axiom,
    ! [A_1,B_6] :
      ( A_1 = B_6
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1)) ),
    file('theBenchmark.p',fact_275_equalityD2) ).

fof(fact_276_equalityD2,axiom,
    ! [A_1,B_6] :
      ( A_1 = B_6
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1)) ),
    file('theBenchmark.p',fact_276_equalityD2) ).

fof(fact_277_equalityD2,axiom,
    ! [A_1,B_6] :
      ( A_1 = B_6
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1)) ),
    file('theBenchmark.p',fact_277_equalityD2) ).

fof(fact_278_in__mono,axiom,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) ) ),
    file('theBenchmark.p',fact_278_in__mono) ).

fof(fact_279_in__mono,axiom,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) ) ),
    file('theBenchmark.p',fact_279_in__mono) ).

fof(fact_280_in__mono,axiom,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) ) ),
    file('theBenchmark.p',fact_280_in__mono) ).

fof(fact_281_set__rev__mp,axiom,
    ! [B_6,X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) ) ),
    file('theBenchmark.p',fact_281_set__rev__mp) ).

fof(fact_282_set__rev__mp,axiom,
    ! [B_6,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) ) ),
    file('theBenchmark.p',fact_282_set__rev__mp) ).

fof(fact_283_set__rev__mp,axiom,
    ! [B_6,X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) ) ),
    file('theBenchmark.p',fact_283_set__rev__mp) ).

fof(fact_284_set__mp,axiom,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) ) ),
    file('theBenchmark.p',fact_284_set__mp) ).

fof(fact_285_set__mp,axiom,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) ) ),
    file('theBenchmark.p',fact_285_set__mp) ).

fof(fact_286_set__mp,axiom,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) ) ),
    file('theBenchmark.p',fact_286_set__mp) ).

fof(fact_287_mem__def,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
    <=> hBOOL(hAPP_nat_bool(A_1,X_3)) ),
    file('theBenchmark.p',fact_287_mem__def) ).

fof(fact_288_mem__def,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
    <=> hBOOL(hAPP_pname_bool(A_1,X_3)) ),
    file('theBenchmark.p',fact_288_mem__def) ).

fof(fact_289_mem__def,axiom,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
    <=> hBOOL(hAPP_a_bool(A_1,X_3)) ),
    file('theBenchmark.p',fact_289_mem__def) ).

fof(fact_290_Collect__def,axiom,
    ! [Pa] :
      ( is_fun_a_bool(Pa)
     => collect_a(Pa) = Pa ),
    file('theBenchmark.p',fact_290_Collect__def) ).

fof(fact_291_Collect__def,axiom,
    ! [Pa] :
      ( is_fun_pname_bool(Pa)
     => collect_pname(Pa) = Pa ),
    file('theBenchmark.p',fact_291_Collect__def) ).

fof(fact_292_Collect__def,axiom,
    ! [Pa] : collect_fun_nat_bool(Pa) = Pa,
    file('theBenchmark.p',fact_292_Collect__def) ).

fof(fact_293_Collect__def,axiom,
    ! [Pa] :
      ( is_fun1661590463l_bool(Pa)
     => collec1974731493e_bool(Pa) = Pa ),
    file('theBenchmark.p',fact_293_Collect__def) ).

fof(fact_294_Collect__def,axiom,
    ! [Pa] :
      ( is_fun949378684l_bool(Pa)
     => collect_fun_a_bool(Pa) = Pa ),
    file('theBenchmark.p',fact_294_Collect__def) ).

fof(fact_295_Collect__def,axiom,
    ! [Pa] : collect_nat(Pa) = Pa,
    file('theBenchmark.p',fact_295_Collect__def) ).

fof(fact_296_subset__trans,axiom,
    ! [C_6,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),C_6))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_6)) ) ),
    file('theBenchmark.p',fact_296_subset__trans) ).

fof(fact_297_subset__trans,axiom,
    ! [C_6,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),C_6))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),C_6)) ) ),
    file('theBenchmark.p',fact_297_subset__trans) ).

fof(fact_298_subset__trans,axiom,
    ! [C_6,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),C_6))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),C_6)) ) ),
    file('theBenchmark.p',fact_298_subset__trans) ).

fof(fact_299_equalityE,axiom,
    ! [A_1,B_6] :
      ( A_1 = B_6
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
         => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1)) ) ),
    file('theBenchmark.p',fact_299_equalityE) ).

fof(fact_300_equalityE,axiom,
    ! [A_1,B_6] :
      ( A_1 = B_6
     => ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
         => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1)) ) ),
    file('theBenchmark.p',fact_300_equalityE) ).

fof(fact_301_equalityE,axiom,
    ! [A_1,B_6] :
      ( A_1 = B_6
     => ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
         => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1)) ) ),
    file('theBenchmark.p',fact_301_equalityE) ).

fof(fact_302_image__iff,axiom,
    ! [Z_1,F,A_1] :
      ( is_a(Z_1)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z_1),image_pname_a(F,A_1)))
      <=> ? [X_1] :
            ( Z_1 = hAPP_pname_a(F,X_1)
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
            & is_pname(X_1) ) ) ),
    file('theBenchmark.p',fact_302_image__iff) ).

fof(fact_303_imageI,axiom,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(F,X_3)),image_pname_nat(F,A_1))) ),
    file('theBenchmark.p',fact_303_imageI) ).

fof(fact_304_imageI,axiom,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(F,X_3)),image_a_nat(F,A_1))) ),
    file('theBenchmark.p',fact_304_imageI) ).

fof(fact_305_imageI,axiom,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(F,X_3)),image_nat_pname(F,A_1))) ),
    file('theBenchmark.p',fact_305_imageI) ).

fof(fact_306_imageI,axiom,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(F,X_3)),image_nat_a(F,A_1))) ),
    file('theBenchmark.p',fact_306_imageI) ).

fof(fact_307_imageI,axiom,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_3)),image_pname_a(F,A_1))) ),
    file('theBenchmark.p',fact_307_imageI) ).

fof(fact_308_rev__image__eqI,axiom,
    ! [B_1,F,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
     => ( B_1 = hAPP_pname_nat(F,X_3)
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_pname_nat(F,A_1))) ) ),
    file('theBenchmark.p',fact_308_rev__image__eqI) ).

fof(fact_309_rev__image__eqI,axiom,
    ! [B_1,F,X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
     => ( B_1 = hAPP_a_nat(F,X_3)
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_a_nat(F,A_1))) ) ),
    file('theBenchmark.p',fact_309_rev__image__eqI) ).

fof(fact_310_rev__image__eqI,axiom,
    ! [B_1,F,X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
     => ( B_1 = hAPP_nat_pname(F,X_3)
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_nat_pname(F,A_1))) ) ),
    file('theBenchmark.p',fact_310_rev__image__eqI) ).

fof(fact_311_rev__image__eqI,axiom,
    ! [B_1,F,X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
     => ( B_1 = hAPP_nat_a(F,X_3)
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_nat_a(F,A_1))) ) ),
    file('theBenchmark.p',fact_311_rev__image__eqI) ).

fof(fact_312_rev__image__eqI,axiom,
    ! [B_1,F,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
     => ( B_1 = hAPP_pname_a(F,X_3)
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1))) ) ),
    file('theBenchmark.p',fact_312_rev__image__eqI) ).

fof(fact_313_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert_fun_nat_bool(X_1,Xa) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X_1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),Xa))),
    file('theBenchmark.p',fact_313_insert__compr__raw) ).

fof(fact_314_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert1325755072e_bool(X_1,Xa) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),Xa))),
    file('theBenchmark.p',fact_314_insert__compr__raw) ).

fof(fact_315_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert_fun_a_bool(X_1,Xa) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X_1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),Xa))),
    file('theBenchmark.p',fact_315_insert__compr__raw) ).

fof(fact_316_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert_nat(X_1,Xa) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),Xa))),
    file('theBenchmark.p',fact_316_insert__compr__raw) ).

fof(fact_317_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert_pname(X_1,Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),Xa))),
    file('theBenchmark.p',fact_317_insert__compr__raw) ).

fof(fact_318_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert_a(X_1,Xa) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),Xa))),
    file('theBenchmark.p',fact_318_insert__compr__raw) ).

fof(fact_319_subset__insertI,axiom,
    ! [B_6,A_3] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),insert_pname(A_3,B_6))),
    file('theBenchmark.p',fact_319_subset__insertI) ).

fof(fact_320_subset__insertI,axiom,
    ! [B_6,A_3] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),insert_nat(A_3,B_6))),
    file('theBenchmark.p',fact_320_subset__insertI) ).

fof(fact_321_subset__insertI,axiom,
    ! [B_6,A_3] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),insert_a(A_3,B_6))),
    file('theBenchmark.p',fact_321_subset__insertI) ).

fof(fact_322_insert__subset,axiom,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X_3,A_1)),B_6))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) ) ),
    file('theBenchmark.p',fact_322_insert__subset) ).

fof(fact_323_insert__subset,axiom,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_3,A_1)),B_6))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) ) ),
    file('theBenchmark.p',fact_323_insert__subset) ).

fof(fact_324_insert__subset,axiom,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_3,A_1)),B_6))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) ) ),
    file('theBenchmark.p',fact_324_insert__subset) ).

fof(fact_325_subset__insert,axiom,
    ! [B_6,X_3,A_1] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(X_3,B_6)))
      <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ) ),
    file('theBenchmark.p',fact_325_subset__insert) ).

fof(fact_326_subset__insert,axiom,
    ! [B_6,X_3,A_1] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(X_3,B_6)))
      <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ) ),
    file('theBenchmark.p',fact_326_subset__insert) ).

fof(fact_327_subset__insert,axiom,
    ! [B_6,X_3,A_1] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(X_3,B_6)))
      <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ) ),
    file('theBenchmark.p',fact_327_subset__insert) ).

fof(fact_328_subset__insertI2,axiom,
    ! [B_1,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(B_1,B_6))) ),
    file('theBenchmark.p',fact_328_subset__insertI2) ).

fof(fact_329_subset__insertI2,axiom,
    ! [B_1,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(B_1,B_6))) ),
    file('theBenchmark.p',fact_329_subset__insertI2) ).

fof(fact_330_subset__insertI2,axiom,
    ! [B_1,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(B_1,B_6))) ),
    file('theBenchmark.p',fact_330_subset__insertI2) ).

fof(fact_331_insert__mono,axiom,
    ! [A_3,C_6,D_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_6),D_1))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(A_3,C_6)),insert_pname(A_3,D_1))) ),
    file('theBenchmark.p',fact_331_insert__mono) ).

fof(fact_332_insert__mono,axiom,
    ! [A_3,C_6,D_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),D_1))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(A_3,C_6)),insert_nat(A_3,D_1))) ),
    file('theBenchmark.p',fact_332_insert__mono) ).

fof(fact_333_insert__mono,axiom,
    ! [A_3,C_6,D_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),D_1))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_3,C_6)),insert_a(A_3,D_1))) ),
    file('theBenchmark.p',fact_333_insert__mono) ).

fof(fact_334_image__insert,axiom,
    ! [F,A_3,B_6] : image_a_pname(F,insert_a(A_3,B_6)) = insert_pname(hAPP_a_pname(F,A_3),image_a_pname(F,B_6)),
    file('theBenchmark.p',fact_334_image__insert) ).

fof(fact_335_image__insert,axiom,
    ! [F,A_3,B_6] : image_a_nat(F,insert_a(A_3,B_6)) = insert_nat(hAPP_a_nat(F,A_3),image_a_nat(F,B_6)),
    file('theBenchmark.p',fact_335_image__insert) ).

fof(fact_336_image__insert,axiom,
    ! [F,A_3,B_6] : image_nat_a(F,insert_nat(A_3,B_6)) = insert_a(hAPP_nat_a(F,A_3),image_nat_a(F,B_6)),
    file('theBenchmark.p',fact_336_image__insert) ).

fof(fact_337_image__insert,axiom,
    ! [F,A_3,B_6] : image_pname_a(F,insert_pname(A_3,B_6)) = insert_a(hAPP_pname_a(F,A_3),image_pname_a(F,B_6)),
    file('theBenchmark.p',fact_337_image__insert) ).

fof(fact_338_insert__image,axiom,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
     => insert_pname(hAPP_pname_pname(F,X_3),image_pname_pname(F,A_1)) = image_pname_pname(F,A_1) ),
    file('theBenchmark.p',fact_338_insert__image) ).

fof(fact_339_insert__image,axiom,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
     => insert_nat(hAPP_pname_nat(F,X_3),image_pname_nat(F,A_1)) = image_pname_nat(F,A_1) ),
    file('theBenchmark.p',fact_339_insert__image) ).

fof(fact_340_insert__image,axiom,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
     => insert_pname(hAPP_a_pname(F,X_3),image_a_pname(F,A_1)) = image_a_pname(F,A_1) ),
    file('theBenchmark.p',fact_340_insert__image) ).

fof(fact_341_insert__image,axiom,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
     => insert_nat(hAPP_a_nat(F,X_3),image_a_nat(F,A_1)) = image_a_nat(F,A_1) ),
    file('theBenchmark.p',fact_341_insert__image) ).

fof(fact_342_insert__image,axiom,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
     => insert_a(hAPP_nat_a(F,X_3),image_nat_a(F,A_1)) = image_nat_a(F,A_1) ),
    file('theBenchmark.p',fact_342_insert__image) ).

fof(fact_343_insert__image,axiom,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
     => insert_a(hAPP_pname_a(F,X_3),image_pname_a(F,A_1)) = image_pname_a(F,A_1) ),
    file('theBenchmark.p',fact_343_insert__image) ).

fof(fact_344_subset__image__iff,axiom,
    ! [B_6,F,A_1] :
      ( is_fun_a_bool(B_6)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1)))
      <=> ? [AA] :
            ( B_6 = image_nat_a(F,AA)
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,AA),A_1)) ) ) ),
    file('theBenchmark.p',fact_344_subset__image__iff) ).

fof(fact_345_subset__image__iff,axiom,
    ! [B_6,F,A_1] :
      ( is_fun_pname_bool(B_6)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1)))
      <=> ? [AA] :
            ( B_6 = image_a_pname(F,AA)
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,AA),A_1))
            & is_fun_a_bool(AA) ) ) ),
    file('theBenchmark.p',fact_345_subset__image__iff) ).

fof(fact_346_subset__image__iff,axiom,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1)))
    <=> ? [AA] :
          ( B_6 = image_a_nat(F,AA)
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,AA),A_1))
          & is_fun_a_bool(AA) ) ),
    file('theBenchmark.p',fact_346_subset__image__iff) ).

fof(fact_347_subset__image__iff,axiom,
    ! [B_6,F,A_1] :
      ( is_fun_a_bool(B_6)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1)))
      <=> ? [AA] :
            ( B_6 = image_pname_a(F,AA)
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A_1))
            & is_fun_pname_bool(AA) ) ) ),
    file('theBenchmark.p',fact_347_subset__image__iff) ).

fof(fact_348_image__mono,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(F,A_1)),image_a_pname(F,B_6))) ),
    file('theBenchmark.p',fact_348_image__mono) ).

fof(fact_349_image__mono,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(F,A_1)),image_a_nat(F,B_6))) ),
    file('theBenchmark.p',fact_349_image__mono) ).

fof(fact_350_image__mono,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(F,A_1)),image_nat_a(F,B_6))) ),
    file('theBenchmark.p',fact_350_image__mono) ).

fof(fact_351_image__mono,axiom,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A_1)),image_pname_a(F,B_6))) ),
    file('theBenchmark.p',fact_351_image__mono) ).

fof(fact_352_imageE,axiom,
    ! [B_1,F,A_1] :
      ( is_pname(B_1)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_nat_pname(F,A_1)))
       => ~ ! [X_1] :
              ( B_1 = hAPP_nat_pname(F,X_1)
             => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_352_imageE) ).

fof(fact_353_imageE,axiom,
    ! [B_1,F,A_1] :
      ( is_a(B_1)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_nat_a(F,A_1)))
       => ~ ! [X_1] :
              ( B_1 = hAPP_nat_a(F,X_1)
             => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_353_imageE) ).

fof(fact_354_imageE,axiom,
    ! [B_1,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_pname_nat(F,A_1)))
     => ~ ! [X_1] :
            ( is_pname(X_1)
           => ( B_1 = hAPP_pname_nat(F,X_1)
             => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_354_imageE) ).

fof(fact_355_imageE,axiom,
    ! [B_1,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_a_nat(F,A_1)))
     => ~ ! [X_1] :
            ( is_a(X_1)
           => ( B_1 = hAPP_a_nat(F,X_1)
             => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_355_imageE) ).

fof(fact_356_imageE,axiom,
    ! [B_1,F,A_1] :
      ( is_a(B_1)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
       => ~ ! [X_1] :
              ( is_pname(X_1)
             => ( B_1 = hAPP_pname_a(F,X_1)
               => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) ) ) ) ),
    file('theBenchmark.p',fact_356_imageE) ).

fof(fact_357_subsetI,axiom,
    ! [B_6,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_6)) )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ),
    file('theBenchmark.p',fact_357_subsetI) ).

fof(fact_358_subsetI,axiom,
    ! [B_6,A_1] :
      ( ! [X_1] :
          ( is_pname(X_1)
         => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
           => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B_6)) ) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ),
    file('theBenchmark.p',fact_358_subsetI) ).

fof(fact_359_subsetI,axiom,
    ! [B_6,A_1] :
      ( ! [X_1] :
          ( is_a(X_1)
         => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
           => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6)) ) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
    file('theBenchmark.p',fact_359_subsetI) ).

fof(fact_360_image__subsetI,axiom,
    ! [F,B_6,A_1] :
      ( ! [X_1] :
          ( is_pname(X_1)
         => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
           => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(F,X_1)),B_6)) ) )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(F,A_1)),B_6)) ),
    file('theBenchmark.p',fact_360_image__subsetI) ).

fof(fact_361_image__subsetI,axiom,
    ! [F,B_6,A_1] :
      ( ! [X_1] :
          ( is_pname(X_1)
         => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
           => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(F,X_1)),B_6)) ) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(F,A_1)),B_6)) ),
    file('theBenchmark.p',fact_361_image__subsetI) ).

fof(fact_362_image__subsetI,axiom,
    ! [F,B_6,A_1] :
      ( ! [X_1] :
          ( is_a(X_1)
         => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
           => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(F,X_1)),B_6)) ) )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(F,A_1)),B_6)) ),
    file('theBenchmark.p',fact_362_image__subsetI) ).

fof(fact_363_image__subsetI,axiom,
    ! [F,B_6,A_1] :
      ( ! [X_1] :
          ( is_a(X_1)
         => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
           => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_a_pname(F,X_1)),B_6)) ) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(F,A_1)),B_6)) ),
    file('theBenchmark.p',fact_363_image__subsetI) ).

fof(fact_364_image__subsetI,axiom,
    ! [F,B_6,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(F,X_1)),B_6)) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(F,A_1)),B_6)) ),
    file('theBenchmark.p',fact_364_image__subsetI) ).

fof(fact_365_image__subsetI,axiom,
    ! [F,B_6,A_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(F,X_1)),B_6)) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(F,A_1)),B_6)) ),
    file('theBenchmark.p',fact_365_image__subsetI) ).

fof(fact_366_image__subsetI,axiom,
    ! [F,B_6,A_1] :
      ( ! [X_1] :
          ( is_pname(X_1)
         => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
           => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_1)),B_6)) ) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A_1)),B_6)) ),
    file('theBenchmark.p',fact_366_image__subsetI) ).

fof(fact_367_order__refl,axiom,
    ! [X_3] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),X_3)),
    file('theBenchmark.p',fact_367_order__refl) ).

fof(fact_368_order__refl,axiom,
    ! [X_3] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),X_3)),
    file('theBenchmark.p',fact_368_order__refl) ).

fof(fact_369_order__refl,axiom,
    ! [X_3] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),X_3)),
    file('theBenchmark.p',fact_369_order__refl) ).

fof(fact_370_order__refl,axiom,
    ! [X_3] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),X_3)),
    file('theBenchmark.p',fact_370_order__refl) ).

fof(fact_371_order__refl,axiom,
    ! [X_10] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_10),X_10)),
    file('theBenchmark.p',fact_371_order__refl) ).

fof(fact_372_finite__nat__set__iff__bounded__le,axiom,
    ! [N_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1))
    <=> ? [M_2] :
        ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M_2)) ) ),
    file('theBenchmark.p',fact_372_finite__nat__set__iff__bounded__le) ).

fof(fact_373_assms_I3_J,axiom,
    ! [G,C_1] :
      ( hBOOL(wt(C_1))
     => ( ! [X_1] :
            ( is_pname(X_1)
           => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),u))
             => hBOOL(hAPP_fun_a_bool_bool(p(G),insert_a(hAPP_pname_a(mgt_call,X_1),bot_bot_fun_a_bool))) ) )
       => hBOOL(hAPP_fun_a_bool_bool(p(G),insert_a(mgt(C_1),bot_bot_fun_a_bool))) ) ),
    file('theBenchmark.p',fact_373_assms_I3_J) ).

fof(fact_374_le__fun__def,axiom,
    ! [F,G_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1))
    <=> ! [X_1] :
          ( is_pname(X_1)
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G_1,X_1))) ) ),
    file('theBenchmark.p',fact_374_le__fun__def) ).

fof(fact_375_le__fun__def,axiom,
    ! [F,G_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1))
    <=> ! [X_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_375_le__fun__def) ).

fof(fact_376_le__fun__def,axiom,
    ! [F,G_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1))
    <=> ! [X_1] :
          ( is_a(X_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_376_le__fun__def) ).

fof(fact_377_le__funD,axiom,
    ! [X_3,F,G_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_3)),hAPP_pname_bool(G_1,X_3))) ),
    file('theBenchmark.p',fact_377_le__funD) ).

fof(fact_378_le__funD,axiom,
    ! [X_3,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_3)),hAPP_nat_bool(G_1,X_3))) ),
    file('theBenchmark.p',fact_378_le__funD) ).

fof(fact_379_le__funD,axiom,
    ! [X_3,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_3)),hAPP_a_bool(G_1,X_3))) ),
    file('theBenchmark.p',fact_379_le__funD) ).

fof(fact_380_le__funE,axiom,
    ! [X_3,F,G_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_3)),hAPP_pname_bool(G_1,X_3))) ),
    file('theBenchmark.p',fact_380_le__funE) ).

fof(fact_381_le__funE,axiom,
    ! [X_3,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_3)),hAPP_nat_bool(G_1,X_3))) ),
    file('theBenchmark.p',fact_381_le__funE) ).

fof(fact_382_le__funE,axiom,
    ! [X_3,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_3)),hAPP_a_bool(G_1,X_3))) ),
    file('theBenchmark.p',fact_382_le__funE) ).

fof(fact_383_emptyE,axiom,
    ! [A_3] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),bot_bot_fun_nat_bool)),
    file('theBenchmark.p',fact_383_emptyE) ).

fof(fact_384_emptyE,axiom,
    ! [A_3] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),bot_bo844097828e_bool)),
    file('theBenchmark.p',fact_384_emptyE) ).

fof(fact_385_emptyE,axiom,
    ! [A_3] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),bot_bot_fun_a_bool)),
    file('theBenchmark.p',fact_385_emptyE) ).

fof(fact_386_finite_OemptyI,axiom,
    hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,bot_bo1701429464l_bool)),
    file('theBenchmark.p',fact_386_finite_OemptyI) ).

fof(fact_387_finite_OemptyI,axiom,
    hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)),
    file('theBenchmark.p',fact_387_finite_OemptyI) ).

fof(fact_388_finite_OemptyI,axiom,
    hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,bot_bo1389914601l_bool)),
    file('theBenchmark.p',fact_388_finite_OemptyI) ).

fof(fact_389_finite_OemptyI,axiom,
    hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
    file('theBenchmark.p',fact_389_finite_OemptyI) ).

fof(fact_390_finite_OemptyI,axiom,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    file('theBenchmark.p',fact_390_finite_OemptyI) ).

fof(fact_391_finite_OemptyI,axiom,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
    file('theBenchmark.p',fact_391_finite_OemptyI) ).

fof(fact_392_empty__subsetI,axiom,
    ! [A_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_1)),
    file('theBenchmark.p',fact_392_empty__subsetI) ).

fof(fact_393_empty__subsetI,axiom,
    ! [A_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_1)),
    file('theBenchmark.p',fact_393_empty__subsetI) ).

fof(fact_394_empty__subsetI,axiom,
    ! [A_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A_1)),
    file('theBenchmark.p',fact_394_empty__subsetI) ).

fof(fact_395_equals0D,axiom,
    ! [A_3,A_1] :
      ( A_1 = bot_bot_fun_nat_bool
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1)) ),
    file('theBenchmark.p',fact_395_equals0D) ).

fof(fact_396_equals0D,axiom,
    ! [A_3,A_1] :
      ( A_1 = bot_bo844097828e_bool
     => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1)) ),
    file('theBenchmark.p',fact_396_equals0D) ).

fof(fact_397_equals0D,axiom,
    ! [A_3,A_1] :
      ( A_1 = bot_bot_fun_a_bool
     => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1)) ),
    file('theBenchmark.p',fact_397_equals0D) ).

fof(fact_398_Collect__empty__eq,axiom,
    ! [Pa] :
      ( collect_pname(Pa) = bot_bo844097828e_bool
    <=> ! [X_1] :
          ( is_pname(X_1)
         => ~ hBOOL(hAPP_pname_bool(Pa,X_1)) ) ),
    file('theBenchmark.p',fact_398_Collect__empty__eq) ).

fof(fact_399_Collect__empty__eq,axiom,
    ! [Pa] :
      ( collect_fun_nat_bool(Pa) = bot_bo1701429464l_bool
    <=> ! [X_1] : ~ hBOOL(hAPP_f54304608l_bool(Pa,X_1)) ),
    file('theBenchmark.p',fact_399_Collect__empty__eq) ).

fof(fact_400_Collect__empty__eq,axiom,
    ! [Pa] :
      ( collec1974731493e_bool(Pa) = bot_bo1649642514l_bool
    <=> ! [X_1] :
          ( is_fun_pname_bool(X_1)
         => ~ hBOOL(hAPP_f1664156314l_bool(Pa,X_1)) ) ),
    file('theBenchmark.p',fact_400_Collect__empty__eq) ).

fof(fact_401_Collect__empty__eq,axiom,
    ! [Pa] :
      ( collect_fun_a_bool(Pa) = bot_bo1389914601l_bool
    <=> ! [X_1] :
          ( is_fun_a_bool(X_1)
         => ~ hBOOL(hAPP_fun_a_bool_bool(Pa,X_1)) ) ),
    file('theBenchmark.p',fact_401_Collect__empty__eq) ).

fof(fact_402_Collect__empty__eq,axiom,
    ! [Pa] :
      ( collect_a(Pa) = bot_bot_fun_a_bool
    <=> ! [X_1] :
          ( is_a(X_1)
         => ~ hBOOL(hAPP_a_bool(Pa,X_1)) ) ),
    file('theBenchmark.p',fact_402_Collect__empty__eq) ).

fof(fact_403_Collect__empty__eq,axiom,
    ! [Pa] :
      ( collect_nat(Pa) = bot_bot_fun_nat_bool
    <=> ! [X_1] : ~ hBOOL(hAPP_nat_bool(Pa,X_1)) ),
    file('theBenchmark.p',fact_403_Collect__empty__eq) ).

fof(fact_404_empty__iff,axiom,
    ! [C_1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),bot_bot_fun_nat_bool)),
    file('theBenchmark.p',fact_404_empty__iff) ).

fof(fact_405_empty__iff,axiom,
    ! [C_1] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),bot_bo844097828e_bool)),
    file('theBenchmark.p',fact_405_empty__iff) ).

fof(fact_406_empty__iff,axiom,
    ! [C_1] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),bot_bot_fun_a_bool)),
    file('theBenchmark.p',fact_406_empty__iff) ).

fof(fact_407_empty__Collect__eq,axiom,
    ! [Pa] :
      ( bot_bo844097828e_bool = collect_pname(Pa)
    <=> ! [X_1] :
          ( is_pname(X_1)
         => ~ hBOOL(hAPP_pname_bool(Pa,X_1)) ) ),
    file('theBenchmark.p',fact_407_empty__Collect__eq) ).

fof(fact_408_empty__Collect__eq,axiom,
    ! [Pa] :
      ( bot_bo1701429464l_bool = collect_fun_nat_bool(Pa)
    <=> ! [X_1] : ~ hBOOL(hAPP_f54304608l_bool(Pa,X_1)) ),
    file('theBenchmark.p',fact_408_empty__Collect__eq) ).

fof(fact_409_empty__Collect__eq,axiom,
    ! [Pa] :
      ( bot_bo1649642514l_bool = collec1974731493e_bool(Pa)
    <=> ! [X_1] :
          ( is_fun_pname_bool(X_1)
         => ~ hBOOL(hAPP_f1664156314l_bool(Pa,X_1)) ) ),
    file('theBenchmark.p',fact_409_empty__Collect__eq) ).

fof(fact_410_empty__Collect__eq,axiom,
    ! [Pa] :
      ( bot_bo1389914601l_bool = collect_fun_a_bool(Pa)
    <=> ! [X_1] :
          ( is_fun_a_bool(X_1)
         => ~ hBOOL(hAPP_fun_a_bool_bool(Pa,X_1)) ) ),
    file('theBenchmark.p',fact_410_empty__Collect__eq) ).

fof(fact_411_empty__Collect__eq,axiom,
    ! [Pa] :
      ( bot_bot_fun_a_bool = collect_a(Pa)
    <=> ! [X_1] :
          ( is_a(X_1)
         => ~ hBOOL(hAPP_a_bool(Pa,X_1)) ) ),
    file('theBenchmark.p',fact_411_empty__Collect__eq) ).

fof(fact_412_empty__Collect__eq,axiom,
    ! [Pa] :
      ( bot_bot_fun_nat_bool = collect_nat(Pa)
    <=> ! [X_1] : ~ hBOOL(hAPP_nat_bool(Pa,X_1)) ),
    file('theBenchmark.p',fact_412_empty__Collect__eq) ).

fof(fact_413_ex__in__conv,axiom,
    ! [A_1] :
      ( ? [X_1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
    <=> A_1 != bot_bot_fun_nat_bool ),
    file('theBenchmark.p',fact_413_ex__in__conv) ).

fof(fact_414_ex__in__conv,axiom,
    ! [A_1] :
      ( is_fun_pname_bool(A_1)
     => ( ? [X_1] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
            & is_pname(X_1) )
      <=> A_1 != bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_414_ex__in__conv) ).

fof(fact_415_ex__in__conv,axiom,
    ! [A_1] :
      ( is_fun_a_bool(A_1)
     => ( ? [X_1] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
            & is_a(X_1) )
      <=> A_1 != bot_bot_fun_a_bool ) ),
    file('theBenchmark.p',fact_415_ex__in__conv) ).

fof(fact_416_all__not__in__conv,axiom,
    ! [A_1] :
      ( ! [X_1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
    <=> A_1 = bot_bot_fun_nat_bool ),
    file('theBenchmark.p',fact_416_all__not__in__conv) ).

fof(fact_417_all__not__in__conv,axiom,
    ! [A_1] :
      ( is_fun_pname_bool(A_1)
     => ( ! [X_1] :
            ( is_pname(X_1)
           => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1)) )
      <=> A_1 = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_417_all__not__in__conv) ).

fof(fact_418_all__not__in__conv,axiom,
    ! [A_1] :
      ( is_fun_a_bool(A_1)
     => ( ! [X_1] :
            ( is_a(X_1)
           => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1)) )
      <=> A_1 = bot_bot_fun_a_bool ) ),
    file('theBenchmark.p',fact_418_all__not__in__conv) ).

fof(fact_419_empty__def,axiom,
    bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)),
    file('theBenchmark.p',fact_419_empty__def) ).

fof(fact_420_empty__def,axiom,
    bot_bo1701429464l_bool = collect_fun_nat_bool(cOMBK_1994329625t_bool(fFalse)),
    file('theBenchmark.p',fact_420_empty__def) ).

fof(fact_421_empty__def,axiom,
    bot_bo1649642514l_bool = collec1974731493e_bool(cOMBK_1857069011e_bool(fFalse)),
    file('theBenchmark.p',fact_421_empty__def) ).

fof(fact_422_empty__def,axiom,
    bot_bo1389914601l_bool = collect_fun_a_bool(cOMBK_324466864a_bool(fFalse)),
    file('theBenchmark.p',fact_422_empty__def) ).

fof(fact_423_empty__def,axiom,
    bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
    file('theBenchmark.p',fact_423_empty__def) ).

fof(fact_424_empty__def,axiom,
    bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
    file('theBenchmark.p',fact_424_empty__def) ).

fof(fact_425_bot__fun__def,axiom,
    ! [X_1] :
      ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_1))
    <=> hBOOL(bot_bot_bool) ),
    file('theBenchmark.p',fact_425_bot__fun__def) ).

fof(fact_426_bot__fun__def,axiom,
    ! [X_1] :
      ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_1))
    <=> hBOOL(bot_bot_bool) ),
    file('theBenchmark.p',fact_426_bot__fun__def) ).

fof(fact_427_bot__fun__def,axiom,
    ! [X_1] :
      ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_1))
    <=> hBOOL(bot_bot_bool) ),
    file('theBenchmark.p',fact_427_bot__fun__def) ).

fof(fact_428_bot__apply,axiom,
    ! [X_3] :
      ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_3))
    <=> hBOOL(bot_bot_bool) ),
    file('theBenchmark.p',fact_428_bot__apply) ).

fof(fact_429_bot__apply,axiom,
    ! [X_3] :
      ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_3))
    <=> hBOOL(bot_bot_bool) ),
    file('theBenchmark.p',fact_429_bot__apply) ).

fof(fact_430_bot__apply,axiom,
    ! [X_3] :
      ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_3))
    <=> hBOOL(bot_bot_bool) ),
    file('theBenchmark.p',fact_430_bot__apply) ).

fof(fact_431_le__bot,axiom,
    ! [A_3] :
      ( is_fun_pname_bool(A_3)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),bot_bo844097828e_bool))
       => A_3 = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_431_le__bot) ).

fof(fact_432_le__bot,axiom,
    ! [A_3] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),bot_bot_bool))
     => ( hBOOL(A_3)
      <=> hBOOL(bot_bot_bool) ) ),
    file('theBenchmark.p',fact_432_le__bot) ).

fof(fact_433_le__bot,axiom,
    ! [A_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),bot_bot_fun_nat_bool))
     => A_3 = bot_bot_fun_nat_bool ),
    file('theBenchmark.p',fact_433_le__bot) ).

fof(fact_434_le__bot,axiom,
    ! [A_3] :
      ( is_fun_a_bool(A_3)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),bot_bot_fun_a_bool))
       => A_3 = bot_bot_fun_a_bool ) ),
    file('theBenchmark.p',fact_434_le__bot) ).

fof(fact_435_le__bot,axiom,
    ! [A_9] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),bot_bot_nat))
     => A_9 = bot_bot_nat ),
    file('theBenchmark.p',fact_435_le__bot) ).

fof(fact_436_bot__unique,axiom,
    ! [A_3] :
      ( is_fun_pname_bool(A_3)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),bot_bo844097828e_bool))
      <=> A_3 = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_436_bot__unique) ).

fof(fact_437_bot__unique,axiom,
    ! [A_3] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),bot_bot_bool))
    <=> ( hBOOL(A_3)
      <=> hBOOL(bot_bot_bool) ) ),
    file('theBenchmark.p',fact_437_bot__unique) ).

fof(fact_438_bot__unique,axiom,
    ! [A_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),bot_bot_fun_nat_bool))
    <=> A_3 = bot_bot_fun_nat_bool ),
    file('theBenchmark.p',fact_438_bot__unique) ).

fof(fact_439_bot__unique,axiom,
    ! [A_3] :
      ( is_fun_a_bool(A_3)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),bot_bot_fun_a_bool))
      <=> A_3 = bot_bot_fun_a_bool ) ),
    file('theBenchmark.p',fact_439_bot__unique) ).

fof(fact_440_bot__unique,axiom,
    ! [A_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_3),bot_bot_nat))
    <=> A_3 = bot_bot_nat ),
    file('theBenchmark.p',fact_440_bot__unique) ).

fof(fact_441_bot__least,axiom,
    ! [A_3] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_3)),
    file('theBenchmark.p',fact_441_bot__least) ).

fof(fact_442_bot__least,axiom,
    ! [A_3] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A_3)),
    file('theBenchmark.p',fact_442_bot__least) ).

fof(fact_443_bot__least,axiom,
    ! [A_3] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_3)),
    file('theBenchmark.p',fact_443_bot__least) ).

fof(fact_444_bot__least,axiom,
    ! [A_3] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A_3)),
    file('theBenchmark.p',fact_444_bot__least) ).

fof(fact_445_bot__least,axiom,
    ! [A_8] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),A_8)),
    file('theBenchmark.p',fact_445_bot__least) ).

fof(fact_446_singleton__inject,axiom,
    ! [A_3,B_1] :
      ( ( is_pname(B_1)
        & is_pname(A_3) )
     => ( insert_pname(A_3,bot_bo844097828e_bool) = insert_pname(B_1,bot_bo844097828e_bool)
       => A_3 = B_1 ) ),
    file('theBenchmark.p',fact_446_singleton__inject) ).

fof(fact_447_singleton__inject,axiom,
    ! [A_3,B_1] :
      ( insert_nat(A_3,bot_bot_fun_nat_bool) = insert_nat(B_1,bot_bot_fun_nat_bool)
     => A_3 = B_1 ),
    file('theBenchmark.p',fact_447_singleton__inject) ).

fof(fact_448_singleton__inject,axiom,
    ! [A_3,B_1] :
      ( ( is_a(B_1)
        & is_a(A_3) )
     => ( insert_a(A_3,bot_bot_fun_a_bool) = insert_a(B_1,bot_bot_fun_a_bool)
       => A_3 = B_1 ) ),
    file('theBenchmark.p',fact_448_singleton__inject) ).

fof(fact_449_singletonE,axiom,
    ! [B_1,A_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),insert_nat(A_3,bot_bot_fun_nat_bool)))
     => B_1 = A_3 ),
    file('theBenchmark.p',fact_449_singletonE) ).

fof(fact_450_singletonE,axiom,
    ! [B_1,A_3] :
      ( ( is_pname(A_3)
        & is_pname(B_1) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_3,bot_bo844097828e_bool)))
       => B_1 = A_3 ) ),
    file('theBenchmark.p',fact_450_singletonE) ).

fof(fact_451_singletonE,axiom,
    ! [B_1,A_3] :
      ( ( is_a(A_3)
        & is_a(B_1) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),insert_a(A_3,bot_bot_fun_a_bool)))
       => B_1 = A_3 ) ),
    file('theBenchmark.p',fact_451_singletonE) ).

fof(fact_452_doubleton__eq__iff,axiom,
    ! [A_3,B_1,C_1,D] :
      ( ( is_pname(D)
        & is_pname(C_1)
        & is_pname(B_1)
        & is_pname(A_3) )
     => ( insert_pname(A_3,insert_pname(B_1,bot_bo844097828e_bool)) = insert_pname(C_1,insert_pname(D,bot_bo844097828e_bool))
      <=> ( ( B_1 = C_1
            & A_3 = D )
          | ( B_1 = D
            & A_3 = C_1 ) ) ) ),
    file('theBenchmark.p',fact_452_doubleton__eq__iff) ).

fof(fact_453_doubleton__eq__iff,axiom,
    ! [A_3,B_1,C_1,D] :
      ( insert_nat(A_3,insert_nat(B_1,bot_bot_fun_nat_bool)) = insert_nat(C_1,insert_nat(D,bot_bot_fun_nat_bool))
    <=> ( ( B_1 = C_1
          & A_3 = D )
        | ( B_1 = D
          & A_3 = C_1 ) ) ),
    file('theBenchmark.p',fact_453_doubleton__eq__iff) ).

fof(fact_454_doubleton__eq__iff,axiom,
    ! [A_3,B_1,C_1,D] :
      ( ( is_a(D)
        & is_a(C_1)
        & is_a(B_1)
        & is_a(A_3) )
     => ( insert_a(A_3,insert_a(B_1,bot_bot_fun_a_bool)) = insert_a(C_1,insert_a(D,bot_bot_fun_a_bool))
      <=> ( ( B_1 = C_1
            & A_3 = D )
          | ( B_1 = D
            & A_3 = C_1 ) ) ) ),
    file('theBenchmark.p',fact_454_doubleton__eq__iff) ).

fof(fact_455_singleton__iff,axiom,
    ! [B_1,A_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),insert_nat(A_3,bot_bot_fun_nat_bool)))
    <=> B_1 = A_3 ),
    file('theBenchmark.p',fact_455_singleton__iff) ).

fof(fact_456_singleton__iff,axiom,
    ! [B_1,A_3] :
      ( ( is_pname(A_3)
        & is_pname(B_1) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_3,bot_bo844097828e_bool)))
      <=> B_1 = A_3 ) ),
    file('theBenchmark.p',fact_456_singleton__iff) ).

fof(fact_457_singleton__iff,axiom,
    ! [B_1,A_3] :
      ( ( is_a(A_3)
        & is_a(B_1) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),insert_a(A_3,bot_bot_fun_a_bool)))
      <=> B_1 = A_3 ) ),
    file('theBenchmark.p',fact_457_singleton__iff) ).

fof(fact_458_insert__not__empty,axiom,
    ! [A_3,A_1] : insert_pname(A_3,A_1) != bot_bo844097828e_bool,
    file('theBenchmark.p',fact_458_insert__not__empty) ).

fof(fact_459_insert__not__empty,axiom,
    ! [A_3,A_1] : insert_nat(A_3,A_1) != bot_bot_fun_nat_bool,
    file('theBenchmark.p',fact_459_insert__not__empty) ).

fof(fact_460_insert__not__empty,axiom,
    ! [A_3,A_1] : insert_a(A_3,A_1) != bot_bot_fun_a_bool,
    file('theBenchmark.p',fact_460_insert__not__empty) ).

fof(fact_461_empty__not__insert,axiom,
    ! [A_3,A_1] : bot_bo844097828e_bool != insert_pname(A_3,A_1),
    file('theBenchmark.p',fact_461_empty__not__insert) ).

fof(fact_462_empty__not__insert,axiom,
    ! [A_3,A_1] : bot_bot_fun_nat_bool != insert_nat(A_3,A_1),
    file('theBenchmark.p',fact_462_empty__not__insert) ).

fof(fact_463_empty__not__insert,axiom,
    ! [A_3,A_1] : bot_bot_fun_a_bool != insert_a(A_3,A_1),
    file('theBenchmark.p',fact_463_empty__not__insert) ).

fof(fact_464_subset__empty,axiom,
    ! [A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),bot_bot_fun_nat_bool))
    <=> A_1 = bot_bot_fun_nat_bool ),
    file('theBenchmark.p',fact_464_subset__empty) ).

fof(fact_465_subset__empty,axiom,
    ! [A_1] :
      ( is_fun_pname_bool(A_1)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),bot_bo844097828e_bool))
      <=> A_1 = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_465_subset__empty) ).

fof(fact_466_subset__empty,axiom,
    ! [A_1] :
      ( is_fun_a_bool(A_1)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),bot_bot_fun_a_bool))
      <=> A_1 = bot_bot_fun_a_bool ) ),
    file('theBenchmark.p',fact_466_subset__empty) ).

fof(fact_467_image__is__empty,axiom,
    ! [F,A_1] :
      ( is_fun_pname_bool(A_1)
     => ( image_pname_a(F,A_1) = bot_bot_fun_a_bool
      <=> A_1 = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_467_image__is__empty) ).

fof(fact_468_image__empty,axiom,
    ! [F] : image_pname_a(F,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    file('theBenchmark.p',fact_468_image__empty) ).

fof(fact_469_empty__is__image,axiom,
    ! [F,A_1] :
      ( is_fun_pname_bool(A_1)
     => ( bot_bot_fun_a_bool = image_pname_a(F,A_1)
      <=> A_1 = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_469_empty__is__image) ).

fof(fact_470_Collect__conv__if,axiom,
    ! [Pa,A_3] :
      ( ( ~ hBOOL(hAPP_nat_bool(Pa,A_3))
       => collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)),Pa)) = bot_bot_fun_nat_bool )
      & ( hBOOL(hAPP_nat_bool(Pa,A_3))
       => collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)),Pa)) = insert_nat(A_3,bot_bot_fun_nat_bool) ) ),
    file('theBenchmark.p',fact_470_Collect__conv__if) ).

fof(fact_471_Collect__conv__if,axiom,
    ! [Pa,A_3] :
      ( ( ~ hBOOL(hAPP_pname_bool(Pa,A_3))
       => collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)),Pa)) = bot_bo844097828e_bool )
      & ( hBOOL(hAPP_pname_bool(Pa,A_3))
       => collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)),Pa)) = insert_pname(A_3,bot_bo844097828e_bool) ) ),
    file('theBenchmark.p',fact_471_Collect__conv__if) ).

fof(fact_472_Collect__conv__if,axiom,
    ! [Pa,A_3] :
      ( ( ~ hBOOL(hAPP_a_bool(Pa,A_3))
       => collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)),Pa)) = bot_bot_fun_a_bool )
      & ( hBOOL(hAPP_a_bool(Pa,A_3))
       => collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)),Pa)) = insert_a(A_3,bot_bot_fun_a_bool) ) ),
    file('theBenchmark.p',fact_472_Collect__conv__if) ).

fof(fact_473_Collect__conv__if,axiom,
    ! [Pa,A_3] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(Pa,A_3))
       => collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)),Pa)) = bot_bo1701429464l_bool )
      & ( hBOOL(hAPP_f54304608l_bool(Pa,A_3))
       => collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)),Pa)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool) ) ),
    file('theBenchmark.p',fact_473_Collect__conv__if) ).

fof(fact_474_Collect__conv__if,axiom,
    ! [Pa,A_3] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(Pa,A_3))
       => collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)),Pa)) = bot_bo1649642514l_bool )
      & ( hBOOL(hAPP_f1664156314l_bool(Pa,A_3))
       => collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)),Pa)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool) ) ),
    file('theBenchmark.p',fact_474_Collect__conv__if) ).

fof(fact_475_Collect__conv__if,axiom,
    ! [Pa,A_3] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(Pa,A_3))
       => collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)),Pa)) = bot_bo1389914601l_bool )
      & ( hBOOL(hAPP_fun_a_bool_bool(Pa,A_3))
       => collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)),Pa)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool) ) ),
    file('theBenchmark.p',fact_475_Collect__conv__if) ).

fof(fact_476_Collect__conv__if2,axiom,
    ! [Pa,A_3] :
      ( ( ~ hBOOL(hAPP_nat_bool(Pa,A_3))
       => collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_3)),Pa)) = bot_bot_fun_nat_bool )
      & ( hBOOL(hAPP_nat_bool(Pa,A_3))
       => collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_3)),Pa)) = insert_nat(A_3,bot_bot_fun_nat_bool) ) ),
    file('theBenchmark.p',fact_476_Collect__conv__if2) ).

fof(fact_477_Collect__conv__if2,axiom,
    ! [Pa,A_3] :
      ( ( ~ hBOOL(hAPP_pname_bool(Pa,A_3))
       => collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_3)),Pa)) = bot_bo844097828e_bool )
      & ( hBOOL(hAPP_pname_bool(Pa,A_3))
       => collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_3)),Pa)) = insert_pname(A_3,bot_bo844097828e_bool) ) ),
    file('theBenchmark.p',fact_477_Collect__conv__if2) ).

fof(fact_478_Collect__conv__if2,axiom,
    ! [Pa,A_3] :
      ( ( ~ hBOOL(hAPP_a_bool(Pa,A_3))
       => collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_3)),Pa)) = bot_bot_fun_a_bool )
      & ( hBOOL(hAPP_a_bool(Pa,A_3))
       => collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_3)),Pa)) = insert_a(A_3,bot_bot_fun_a_bool) ) ),
    file('theBenchmark.p',fact_478_Collect__conv__if2) ).

fof(fact_479_Collect__conv__if2,axiom,
    ! [Pa,A_3] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(Pa,A_3))
       => collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,A_3)),Pa)) = bot_bo1701429464l_bool )
      & ( hBOOL(hAPP_f54304608l_bool(Pa,A_3))
       => collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,A_3)),Pa)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool) ) ),
    file('theBenchmark.p',fact_479_Collect__conv__if2) ).

fof(fact_480_Collect__conv__if2,axiom,
    ! [Pa,A_3] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(Pa,A_3))
       => collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_3)),Pa)) = bot_bo1649642514l_bool )
      & ( hBOOL(hAPP_f1664156314l_bool(Pa,A_3))
       => collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_3)),Pa)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool) ) ),
    file('theBenchmark.p',fact_480_Collect__conv__if2) ).

fof(fact_481_Collect__conv__if2,axiom,
    ! [Pa,A_3] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(Pa,A_3))
       => collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,A_3)),Pa)) = bot_bo1389914601l_bool )
      & ( hBOOL(hAPP_fun_a_bool_bool(Pa,A_3))
       => collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,A_3)),Pa)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool) ) ),
    file('theBenchmark.p',fact_481_Collect__conv__if2) ).

fof(fact_482_singleton__conv,axiom,
    ! [A_3] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)) = insert_nat(A_3,bot_bot_fun_nat_bool),
    file('theBenchmark.p',fact_482_singleton__conv) ).

fof(fact_483_singleton__conv,axiom,
    ! [A_3] : collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)) = insert_pname(A_3,bot_bo844097828e_bool),
    file('theBenchmark.p',fact_483_singleton__conv) ).

fof(fact_484_singleton__conv,axiom,
    ! [A_3] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)) = insert_a(A_3,bot_bot_fun_a_bool),
    file('theBenchmark.p',fact_484_singleton__conv) ).

fof(fact_485_singleton__conv,axiom,
    ! [A_3] : collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool),
    file('theBenchmark.p',fact_485_singleton__conv) ).

fof(fact_486_singleton__conv,axiom,
    ! [A_3] : collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool),
    file('theBenchmark.p',fact_486_singleton__conv) ).

fof(fact_487_singleton__conv,axiom,
    ! [A_3] : collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool),
    file('theBenchmark.p',fact_487_singleton__conv) ).

fof(fact_488_singleton__conv2,axiom,
    ! [A_3] : collect_nat(hAPP_n1699378549t_bool(fequal_nat,A_3)) = insert_nat(A_3,bot_bot_fun_nat_bool),
    file('theBenchmark.p',fact_488_singleton__conv2) ).

fof(fact_489_singleton__conv2,axiom,
    ! [A_3] : collect_pname(hAPP_p61793385e_bool(fequal_pname,A_3)) = insert_pname(A_3,bot_bo844097828e_bool),
    file('theBenchmark.p',fact_489_singleton__conv2) ).

fof(fact_490_singleton__conv2,axiom,
    ! [A_3] : collect_a(hAPP_a_fun_a_bool(fequal_a,A_3)) = insert_a(A_3,bot_bot_fun_a_bool),
    file('theBenchmark.p',fact_490_singleton__conv2) ).

fof(fact_491_singleton__conv2,axiom,
    ! [A_3] : collect_fun_nat_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,A_3)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool),
    file('theBenchmark.p',fact_491_singleton__conv2) ).

fof(fact_492_singleton__conv2,axiom,
    ! [A_3] : collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,A_3)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool),
    file('theBenchmark.p',fact_492_singleton__conv2) ).

fof(fact_493_singleton__conv2,axiom,
    ! [A_3] : collect_fun_a_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,A_3)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool),
    file('theBenchmark.p',fact_493_singleton__conv2) ).

fof(fact_494_subset__singletonD,axiom,
    ! [A_1,X_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(X_3,bot_bot_fun_nat_bool)))
     => ( A_1 = insert_nat(X_3,bot_bot_fun_nat_bool)
        | A_1 = bot_bot_fun_nat_bool ) ),
    file('theBenchmark.p',fact_494_subset__singletonD) ).

fof(fact_495_subset__singletonD,axiom,
    ! [A_1,X_3] :
      ( is_fun_pname_bool(A_1)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(X_3,bot_bo844097828e_bool)))
       => ( A_1 = insert_pname(X_3,bot_bo844097828e_bool)
          | A_1 = bot_bo844097828e_bool ) ) ),
    file('theBenchmark.p',fact_495_subset__singletonD) ).

fof(fact_496_subset__singletonD,axiom,
    ! [A_1,X_3] :
      ( is_fun_a_bool(A_1)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(X_3,bot_bot_fun_a_bool)))
       => ( A_1 = insert_a(X_3,bot_bot_fun_a_bool)
          | A_1 = bot_bot_fun_a_bool ) ) ),
    file('theBenchmark.p',fact_496_subset__singletonD) ).

fof(fact_497_image__constant,axiom,
    ! [C_1,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
     => image_pname_a(cOMBK_a_pname(C_1),A_1) = insert_a(C_1,bot_bot_fun_a_bool) ),
    file('theBenchmark.p',fact_497_image__constant) ).

fof(fact_498_image__constant__conv,axiom,
    ! [C_1,A_1] :
      ( is_fun_pname_bool(A_1)
     => ( ( A_1 != bot_bo844097828e_bool
         => image_pname_a(cOMBK_a_pname(C_1),A_1) = insert_a(C_1,bot_bot_fun_a_bool) )
        & ( A_1 = bot_bo844097828e_bool
         => image_pname_a(cOMBK_a_pname(C_1),A_1) = bot_bot_fun_a_bool ) ) ),
    file('theBenchmark.p',fact_498_image__constant__conv) ).

fof(fact_499_linorder__le__cases,axiom,
    ! [X_9,Y_8] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_9),Y_8))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_8),X_9)) ),
    file('theBenchmark.p',fact_499_linorder__le__cases) ).

fof(fact_500_xt1_I6_J,axiom,
    ! [Z_1,Y_2,X_3] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),X_3)) ) ),
    file('theBenchmark.p',fact_500_xt1_I6_J) ).

fof(fact_501_xt1_I6_J,axiom,
    ! [Z_1,Y_2,X_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),X_3)) ) ),
    file('theBenchmark.p',fact_501_xt1_I6_J) ).

fof(fact_502_xt1_I6_J,axiom,
    ! [Z_1,Y_2,X_3] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z_1),Y_2))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z_1),X_3)) ) ),
    file('theBenchmark.p',fact_502_xt1_I6_J) ).

fof(fact_503_xt1_I6_J,axiom,
    ! [Z_3,Y_7,X_8] :
      ( 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,Z_3),Y_7))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_3),X_8)) ) ),
    file('theBenchmark.p',fact_503_xt1_I6_J) ).

fof(fact_504_xt1_I6_J,axiom,
    ! [Z_1,Y_2,X_3] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_1),Y_2))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_1),X_3)) ) ),
    file('theBenchmark.p',fact_504_xt1_I6_J) ).

fof(fact_505_xt1_I5_J,axiom,
    ! [Y_2,X_3] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2))
       => ( hBOOL(X_3)
        <=> hBOOL(Y_2) ) ) ),
    file('theBenchmark.p',fact_505_xt1_I5_J) ).

fof(fact_506_xt1_I5_J,axiom,
    ! [Y_2,X_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2))
       => X_3 = Y_2 ) ),
    file('theBenchmark.p',fact_506_xt1_I5_J) ).

fof(fact_507_xt1_I5_J,axiom,
    ! [Y_2,X_3] :
      ( ( is_fun_pname_bool(X_3)
        & is_fun_pname_bool(Y_2) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2))
         => X_3 = Y_2 ) ) ),
    file('theBenchmark.p',fact_507_xt1_I5_J) ).

fof(fact_508_xt1_I5_J,axiom,
    ! [Y_6,X_7] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),X_7))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_6))
       => X_7 = Y_6 ) ),
    file('theBenchmark.p',fact_508_xt1_I5_J) ).

fof(fact_509_xt1_I5_J,axiom,
    ! [Y_2,X_3] :
      ( ( is_fun_a_bool(X_3)
        & is_fun_a_bool(Y_2) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2))
         => X_3 = Y_2 ) ) ),
    file('theBenchmark.p',fact_509_xt1_I5_J) ).

fof(fact_510_order__trans,axiom,
    ! [Z_1,X_3,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Z_1)) ) ),
    file('theBenchmark.p',fact_510_order__trans) ).

fof(fact_511_order__trans,axiom,
    ! [Z_1,X_3,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Z_1)) ) ),
    file('theBenchmark.p',fact_511_order__trans) ).

fof(fact_512_order__trans,axiom,
    ! [Z_1,X_3,Y_2] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),Z_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Z_1)) ) ),
    file('theBenchmark.p',fact_512_order__trans) ).

fof(fact_513_order__trans,axiom,
    ! [Z_2,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),Z_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Z_2)) ) ),
    file('theBenchmark.p',fact_513_order__trans) ).

fof(fact_514_order__trans,axiom,
    ! [Z_1,X_3,Y_2] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),Z_1))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Z_1)) ) ),
    file('theBenchmark.p',fact_514_order__trans) ).

fof(fact_515_order__antisym,axiom,
    ! [X_3,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3))
       => ( hBOOL(X_3)
        <=> hBOOL(Y_2) ) ) ),
    file('theBenchmark.p',fact_515_order__antisym) ).

fof(fact_516_order__antisym,axiom,
    ! [X_3,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3))
       => X_3 = Y_2 ) ),
    file('theBenchmark.p',fact_516_order__antisym) ).

fof(fact_517_order__antisym,axiom,
    ! [X_3,Y_2] :
      ( ( is_fun_pname_bool(Y_2)
        & is_fun_pname_bool(X_3) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3))
         => X_3 = Y_2 ) ) ),
    file('theBenchmark.p',fact_517_order__antisym) ).

fof(fact_518_order__antisym,axiom,
    ! [X_5,Y_4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_5),Y_4))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_4),X_5))
       => X_5 = Y_4 ) ),
    file('theBenchmark.p',fact_518_order__antisym) ).

fof(fact_519_order__antisym,axiom,
    ! [X_3,Y_2] :
      ( ( is_fun_a_bool(Y_2)
        & is_fun_a_bool(X_3) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3))
         => X_3 = Y_2 ) ) ),
    file('theBenchmark.p',fact_519_order__antisym) ).

fof(fact_520_xt1_I4_J,axiom,
    ! [C_1,B_1,A_3] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),A_3))
     => ( ( hBOOL(B_1)
        <=> hBOOL(C_1) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C_1),A_3)) ) ),
    file('theBenchmark.p',fact_520_xt1_I4_J) ).

fof(fact_521_xt1_I4_J,axiom,
    ! [C_1,B_1,A_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_1),A_3))
     => ( B_1 = C_1
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_1),A_3)) ) ),
    file('theBenchmark.p',fact_521_xt1_I4_J) ).

fof(fact_522_xt1_I4_J,axiom,
    ! [C_1,B_1,A_3] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A_3))
     => ( B_1 = C_1
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_3)) ) ),
    file('theBenchmark.p',fact_522_xt1_I4_J) ).

fof(fact_523_xt1_I4_J,axiom,
    ! [C_5,B_5,A_7] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_5),A_7))
     => ( B_5 = C_5
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_5),A_7)) ) ),
    file('theBenchmark.p',fact_523_xt1_I4_J) ).

fof(fact_524_xt1_I4_J,axiom,
    ! [C_1,B_1,A_3] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_1),A_3))
     => ( B_1 = C_1
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_1),A_3)) ) ),
    file('theBenchmark.p',fact_524_xt1_I4_J) ).

fof(fact_525_ord__le__eq__trans,axiom,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),B_1))
     => ( ( hBOOL(B_1)
        <=> hBOOL(C_1) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),C_1)) ) ),
    file('theBenchmark.p',fact_525_ord__le__eq__trans) ).

fof(fact_526_ord__le__eq__trans,axiom,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),B_1))
     => ( B_1 = C_1
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),C_1)) ) ),
    file('theBenchmark.p',fact_526_ord__le__eq__trans) ).

fof(fact_527_ord__le__eq__trans,axiom,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),B_1))
     => ( B_1 = C_1
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),C_1)) ) ),
    file('theBenchmark.p',fact_527_ord__le__eq__trans) ).

fof(fact_528_ord__le__eq__trans,axiom,
    ! [C_4,A_6,B_4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),B_4))
     => ( B_4 = C_4
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),C_4)) ) ),
    file('theBenchmark.p',fact_528_ord__le__eq__trans) ).

fof(fact_529_ord__le__eq__trans,axiom,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),B_1))
     => ( B_1 = C_1
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),C_1)) ) ),
    file('theBenchmark.p',fact_529_ord__le__eq__trans) ).

fof(fact_530_xt1_I3_J,axiom,
    ! [C_1,B_1,A_3] :
      ( ( hBOOL(A_3)
      <=> hBOOL(B_1) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C_1),B_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C_1),A_3)) ) ),
    file('theBenchmark.p',fact_530_xt1_I3_J) ).

fof(fact_531_xt1_I3_J,axiom,
    ! [C_1,A_3,B_1] :
      ( A_3 = B_1
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_1),B_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_1),A_3)) ) ),
    file('theBenchmark.p',fact_531_xt1_I3_J) ).

fof(fact_532_xt1_I3_J,axiom,
    ! [C_1,A_3,B_1] :
      ( A_3 = B_1
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),B_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_3)) ) ),
    file('theBenchmark.p',fact_532_xt1_I3_J) ).

fof(fact_533_xt1_I3_J,axiom,
    ! [C_3,A_5,B_3] :
      ( A_5 = B_3
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_3),B_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_3),A_5)) ) ),
    file('theBenchmark.p',fact_533_xt1_I3_J) ).

fof(fact_534_xt1_I3_J,axiom,
    ! [C_1,A_3,B_1] :
      ( A_3 = B_1
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_1),B_1))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_1),A_3)) ) ),
    file('theBenchmark.p',fact_534_xt1_I3_J) ).

fof(fact_535_ord__eq__le__trans,axiom,
    ! [C_1,B_1,A_3] :
      ( ( hBOOL(A_3)
      <=> hBOOL(B_1) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),C_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),C_1)) ) ),
    file('theBenchmark.p',fact_535_ord__eq__le__trans) ).

fof(fact_536_ord__eq__le__trans,axiom,
    ! [C_1,A_3,B_1] :
      ( A_3 = B_1
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_1),C_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),C_1)) ) ),
    file('theBenchmark.p',fact_536_ord__eq__le__trans) ).

fof(fact_537_ord__eq__le__trans,axiom,
    ! [C_1,A_3,B_1] :
      ( A_3 = B_1
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),C_1))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),C_1)) ) ),
    file('theBenchmark.p',fact_537_ord__eq__le__trans) ).

fof(fact_538_ord__eq__le__trans,axiom,
    ! [C_2,A_4,B_2] :
      ( A_4 = B_2
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),C_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_4),C_2)) ) ),
    file('theBenchmark.p',fact_538_ord__eq__le__trans) ).

fof(fact_539_ord__eq__le__trans,axiom,
    ! [C_1,A_3,B_1] :
      ( A_3 = B_1
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_1),C_1))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),C_1)) ) ),
    file('theBenchmark.p',fact_539_ord__eq__le__trans) ).

fof(fact_540_order__antisym__conv,axiom,
    ! [Y_2,X_3] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2))
      <=> ( hBOOL(X_3)
        <=> hBOOL(Y_2) ) ) ),
    file('theBenchmark.p',fact_540_order__antisym__conv) ).

fof(fact_541_order__antisym__conv,axiom,
    ! [Y_2,X_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2))
      <=> X_3 = Y_2 ) ),
    file('theBenchmark.p',fact_541_order__antisym__conv) ).

fof(fact_542_order__antisym__conv,axiom,
    ! [Y_2,X_3] :
      ( ( is_fun_pname_bool(X_3)
        & is_fun_pname_bool(Y_2) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2))
        <=> X_3 = Y_2 ) ) ),
    file('theBenchmark.p',fact_542_order__antisym__conv) ).

fof(fact_543_order__antisym__conv,axiom,
    ! [Y_2,X_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),Y_2))
      <=> X_3 = Y_2 ) ),
    file('theBenchmark.p',fact_543_order__antisym__conv) ).

fof(fact_544_order__antisym__conv,axiom,
    ! [Y_2,X_3] :
      ( ( is_fun_a_bool(X_3)
        & is_fun_a_bool(Y_2) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2))
        <=> X_3 = Y_2 ) ) ),
    file('theBenchmark.p',fact_544_order__antisym__conv) ).

fof(fact_545_order__eq__refl,axiom,
    ! [Y_2,X_3] :
      ( ( hBOOL(X_3)
      <=> hBOOL(Y_2) )
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) ),
    file('theBenchmark.p',fact_545_order__eq__refl) ).

fof(fact_546_order__eq__refl,axiom,
    ! [X_3,Y_2] :
      ( X_3 = Y_2
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) ),
    file('theBenchmark.p',fact_546_order__eq__refl) ).

fof(fact_547_order__eq__refl,axiom,
    ! [X_3,Y_2] :
      ( X_3 = Y_2
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) ),
    file('theBenchmark.p',fact_547_order__eq__refl) ).

fof(fact_548_order__eq__refl,axiom,
    ! [X_4,Y_3] :
      ( X_4 = Y_3
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_3)) ),
    file('theBenchmark.p',fact_548_order__eq__refl) ).

fof(fact_549_order__eq__refl,axiom,
    ! [X_3,Y_2] :
      ( X_3 = Y_2
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) ),
    file('theBenchmark.p',fact_549_order__eq__refl) ).

fof(fact_550_order__eq__iff,axiom,
    ! [Y_2,X_3] :
      ( ( hBOOL(X_3)
      <=> hBOOL(Y_2) )
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) ) ),
    file('theBenchmark.p',fact_550_order__eq__iff) ).

fof(fact_551_order__eq__iff,axiom,
    ! [X_3,Y_2] :
      ( X_3 = Y_2
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) ) ),
    file('theBenchmark.p',fact_551_order__eq__iff) ).

fof(fact_552_order__eq__iff,axiom,
    ! [X_3,Y_2] :
      ( ( is_fun_pname_bool(Y_2)
        & is_fun_pname_bool(X_3) )
     => ( X_3 = Y_2
      <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) ) ) ),
    file('theBenchmark.p',fact_552_order__eq__iff) ).

fof(fact_553_order__eq__iff,axiom,
    ! [X_3,Y_2] :
      ( X_3 = Y_2
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_3))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),Y_2)) ) ),
    file('theBenchmark.p',fact_553_order__eq__iff) ).

fof(fact_554_order__eq__iff,axiom,
    ! [X_3,Y_2] :
      ( ( is_fun_a_bool(Y_2)
        & is_fun_a_bool(X_3) )
     => ( X_3 = Y_2
      <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) ) ) ),
    file('theBenchmark.p',fact_554_order__eq__iff) ).

fof(fact_555_linorder__linear,axiom,
    ! [X_2,Y_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_1)) ),
    file('theBenchmark.p',fact_555_linorder__linear) ).

fof(fact_556_finite__subset__induct,axiom,
    ! [Pa,A_1,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F_1),A_1))
       => ( hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool))
         => ( ! [A_2,F_2] :
                ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2))
               => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1))
                 => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),F_2))
                   => ( hBOOL(hAPP_f54304608l_bool(Pa,F_2))
                     => hBOOL(hAPP_f54304608l_bool(Pa,insert_nat(A_2,F_2))) ) ) ) )
           => hBOOL(hAPP_f54304608l_bool(Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_556_finite__subset__induct) ).

fof(fact_557_finite__subset__induct,axiom,
    ! [Pa,A_1,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F_1),A_1))
       => ( hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool))
         => ( ! [A_2,F_2] :
                ( ( is_fun_pname_bool(F_2)
                  & is_pname(A_2) )
               => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
                 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1))
                   => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),F_2))
                     => ( hBOOL(hAPP_f1664156314l_bool(Pa,F_2))
                       => hBOOL(hAPP_f1664156314l_bool(Pa,insert_pname(A_2,F_2))) ) ) ) ) )
           => hBOOL(hAPP_f1664156314l_bool(Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_557_finite__subset__induct) ).

fof(fact_558_finite__subset__induct,axiom,
    ! [Pa,A_1,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_1))
       => ( hBOOL(hAPP_fun_a_bool_bool(Pa,bot_bot_fun_a_bool))
         => ( ! [A_2,F_2] :
                ( ( is_fun_a_bool(F_2)
                  & is_a(A_2) )
               => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_2))
                 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A_1))
                   => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),F_2))
                     => ( hBOOL(hAPP_fun_a_bool_bool(Pa,F_2))
                       => hBOOL(hAPP_fun_a_bool_bool(Pa,insert_a(A_2,F_2))) ) ) ) ) )
           => hBOOL(hAPP_fun_a_bool_bool(Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_558_finite__subset__induct) ).

fof(fact_559_finite__subset__induct,axiom,
    ! [Pa,A_1,F_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,F_1),A_1))
       => ( hBOOL(hAPP_f1637334154l_bool(Pa,bot_bo1701429464l_bool))
         => ( ! [A_2,F_2] :
                ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_2))
               => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,A_2),A_1))
                 => ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,A_2),F_2))
                   => ( hBOOL(hAPP_f1637334154l_bool(Pa,F_2))
                     => hBOOL(hAPP_f1637334154l_bool(Pa,insert_fun_nat_bool(A_2,F_2))) ) ) ) )
           => hBOOL(hAPP_f1637334154l_bool(Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_559_finite__subset__induct) ).

fof(fact_560_finite__subset__induct,axiom,
    ! [Pa,A_1,F_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,F_1),A_1))
       => ( hBOOL(hAPP_f1935102916l_bool(Pa,bot_bo1649642514l_bool))
         => ( ! [A_2,F_2] :
                ( ( is_fun1661590463l_bool(F_2)
                  & is_fun_pname_bool(A_2) )
               => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2))
                 => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A_1))
                   => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),F_2))
                     => ( hBOOL(hAPP_f1935102916l_bool(Pa,F_2))
                       => hBOOL(hAPP_f1935102916l_bool(Pa,insert1325755072e_bool(A_2,F_2))) ) ) ) ) )
           => hBOOL(hAPP_f1935102916l_bool(Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_560_finite__subset__induct) ).

fof(fact_561_finite__subset__induct,axiom,
    ! [Pa,A_1,F_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,F_1),A_1))
       => ( hBOOL(hAPP_f621171935l_bool(Pa,bot_bo1389914601l_bool))
         => ( ! [A_2,F_2] :
                ( ( is_fun949378684l_bool(F_2)
                  & is_fun_a_bool(A_2) )
               => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_2))
                 => ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,A_2),A_1))
                   => ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,A_2),F_2))
                     => ( hBOOL(hAPP_f621171935l_bool(Pa,F_2))
                       => hBOOL(hAPP_f621171935l_bool(Pa,insert_fun_a_bool(A_2,F_2))) ) ) ) ) )
           => hBOOL(hAPP_f621171935l_bool(Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_561_finite__subset__induct) ).

fof(fact_562_assms_I2_J,axiom,
    ! [Pn,G] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(insert_a(hAPP_pname_a(mgt_call,Pn),G)),insert_a(mgt(the_com(body(Pn))),bot_bot_fun_a_bool)))
     => hBOOL(hAPP_fun_a_bool_bool(p(G),insert_a(hAPP_pname_a(mgt_call,Pn),bot_bot_fun_a_bool))) ),
    file('theBenchmark.p',fact_562_assms_I2_J) ).

fof(fact_563_finite__induct,axiom,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1))
     => ( hBOOL(hAPP_f1637334154l_bool(Pa,bot_bo1701429464l_bool))
       => ( ! [X_1,F_2] :
              ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_2))
             => ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),F_2))
               => ( hBOOL(hAPP_f1637334154l_bool(Pa,F_2))
                 => hBOOL(hAPP_f1637334154l_bool(Pa,insert_fun_nat_bool(X_1,F_2))) ) ) )
         => hBOOL(hAPP_f1637334154l_bool(Pa,F_1)) ) ) ),
    file('theBenchmark.p',fact_563_finite__induct) ).

fof(fact_564_finite__induct,axiom,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
     => ( hBOOL(hAPP_f1935102916l_bool(Pa,bot_bo1649642514l_bool))
       => ( ! [X_1,F_2] :
              ( ( is_fun1661590463l_bool(F_2)
                & is_fun_pname_bool(X_1) )
             => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2))
               => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),F_2))
                 => ( hBOOL(hAPP_f1935102916l_bool(Pa,F_2))
                   => hBOOL(hAPP_f1935102916l_bool(Pa,insert1325755072e_bool(X_1,F_2))) ) ) ) )
         => hBOOL(hAPP_f1935102916l_bool(Pa,F_1)) ) ) ),
    file('theBenchmark.p',fact_564_finite__induct) ).

fof(fact_565_finite__induct,axiom,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1))
     => ( hBOOL(hAPP_f621171935l_bool(Pa,bot_bo1389914601l_bool))
       => ( ! [X_1,F_2] :
              ( ( is_fun949378684l_bool(F_2)
                & is_fun_a_bool(X_1) )
             => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_2))
               => ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),F_2))
                 => ( hBOOL(hAPP_f621171935l_bool(Pa,F_2))
                   => hBOOL(hAPP_f621171935l_bool(Pa,insert_fun_a_bool(X_1,F_2))) ) ) ) )
         => hBOOL(hAPP_f621171935l_bool(Pa,F_1)) ) ) ),
    file('theBenchmark.p',fact_565_finite__induct) ).

fof(fact_566_finite__less__ub,axiom,
    ! [U,F] :
      ( ! [N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),hAPP_nat_nat(F,N_2)))
     => 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_566_finite__less__ub) ).

fof(fact_567_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_567_assms_I4_J) ).

fof(fact_568_diff__Suc__eq__diff__pred,axiom,
    ! [M,N] : hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N),
    file('theBenchmark.p',fact_568_diff__Suc__eq__diff__pred) ).

fof(fact_569_diff__Suc__1,axiom,
    ! [N] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,N)),one_one_nat) = N,
    file('theBenchmark.p',fact_569_diff__Suc__1) ).

fof(fact_570_less__eq__nat_Osimps_I2_J,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na))
    <=> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M_1)),Na)) ),
    file('theBenchmark.p',fact_570_less__eq__nat_Osimps_I2_J) ).

fof(fact_571_add__Suc__right,axiom,
    ! [M,N] : hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N)),
    file('theBenchmark.p',fact_571_add__Suc__right) ).

fof(fact_572_add__Suc,axiom,
    ! [M,N] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N)),
    file('theBenchmark.p',fact_572_add__Suc) ).

fof(fact_573_add__Suc__shift,axiom,
    ! [M,N] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N)),
    file('theBenchmark.p',fact_573_add__Suc__shift) ).

fof(fact_574_nat__add__right__cancel,axiom,
    ! [M_1,K_2,Na] :
      ( hAPP_nat_nat(plus_plus_nat(M_1),K_2) = hAPP_nat_nat(plus_plus_nat(Na),K_2)
    <=> M_1 = Na ),
    file('theBenchmark.p',fact_574_nat__add__right__cancel) ).

fof(fact_575_nat__add__left__cancel,axiom,
    ! [K_2,M_1,Na] :
      ( hAPP_nat_nat(plus_plus_nat(K_2),M_1) = hAPP_nat_nat(plus_plus_nat(K_2),Na)
    <=> M_1 = Na ),
    file('theBenchmark.p',fact_575_nat__add__left__cancel) ).

fof(fact_576_nat__add__assoc,axiom,
    ! [M,N,K] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(M),N)),K) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(plus_plus_nat(N),K)),
    file('theBenchmark.p',fact_576_nat__add__assoc) ).

fof(fact_577_nat__add__left__commute,axiom,
    ! [X,Y,Z] : hAPP_nat_nat(plus_plus_nat(X),hAPP_nat_nat(plus_plus_nat(Y),Z)) = hAPP_nat_nat(plus_plus_nat(Y),hAPP_nat_nat(plus_plus_nat(X),Z)),
    file('theBenchmark.p',fact_577_nat__add__left__commute) ).

fof(fact_578_nat__add__commute,axiom,
    ! [M,N] : hAPP_nat_nat(plus_plus_nat(M),N) = hAPP_nat_nat(plus_plus_nat(N),M),
    file('theBenchmark.p',fact_578_nat__add__commute) ).

fof(fact_579_diff__add__inverse2,axiom,
    ! [M,N] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),N)),N) = M,
    file('theBenchmark.p',fact_579_diff__add__inverse2) ).

fof(fact_580_diff__add__inverse,axiom,
    ! [N,M] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N),M)),N) = M,
    file('theBenchmark.p',fact_580_diff__add__inverse) ).

fof(fact_581_diff__diff__left,axiom,
    ! [I,J_2,K] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J_2)),K) = hAPP_nat_nat(minus_minus_nat(I),hAPP_nat_nat(plus_plus_nat(J_2),K)),
    file('theBenchmark.p',fact_581_diff__diff__left) ).

fof(fact_582_diff__cancel,axiom,
    ! [K,M,N] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(K),M)),hAPP_nat_nat(plus_plus_nat(K),N)) = hAPP_nat_nat(minus_minus_nat(M),N),
    file('theBenchmark.p',fact_582_diff__cancel) ).

fof(fact_583_diff__cancel2,axiom,
    ! [M,K,N] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K)),hAPP_nat_nat(plus_plus_nat(N),K)) = hAPP_nat_nat(minus_minus_nat(M),N),
    file('theBenchmark.p',fact_583_diff__cancel2) ).

fof(fact_584_le__add2,axiom,
    ! [N,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(plus_plus_nat(M),N))),
    file('theBenchmark.p',fact_584_le__add2) ).

fof(fact_585_le__add1,axiom,
    ! [N,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(plus_plus_nat(N),M))),
    file('theBenchmark.p',fact_585_le__add1) ).

fof(fact_586_le__iff__add,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
    <=> ? [K_1] : Na = hAPP_nat_nat(plus_plus_nat(M_1),K_1) ),
    file('theBenchmark.p',fact_586_le__iff__add) ).

fof(fact_587_nat__add__left__cancel__le,axiom,
    ! [K_2,M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(K_2),M_1)),hAPP_nat_nat(plus_plus_nat(K_2),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ),
    file('theBenchmark.p',fact_587_nat__add__left__cancel__le) ).

fof(fact_588_trans__le__add1,axiom,
    ! [M,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(plus_plus_nat(J_2),M))) ),
    file('theBenchmark.p',fact_588_trans__le__add1) ).

fof(fact_589_trans__le__add2,axiom,
    ! [M,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(plus_plus_nat(M),J_2))) ),
    file('theBenchmark.p',fact_589_trans__le__add2) ).

fof(fact_590_add__le__mono1,axiom,
    ! [K,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),K))) ),
    file('theBenchmark.p',fact_590_add__le__mono1) ).

fof(fact_591_add__le__mono,axiom,
    ! [K,L,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),L))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),L))) ) ),
    file('theBenchmark.p',fact_591_add__le__mono) ).

fof(fact_592_add__leD2,axiom,
    ! [M,K,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) ),
    file('theBenchmark.p',fact_592_add__leD2) ).

fof(fact_593_add__leD1,axiom,
    ! [M,K,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    file('theBenchmark.p',fact_593_add__leD1) ).

fof(fact_594_add__leE,axiom,
    ! [M,K,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N))
     => ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
         => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) ) ),
    file('theBenchmark.p',fact_594_add__leE) ).

fof(fact_595_diff__add__assoc2,axiom,
    ! [I,K,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2))
     => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J_2),I)),K) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J_2),K)),I) ),
    file('theBenchmark.p',fact_595_diff__add__assoc2) ).

fof(fact_596_add__diff__assoc2,axiom,
    ! [I,K,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2))
     => hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J_2),K)),I) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J_2),I)),K) ),
    file('theBenchmark.p',fact_596_add__diff__assoc2) ).

fof(fact_597_diff__add__assoc,axiom,
    ! [I,K,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2))
     => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),J_2)),K) = hAPP_nat_nat(plus_plus_nat(I),hAPP_nat_nat(minus_minus_nat(J_2),K)) ),
    file('theBenchmark.p',fact_597_diff__add__assoc) ).

fof(fact_598_le__imp__diff__is__add,axiom,
    ! [K_2,I_1,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
     => ( hAPP_nat_nat(minus_minus_nat(J_1),I_1) = K_2
      <=> J_1 = hAPP_nat_nat(plus_plus_nat(K_2),I_1) ) ),
    file('theBenchmark.p',fact_598_le__imp__diff__is__add) ).

fof(fact_599_le__add__diff__inverse2,axiom,
    ! [N,M] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M))
     => hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),N)),N) = M ),
    file('theBenchmark.p',fact_599_le__add__diff__inverse2) ).

fof(fact_600_le__diff__conv2,axiom,
    ! [I_1,K_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_2)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_2)),J_1)) ) ),
    file('theBenchmark.p',fact_600_le__diff__conv2) ).

fof(fact_601_add__diff__assoc,axiom,
    ! [I,K,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2))
     => hAPP_nat_nat(plus_plus_nat(I),hAPP_nat_nat(minus_minus_nat(J_2),K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),J_2)),K) ),
    file('theBenchmark.p',fact_601_add__diff__assoc) ).

fof(fact_602_le__add__diff__inverse,axiom,
    ! [N,M] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M))
     => hAPP_nat_nat(plus_plus_nat(N),hAPP_nat_nat(minus_minus_nat(M),N)) = M ),
    file('theBenchmark.p',fact_602_le__add__diff__inverse) ).

fof(fact_603_le__add__diff,axiom,
    ! [M,K,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N),M)),K))) ),
    file('theBenchmark.p',fact_603_le__add__diff) ).

fof(fact_604_le__diff__conv,axiom,
    ! [J_1,K_2,I_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(J_1),K_2)),I_1))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_nat_nat(plus_plus_nat(I_1),K_2))) ),
    file('theBenchmark.p',fact_604_le__diff__conv) ).

fof(fact_605_diff__diff__right,axiom,
    ! [I,K,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2))
     => hAPP_nat_nat(minus_minus_nat(I),hAPP_nat_nat(minus_minus_nat(J_2),K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),K)),J_2) ),
    file('theBenchmark.p',fact_605_diff__diff__right) ).

fof(fact_606_Suc__eq__plus1,axiom,
    ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(plus_plus_nat(N),one_one_nat),
    file('theBenchmark.p',fact_606_Suc__eq__plus1) ).

fof(fact_607_Suc__eq__plus1__left,axiom,
    ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(plus_plus_nat(one_one_nat),N),
    file('theBenchmark.p',fact_607_Suc__eq__plus1__left) ).

fof(fact_608_diff__Suc__diff__eq2,axiom,
    ! [M,K,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2))
     => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J_2),K))),M) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,J_2)),hAPP_nat_nat(plus_plus_nat(K),M)) ),
    file('theBenchmark.p',fact_608_diff__Suc__diff__eq2) ).

fof(fact_609_diff__Suc__diff__eq1,axiom,
    ! [M,K,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2))
     => hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J_2),K))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K)),hAPP_nat_nat(suc,J_2)) ),
    file('theBenchmark.p',fact_609_diff__Suc__diff__eq1) ).

fof(fact_610_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(plus_plus_nat(Y),Z))) ),
    file('theBenchmark.p',fact_610_termination__basic__simps_I3_J) ).

fof(fact_611_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(plus_plus_nat(Y),Z))) ),
    file('theBenchmark.p',fact_611_termination__basic__simps_I4_J) ).

fof(fact_612_lessI,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N))),
    file('theBenchmark.p',fact_612_lessI) ).

fof(fact_613_Suc__mono,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))) ),
    file('theBenchmark.p',fact_613_Suc__mono) ).

fof(fact_614_finite__Collect__less__nat,axiom,
    ! [K_2] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),K_2)))),
    file('theBenchmark.p',fact_614_finite__Collect__less__nat) ).

fof(fact_615_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(plus_plus_nat(Y),Z))) ),
    file('theBenchmark.p',fact_615_termination__basic__simps_I1_J) ).

fof(fact_616_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(plus_plus_nat(Y),Z))) ),
    file('theBenchmark.p',fact_616_termination__basic__simps_I2_J) ).

fof(fact_617_add__lessD1,axiom,
    ! [I,J_2,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),J_2)),K))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K)) ),
    file('theBenchmark.p',fact_617_add__lessD1) ).

fof(fact_618_less__add__eq__less,axiom,
    ! [M,N,K,L] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L))
     => ( hAPP_nat_nat(plus_plus_nat(M),L) = hAPP_nat_nat(plus_plus_nat(K),N)
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ),
    file('theBenchmark.p',fact_618_less__add__eq__less) ).

fof(fact_619_add__less__mono,axiom,
    ! [K,L,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,K),L))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),L))) ) ),
    file('theBenchmark.p',fact_619_add__less__mono) ).

fof(fact_620_add__less__mono1,axiom,
    ! [K,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(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),K))) ),
    file('theBenchmark.p',fact_620_add__less__mono1) ).

fof(fact_621_trans__less__add2,axiom,
    ! [M,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,I),hAPP_nat_nat(plus_plus_nat(M),J_2))) ),
    file('theBenchmark.p',fact_621_trans__less__add2) ).

fof(fact_622_trans__less__add1,axiom,
    ! [M,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,I),hAPP_nat_nat(plus_plus_nat(J_2),M))) ),
    file('theBenchmark.p',fact_622_trans__less__add1) ).

fof(fact_623_nat__add__left__cancel__less,axiom,
    ! [K_2,M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(K_2),M_1)),hAPP_nat_nat(plus_plus_nat(K_2),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ),
    file('theBenchmark.p',fact_623_nat__add__left__cancel__less) ).

fof(fact_624_not__add__less2,axiom,
    ! [J_2,I] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(J_2),I)),I)),
    file('theBenchmark.p',fact_624_not__add__less2) ).

fof(fact_625_not__add__less1,axiom,
    ! [I,J_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),J_2)),I)),
    file('theBenchmark.p',fact_625_not__add__less1) ).

fof(fact_626_Suc__less__SucD,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ),
    file('theBenchmark.p',fact_626_Suc__less__SucD) ).

fof(fact_627_Suc__lessD,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ),
    file('theBenchmark.p',fact_627_Suc__lessD) ).

fof(fact_628_less__SucE,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
       => M = N ) ),
    file('theBenchmark.p',fact_628_less__SucE) ).

fof(fact_629_less__trans__Suc,axiom,
    ! [K,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,J_2),K))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K)) ) ),
    file('theBenchmark.p',fact_629_less__trans__Suc) ).

fof(fact_630_Suc__lessI,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => ( hAPP_nat_nat(suc,M) != N
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N)) ) ),
    file('theBenchmark.p',fact_630_Suc__lessI) ).

fof(fact_631_less__SucI,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) ),
    file('theBenchmark.p',fact_631_less__SucI) ).

fof(fact_632_less__antisym,axiom,
    ! [N,M] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M)))
       => M = N ) ),
    file('theBenchmark.p',fact_632_less__antisym) ).

fof(fact_633_not__less__less__Suc__eq,axiom,
    ! [Na,M_1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
      <=> Na = M_1 ) ),
    file('theBenchmark.p',fact_633_not__less__less__Suc__eq) ).

fof(fact_634_Suc__less__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ),
    file('theBenchmark.p',fact_634_Suc__less__eq) ).

fof(fact_635_less__Suc__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
    <=> ( M_1 = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_635_less__Suc__eq) ).

fof(fact_636_not__less__eq,axiom,
    ! [M_1,Na] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) ),
    file('theBenchmark.p',fact_636_not__less__eq) ).

fof(fact_637_less__or__eq__imp__le,axiom,
    ! [M,N] :
      ( ( M = N
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    file('theBenchmark.p',fact_637_less__or__eq__imp__le) ).

fof(fact_638_le__neq__implies__less,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => ( M != N
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ),
    file('theBenchmark.p',fact_638_le__neq__implies__less) ).

fof(fact_639_less__imp__le__nat,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    file('theBenchmark.p',fact_639_less__imp__le__nat) ).

fof(fact_640_le__eq__less__or__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
    <=> ( M_1 = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_640_le__eq__less__or__eq) ).

fof(fact_641_nat__less__le,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
    <=> ( M_1 != Na
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_641_nat__less__le) ).

fof(fact_642_diff__less__mono2,axiom,
    ! [L,M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),L))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(L),N)),hAPP_nat_nat(minus_minus_nat(L),M))) ) ),
    file('theBenchmark.p',fact_642_diff__less__mono2) ).

fof(fact_643_less__imp__diff__less,axiom,
    ! [N,J_2,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(J_2),N)),K)) ),
    file('theBenchmark.p',fact_643_less__imp__diff__less) ).

fof(fact_644_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_644_termination__basic__simps_I5_J) ).

fof(fact_645_less__not__refl,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)),
    file('theBenchmark.p',fact_645_less__not__refl) ).

fof(fact_646_nat__neq__iff,axiom,
    ! [M_1,Na] :
      ( M_1 != Na
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    file('theBenchmark.p',fact_646_nat__neq__iff) ).

fof(fact_647_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_647_linorder__neqE__nat) ).

fof(fact_648_less__irrefl__nat,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)),
    file('theBenchmark.p',fact_648_less__irrefl__nat) ).

fof(fact_649_less__not__refl2,axiom,
    ! [N,M] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
     => M != N ),
    file('theBenchmark.p',fact_649_less__not__refl2) ).

fof(fact_650_less__not__refl3,axiom,
    ! [S,T] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
     => S != T ),
    file('theBenchmark.p',fact_650_less__not__refl3) ).

fof(fact_651_nat__less__cases,axiom,
    ! [Pa,M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) )
     => ( ( M_1 = Na
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) )
       => ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
           => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) ) ) ),
    file('theBenchmark.p',fact_651_nat__less__cases) ).

fof(fact_652_finite__nat__set__iff__bounded,axiom,
    ! [N_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1))
    <=> ? [M_2] :
        ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),M_2)) ) ),
    file('theBenchmark.p',fact_652_finite__nat__set__iff__bounded) ).

fof(fact_653_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_653_card__Collect__less__nat) ).

fof(fact_654_finite__M__bounded__by__nat,axiom,
    ! [Pa,I_1] : 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_1))))),
    file('theBenchmark.p',fact_654_finite__M__bounded__by__nat) ).

fof(fact_655_less__add__Suc1,axiom,
    ! [I,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(I),M)))),
    file('theBenchmark.p',fact_655_less__add__Suc1) ).

fof(fact_656_less__add__Suc2,axiom,
    ! [I,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),I)))),
    file('theBenchmark.p',fact_656_less__add__Suc2) ).

fof(fact_657_less__iff__Suc__add,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
    <=> ? [K_1] : Na = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M_1),K_1)) ),
    file('theBenchmark.p',fact_657_less__iff__Suc__add) ).

fof(fact_658_less__eq__Suc__le,axiom,
    ! [Na,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) ),
    file('theBenchmark.p',fact_658_less__eq__Suc__le) ).

fof(fact_659_less__Suc__eq__le,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ),
    file('theBenchmark.p',fact_659_less__Suc__eq__le) ).

fof(fact_660_Suc__le__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ),
    file('theBenchmark.p',fact_660_Suc__le__eq) ).

fof(fact_661_le__imp__less__Suc,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) ),
    file('theBenchmark.p',fact_661_le__imp__less__Suc) ).

fof(fact_662_Suc__leI,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) ),
    file('theBenchmark.p',fact_662_Suc__leI) ).

fof(fact_663_le__less__Suc__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
      <=> Na = M_1 ) ),
    file('theBenchmark.p',fact_663_le__less__Suc__eq) ).

fof(fact_664_Suc__le__lessD,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ),
    file('theBenchmark.p',fact_664_Suc__le__lessD) ).

fof(fact_665_diff__less__Suc,axiom,
    ! [M,N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M),N)),hAPP_nat_nat(suc,M))),
    file('theBenchmark.p',fact_665_diff__less__Suc) ).

fof(fact_666_add__diff__inverse,axiom,
    ! [M,N] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => hAPP_nat_nat(plus_plus_nat(N),hAPP_nat_nat(minus_minus_nat(M),N)) = M ),
    file('theBenchmark.p',fact_666_add__diff__inverse) ).

fof(fact_667_less__diff__conv,axiom,
    ! [I_1,J_1,K_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_2)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_2)),J_1)) ),
    file('theBenchmark.p',fact_667_less__diff__conv) ).

fof(fact_668_diff__less__mono,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(A),C)),hAPP_nat_nat(minus_minus_nat(B),C))) ) ),
    file('theBenchmark.p',fact_668_diff__less__mono) ).

fof(fact_669_less__diff__iff,axiom,
    ! [Na,K_2,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M_1),K_2)),hAPP_nat_nat(minus_minus_nat(Na),K_2)))
        <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ) ),
    file('theBenchmark.p',fact_669_less__diff__iff) ).

fof(fact_670_less__eq__Suc__le__raw,axiom,
    ! [X_1] : hAPP_n1699378549t_bool(ord_less_nat,X_1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_1)),
    file('theBenchmark.p',fact_670_less__eq__Suc__le__raw) ).

fof(fact_671_mono__nat__linear__lb,axiom,
    ! [M_1,K_2,F] :
      ( ! [M_2,N_2] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_2)),hAPP_nat_nat(F,N_2))) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(F,M_1)),K_2)),hAPP_nat_nat(F,hAPP_nat_nat(plus_plus_nat(M_1),K_2)))) ),
    file('theBenchmark.p',fact_671_mono__nat__linear__lb) ).

fof(fact_672_inc__induct,axiom,
    ! [Pa,I_1,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
     => ( hBOOL(hAPP_nat_bool(Pa,J_1))
       => ( ! [I_2] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
             => ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_2)))
               => hBOOL(hAPP_nat_bool(Pa,I_2)) ) )
         => hBOOL(hAPP_nat_bool(Pa,I_1)) ) ) ),
    file('theBenchmark.p',fact_672_inc__induct) ).

fof(fact_673_less__imp__Suc__add,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
     => ? [K_1] : N = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),K_1)) ),
    file('theBenchmark.p',fact_673_less__imp__Suc__add) ).

fof(fact_674_bounded__nat__set__is__finite,axiom,
    ! [Na,N_1] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Na)) )
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1)) ),
    file('theBenchmark.p',fact_674_bounded__nat__set__is__finite) ).

fof(fact_675_less__mono__imp__le__mono,axiom,
    ! [I_1,J_1,F] :
      ( ! [I_2,J] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J))) )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_1))) ) ),
    file('theBenchmark.p',fact_675_less__mono__imp__le__mono) ).

fof(fact_676_Suc__lessE,axiom,
    ! [I,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K))
     => ~ ! [J] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J))
           => K != hAPP_nat_nat(suc,J) ) ),
    file('theBenchmark.p',fact_676_Suc__lessE) ).

fof(fact_677_lessE,axiom,
    ! [I,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K))
     => ( K != hAPP_nat_nat(suc,I)
       => ~ ! [J] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J))
             => K != hAPP_nat_nat(suc,J) ) ) ),
    file('theBenchmark.p',fact_677_lessE) ).

fof(fact_678_less__zeroE,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    file('theBenchmark.p',fact_678_less__zeroE) ).

fof(fact_679_le0,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)),
    file('theBenchmark.p',fact_679_le0) ).

fof(fact_680_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_680_zero__less__Suc) ).

fof(fact_681_add__is__1,axiom,
    ! [M_1,Na] :
      ( hAPP_nat_nat(plus_plus_nat(M_1),Na) = hAPP_nat_nat(suc,zero_zero_nat)
    <=> ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_1 = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M_1 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ),
    file('theBenchmark.p',fact_681_add__is__1) ).

fof(fact_682_one__is__add,axiom,
    ! [M_1,Na] :
      ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(M_1),Na)
    <=> ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_1 = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M_1 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ),
    file('theBenchmark.p',fact_682_one__is__add) ).

fof(fact_683_diff__add__0,axiom,
    ! [N,M] : hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(plus_plus_nat(N),M)) = zero_zero_nat,
    file('theBenchmark.p',fact_683_diff__add__0) ).

fof(fact_684_diff__is__0__eq_H,axiom,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => hAPP_nat_nat(minus_minus_nat(M),N) = zero_zero_nat ),
    file('theBenchmark.p',fact_684_diff__is__0__eq_H) ).

fof(fact_685_diff__is__0__eq,axiom,
    ! [M_1,Na] :
      ( hAPP_nat_nat(minus_minus_nat(M_1),Na) = zero_zero_nat
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ),
    file('theBenchmark.p',fact_685_diff__is__0__eq) ).

fof(fact_686_One__nat__def,axiom,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    file('theBenchmark.p',fact_686_One__nat__def) ).

fof(fact_687_diffs0__imp__equal,axiom,
    ! [M,N] :
      ( hAPP_nat_nat(minus_minus_nat(M),N) = zero_zero_nat
     => ( hAPP_nat_nat(minus_minus_nat(N),M) = zero_zero_nat
       => M = N ) ),
    file('theBenchmark.p',fact_687_diffs0__imp__equal) ).

fof(fact_688_diff__self__eq__0,axiom,
    ! [M] : hAPP_nat_nat(minus_minus_nat(M),M) = zero_zero_nat,
    file('theBenchmark.p',fact_688_diff__self__eq__0) ).

fof(fact_689_minus__nat_Odiff__0,axiom,
    ! [M] : hAPP_nat_nat(minus_minus_nat(M),zero_zero_nat) = M,
    file('theBenchmark.p',fact_689_minus__nat_Odiff__0) ).

fof(fact_690_diff__0__eq__0,axiom,
    ! [N] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),N) = zero_zero_nat,
    file('theBenchmark.p',fact_690_diff__0__eq__0) ).

fof(fact_691_Suc__neq__Zero,axiom,
    ! [M] : hAPP_nat_nat(suc,M) != zero_zero_nat,
    file('theBenchmark.p',fact_691_Suc__neq__Zero) ).

fof(fact_692_Zero__neq__Suc,axiom,
    ! [M] : zero_zero_nat != hAPP_nat_nat(suc,M),
    file('theBenchmark.p',fact_692_Zero__neq__Suc) ).

fof(fact_693_nat_Osimps_I3_J,axiom,
    ! [Nat_1] : hAPP_nat_nat(suc,Nat_1) != zero_zero_nat,
    file('theBenchmark.p',fact_693_nat_Osimps_I3_J) ).

fof(fact_694_Suc__not__Zero,axiom,
    ! [M] : hAPP_nat_nat(suc,M) != zero_zero_nat,
    file('theBenchmark.p',fact_694_Suc__not__Zero) ).

fof(fact_695_nat_Osimps_I2_J,axiom,
    ! [Nat] : zero_zero_nat != hAPP_nat_nat(suc,Nat),
    file('theBenchmark.p',fact_695_nat_Osimps_I2_J) ).

fof(fact_696_Zero__not__Suc,axiom,
    ! [M] : zero_zero_nat != hAPP_nat_nat(suc,M),
    file('theBenchmark.p',fact_696_Zero__not__Suc) ).

fof(fact_697_bot__nat__def,axiom,
    bot_bot_nat = zero_zero_nat,
    file('theBenchmark.p',fact_697_bot__nat__def) ).

fof(fact_698_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_698_le__0__eq) ).

fof(fact_699_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_699_less__eq__nat_Osimps_I1_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_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__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_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_pname_bool(cOMBK_bool_pname(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) ).

fof(help_COMBC_1_1_COMBC_000t__a_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_a_bool(hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_a_fun_nat_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__Nat__Onat_000tc__HOL__Obool_U) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000t__a_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(P),Q),R) = hAPP_a_bool(hAPP_nat_fun_a_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_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_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_a_bool(hAPP_p1534023578a_bool(cOMBC_a_pname_bool(P),Q),R) = hAPP_pname_bool(hAPP_a93125764e_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U) ).

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

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

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

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

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

fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a_U,axiom,
    ! [P,Q,R] : hAPP_a_fun_a_bool(cOMBB_a_fun_a_bool_a(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_a_a(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a_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__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_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_fun_a_bool_bool(cOMBK_324466864a_bool(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_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_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_pname_bool(hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_p1499970991t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(P),Q),R) = hAPP_pname_bool(hAPP_n1025906991e_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_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__Nat__Onat,axiom,
    ! [P,Q,R] : hAPP_nat_fun_a_bool(cOMBB_1885489796ol_nat(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_nat_a(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat) ).

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_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_f54304608l_bool(cOMBK_1994329625t_bool(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).

fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [P,Q,R] : hAPP_a_fun_nat_bool(cOMBB_1321347587bool_a(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_a_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_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__,axiom,
    ! [P,Q,R] : hAPP_a_bool(hAPP_f1549043526a_bool(cOMBC_777206479l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_a1392362872l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Nat__Onat_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_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat_000tc__,axiom,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(cOMBC_619334683t_bool(P),Q),R) = hAPP_nat_bool(hAPP_f282463732t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat_000tc__) ).

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

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

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

fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc,axiom,
    ! [P,Q,R] : hAPP_a_bool(hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_a217006258l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc) ).

fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc,axiom,
    ! [P,Q,R] : hAPP_pname_bool(hAPP_f1794073134e_bool(cOMBC_445755039l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname_000tc,axiom,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(P),Q),R) = hAPP_pname_bool(hAPP_f1794073134e_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname_000tc) ).

fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
    ! [P,Q,R] : hAPP_a93125764e_bool(cOMBB_610033911bool_a(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_a_pname(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).

fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__003,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__003) ).

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_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona,axiom,
    ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_n215258509l_bool(cOMBC_385542954t_bool(P),Q),R) = hAPP_nat_bool(hAPP_f800510211t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona) ).

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

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_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_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__005,axiom,
    ! [P,Q,R] : hAPP_p1499970991t_bool(cOMBB_523834888_pname(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_pname_nat(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__005) ).

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__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo,axiom,
    ! [P,Q,R] : hAPP_pname_bool(hAPP_f654413245e_bool(cOMBC_267053842l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_p130839763l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Nat__Onat_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_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Nat__O,axiom,
    ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_n850744903l_bool(cOMBC_1666426608t_bool(P),Q),R) = hAPP_nat_bool(hAPP_f1066163005t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Nat__O) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn,axiom,
    ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_p130839763l_bool(cOMBC_615407716e_bool(P),Q),R) = hAPP_pname_bool(hAPP_f654413245e_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn) ).

fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_006,axiom,
    ! [P,Q,R] : hAPP_n1025906991e_bool(cOMBB_1212655066ol_nat(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_nat_pname(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_006) ).

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

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

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

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

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O,axiom,
    ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_p338031245l_bool(cOMBC_1004116266e_bool(P),Q),R) = hAPP_pname_bool(hAPP_f759274231e_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) ).

fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_008,axiom,
    ! [P,Q,R] : hAPP_p61793385e_bool(cOMBB_542850580_pname(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_pname_pname(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_008) ).

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__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__009,axiom,
    ! [P,Q,R] : hAPP_f282463732t_bool(cOMBB_164527437a_bool(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_fun_a_bool_nat(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__009) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010,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_010) ).

fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_011,axiom,
    ! [P,Q,R] : hAPP_f1794073134e_bool(cOMBB_1693087065a_bool(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_f1128469712_pname(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_011) ).

fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__012,axiom,
    ! [P,Q,R] : hAPP_f800510211t_bool(cOMBB_1250273980t_bool(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_f22106695ol_nat(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__012) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,axiom,
    ! [P,Q,R] : hAPP_a85458249l_bool(cOMBB_472261505bool_a(P,Q),R) = hAPP_f1631501043l_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__fun_Itc__fun_It__) ).

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_013,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_013) ).

fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__014,axiom,
    ! [P,Q,R] : hAPP_f1066163005t_bool(cOMBB_1896684278e_bool(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_f921600141ol_nat(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__014) ).

fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_015,axiom,
    ! [P,Q,R] : hAPP_f654413245e_bool(cOMBB_141086128t_bool(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_f1291551745_pname(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_015) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_016,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_016) ).

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__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_017,axiom,
    ! [P,Q,R] : hAPP_f759274231e_bool(cOMBB_598082538e_bool(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_f1297739591_pname(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_017) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___018,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___018) ).

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

fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___019,axiom,
    ! [P,Q,R] : hAPP_p1824510254l_bool(cOMBB_392435466_pname(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_p1534023578a_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___019) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
    ! [P,Q,R] : hAPP_a1392362872l_bool(cOMBB_743407885bool_a(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_a_fun_nat_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__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
    ! [P,Q,R] : hAPP_a217006258l_bool(cOMBB_1137537805bool_a(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_a93125764e_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__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__020,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__020) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__021,axiom,
    ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__021) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__022,axiom,
    ! [P,Q,R] : hAPP_p130839763l_bool(cOMBB_928955006_pname(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_p1499970991t_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__022) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_023,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_023) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_024,axiom,
    ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_024) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_025,axiom,
    ! [P,Q,R] : hAPP_p338031245l_bool(cOMBB_408569982_pname(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_p61793385e_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_025) ).

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

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

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

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

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

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

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

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

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

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

fof(f_1_1,plain,
    ! [B_1_1,B_2_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_fun949378684l_bool(cOMBB_2140588453a_bool(B_1_1,B_2_1))
      | ~ is_fun949378684l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool]) ).

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

fof(f_3_3,plain,
    ! [U_4,U_5] :
      ( is_fun949378684l_bool(cOMBB_2140588453a_bool(U_5,U_4))
      | ~ is_fun949378684l_bool(U_4) ),
    inference(definitional_conversion,[status(esa)],[f_3_2]) ).

cnf(f_3_4,plain,
    ( is_fun949378684l_bool(cOMBB_2140588453a_bool(U_5,U_4))
    | ~ is_fun949378684l_bool(U_4) ),
    inference(clausify,[status(thm)],[f_3_3]) ).

fof(f_4_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1661590463l_bool(cOMBB_307249310e_bool(B_1_1,B_2_1))
      | ~ is_fun1661590463l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_]) ).

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

fof(f_4_3,plain,
    ! [U_6,U_7] :
      ( is_fun1661590463l_bool(cOMBB_307249310e_bool(U_7,U_6))
      | ~ is_fun1661590463l_bool(U_6) ),
    inference(definitional_conversion,[status(esa)],[f_4_2]) ).

cnf(f_4_4,plain,
    ( is_fun1661590463l_bool(cOMBB_307249310e_bool(U_7,U_6))
    | ~ is_fun1661590463l_bool(U_6) ),
    inference(clausify,[status(thm)],[f_4_3]) ).

fof(f_5_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_5_2,plain,
    ! [U_8] :
      ( is_fun_a_bool(cOMBK_bool_a(U_8))
      | ~ is_bool(U_8) ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

fof(f_5_3,plain,
    ! [U_8] :
      ( is_fun_a_bool(cOMBK_bool_a(U_8))
      | ~ is_bool(U_8) ),
    inference(definitional_conversion,[status(esa)],[f_5_2]) ).

cnf(f_5_4,plain,
    ( is_fun_a_bool(cOMBK_bool_a(U_8))
    | ~ is_bool(U_8) ),
    inference(clausify,[status(thm)],[f_5_3]) ).

fof(f_6_1,plain,
    ! [B_1_1] :
      ( is_fun_pname_bool(cOMBK_bool_pname(B_1_1))
      | ~ is_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname]) ).

fof(f_6_2,plain,
    ! [U_9] :
      ( is_fun_pname_bool(cOMBK_bool_pname(U_9))
      | ~ is_bool(U_9) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

fof(f_6_3,plain,
    ! [U_9] :
      ( is_fun_pname_bool(cOMBK_bool_pname(U_9))
      | ~ is_bool(U_9) ),
    inference(definitional_conversion,[status(esa)],[f_6_2]) ).

cnf(f_6_4,plain,
    ( is_fun_pname_bool(cOMBK_bool_pname(U_9))
    | ~ is_bool(U_9) ),
    inference(clausify,[status(thm)],[f_6_3]) ).

fof(f_7_1,plain,
    ! [B_1_1] :
      ( is_fun949378684l_bool(cOMBK_324466864a_bool(B_1_1))
      | ~ is_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_7_2,plain,
    ! [U_10] :
      ( is_fun949378684l_bool(cOMBK_324466864a_bool(U_10))
      | ~ is_bool(U_10) ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

fof(f_7_3,plain,
    ! [U_10] :
      ( is_fun949378684l_bool(cOMBK_324466864a_bool(U_10))
      | ~ is_bool(U_10) ),
    inference(definitional_conversion,[status(esa)],[f_7_2]) ).

cnf(f_7_4,plain,
    ( is_fun949378684l_bool(cOMBK_324466864a_bool(U_10))
    | ~ is_bool(U_10) ),
    inference(clausify,[status(thm)],[f_7_3]) ).

fof(f_8_1,plain,
    ! [B_1_1] :
      ( is_fun1661590463l_bool(cOMBK_1857069011e_bool(B_1_1))
      | ~ is_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_8_2,plain,
    ! [U_11] :
      ( is_fun1661590463l_bool(cOMBK_1857069011e_bool(U_11))
      | ~ is_bool(U_11) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ! [U_11] :
      ( is_fun1661590463l_bool(cOMBK_1857069011e_bool(U_11))
      | ~ is_bool(U_11) ),
    inference(definitional_conversion,[status(esa)],[f_8_2]) ).

cnf(f_8_4,plain,
    ( is_fun1661590463l_bool(cOMBK_1857069011e_bool(U_11))
    | ~ is_bool(U_11) ),
    inference(clausify,[status(thm)],[f_8_3]) ).

fof(f_9_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_9_2,plain,
    ! [U_13,U_12] :
      ( is_fun_a_bool(cOMBS_a_bool_bool(U_13,U_12))
      | ~ is_fun_a_bool(U_12) ),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

fof(f_9_3,plain,
    ! [U_12,U_13] :
      ( is_fun_a_bool(cOMBS_a_bool_bool(U_13,U_12))
      | ~ is_fun_a_bool(U_12) ),
    inference(definitional_conversion,[status(esa)],[f_9_2]) ).

cnf(f_9_4,plain,
    ( is_fun_a_bool(cOMBS_a_bool_bool(U_13,U_12))
    | ~ is_fun_a_bool(U_12) ),
    inference(clausify,[status(thm)],[f_9_3]) ).

fof(f_10_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_10_2,plain,
    ! [U_15,U_14] :
      ( is_fun_pname_bool(cOMBS_568398431l_bool(U_15,U_14))
      | ~ is_fun_pname_bool(U_14) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

fof(f_10_3,plain,
    ! [U_14,U_15] :
      ( is_fun_pname_bool(cOMBS_568398431l_bool(U_15,U_14))
      | ~ is_fun_pname_bool(U_14) ),
    inference(definitional_conversion,[status(esa)],[f_10_2]) ).

cnf(f_10_4,plain,
    ( is_fun_pname_bool(cOMBS_568398431l_bool(U_15,U_14))
    | ~ is_fun_pname_bool(U_14) ),
    inference(clausify,[status(thm)],[f_10_3]) ).

fof(f_11_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_11_2,plain,
    ! [U_17,U_16] :
      ( is_fun949378684l_bool(cOMBS_1035972772l_bool(U_17,U_16))
      | ~ is_fun949378684l_bool(U_16) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ! [U_16,U_17] :
      ( is_fun949378684l_bool(cOMBS_1035972772l_bool(U_17,U_16))
      | ~ is_fun949378684l_bool(U_16) ),
    inference(definitional_conversion,[status(esa)],[f_11_2]) ).

cnf(f_11_4,plain,
    ( is_fun949378684l_bool(cOMBS_1035972772l_bool(U_17,U_16))
    | ~ is_fun949378684l_bool(U_16) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_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_12_2,plain,
    ! [U_19,U_18] :
      ( is_fun1661590463l_bool(cOMBS_350070575l_bool(U_19,U_18))
      | ~ is_fun1661590463l_bool(U_18) ),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

fof(f_12_3,plain,
    ! [U_18,U_19] :
      ( is_fun1661590463l_bool(cOMBS_350070575l_bool(U_19,U_18))
      | ~ is_fun1661590463l_bool(U_18) ),
    inference(definitional_conversion,[status(esa)],[f_12_2]) ).

cnf(f_12_4,plain,
    ( is_fun1661590463l_bool(cOMBS_350070575l_bool(U_19,U_18))
    | ~ is_fun1661590463l_bool(U_18) ),
    inference(clausify,[status(thm)],[f_12_3]) ).

fof(f_13_1,plain,
    is_fun949378684l_bool(finite_finite_a),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofinite_000t__a]) ).

fof(f_13_2,plain,
    is_fun949378684l_bool(finite_finite_a),
    inference(definitional_conversion,[status(esa)],[f_13_1]) ).

cnf(f_13_3,plain,
    is_fun949378684l_bool(finite_finite_a),
    inference(clausify,[status(thm)],[f_13_2]) ).

fof(f_14_1,plain,
    is_fun1661590463l_bool(finite_finite_pname),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofinite_000tc__Com__Opname]) ).

fof(f_14_2,plain,
    is_fun1661590463l_bool(finite_finite_pname),
    inference(definitional_conversion,[status(esa)],[f_14_1]) ).

cnf(f_14_3,plain,
    is_fun1661590463l_bool(finite_finite_pname),
    inference(clausify,[status(thm)],[f_14_2]) ).

fof(f_15_1,plain,
    is_a(undefined_a(x_a)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000t__a]) ).

fof(f_15_2,plain,
    is_a(undefined_a(x_a)),
    inference(definitional_conversion,[status(esa)],[f_15_1]) ).

cnf(f_15_3,plain,
    is_a(undefined_a(x_a)),
    inference(clausify,[status(thm)],[f_15_2]) ).

fof(f_16_1,plain,
    is_pname(undefined_pname(pname)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Com__Opname]) ).

fof(f_16_2,plain,
    is_pname(undefined_pname(pname)),
    inference(definitional_conversion,[status(esa)],[f_16_1]) ).

cnf(f_16_3,plain,
    is_pname(undefined_pname(pname)),
    inference(clausify,[status(thm)],[f_16_2]) ).

fof(f_17_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_17_2,plain,
    is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
    inference(definitional_conversion,[status(esa)],[f_17_1]) ).

cnf(f_17_3,plain,
    is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
    inference(clausify,[status(thm)],[f_17_2]) ).

fof(f_18_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_18_2,plain,
    is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
    inference(definitional_conversion,[status(esa)],[f_18_1]) ).

cnf(f_18_3,plain,
    is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
    inference(clausify,[status(thm)],[f_18_2]) ).

fof(f_19_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_19_2,plain,
    is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
    inference(definitional_conversion,[status(esa)],[f_19_1]) ).

cnf(f_19_3,plain,
    is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
    inference(clausify,[status(thm)],[f_19_2]) ).

fof(f_20_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_20_2,plain,
    is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
    inference(definitional_conversion,[status(esa)],[f_20_1]) ).

cnf(f_20_3,plain,
    is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
    inference(clausify,[status(thm)],[f_20_2]) ).

fof(f_21_1,plain,
    is_bool(bot_bot_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool]) ).

fof(f_21_2,plain,
    is_bool(bot_bot_bool),
    inference(definitional_conversion,[status(esa)],[f_21_1]) ).

cnf(f_21_3,plain,
    is_bool(bot_bot_bool),
    inference(clausify,[status(thm)],[f_21_2]) ).

fof(f_22_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_22_2,plain,
    is_fun_a_bool(bot_bot_fun_a_bool),
    inference(definitional_conversion,[status(esa)],[f_22_1]) ).

cnf(f_22_3,plain,
    is_fun_a_bool(bot_bot_fun_a_bool),
    inference(clausify,[status(thm)],[f_22_2]) ).

fof(f_23_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_23_2,plain,
    is_fun_pname_bool(bot_bo844097828e_bool),
    inference(definitional_conversion,[status(esa)],[f_23_1]) ).

cnf(f_23_3,plain,
    is_fun_pname_bool(bot_bo844097828e_bool),
    inference(clausify,[status(thm)],[f_23_2]) ).

fof(f_24_1,plain,
    is_fun949378684l_bool(bot_bo1389914601l_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc]) ).

fof(f_24_2,plain,
    is_fun949378684l_bool(bot_bo1389914601l_bool),
    inference(definitional_conversion,[status(esa)],[f_24_1]) ).

cnf(f_24_3,plain,
    is_fun949378684l_bool(bot_bo1389914601l_bool),
    inference(clausify,[status(thm)],[f_24_2]) ).

fof(f_25_1,plain,
    is_fun1661590463l_bool(bot_bo1649642514l_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__]) ).

fof(f_25_2,plain,
    is_fun1661590463l_bool(bot_bo1649642514l_bool),
    inference(definitional_conversion,[status(esa)],[f_25_1]) ).

cnf(f_25_3,plain,
    is_fun1661590463l_bool(bot_bo1649642514l_bool),
    inference(clausify,[status(thm)],[f_25_2]) ).

fof(f_26_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_26_2,plain,
    ! [U_20] :
      ( is_fun_a_bool(collect_a(U_20))
      | ~ is_fun_a_bool(U_20) ),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

fof(f_26_3,plain,
    ! [U_20] :
      ( is_fun_a_bool(collect_a(U_20))
      | ~ is_fun_a_bool(U_20) ),
    inference(definitional_conversion,[status(esa)],[f_26_2]) ).

cnf(f_26_4,plain,
    ( is_fun_a_bool(collect_a(U_20))
    | ~ is_fun_a_bool(U_20) ),
    inference(clausify,[status(thm)],[f_26_3]) ).

fof(f_27_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_27_2,plain,
    ! [U_21] :
      ( is_fun_pname_bool(collect_pname(U_21))
      | ~ is_fun_pname_bool(U_21) ),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

fof(f_27_3,plain,
    ! [U_21] :
      ( is_fun_pname_bool(collect_pname(U_21))
      | ~ is_fun_pname_bool(U_21) ),
    inference(definitional_conversion,[status(esa)],[f_27_2]) ).

cnf(f_27_4,plain,
    ( is_fun_pname_bool(collect_pname(U_21))
    | ~ is_fun_pname_bool(U_21) ),
    inference(clausify,[status(thm)],[f_27_3]) ).

fof(f_28_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_28_2,plain,
    ! [U_22] :
      ( is_fun949378684l_bool(collect_fun_a_bool(U_22))
      | ~ is_fun949378684l_bool(U_22) ),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

fof(f_28_3,plain,
    ! [U_22] :
      ( is_fun949378684l_bool(collect_fun_a_bool(U_22))
      | ~ is_fun949378684l_bool(U_22) ),
    inference(definitional_conversion,[status(esa)],[f_28_2]) ).

cnf(f_28_4,plain,
    ( is_fun949378684l_bool(collect_fun_a_bool(U_22))
    | ~ is_fun949378684l_bool(U_22) ),
    inference(clausify,[status(thm)],[f_28_3]) ).

fof(f_29_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_29_2,plain,
    ! [U_23] :
      ( is_fun1661590463l_bool(collec1974731493e_bool(U_23))
      | ~ is_fun1661590463l_bool(U_23) ),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

fof(f_29_3,plain,
    ! [U_23] :
      ( is_fun1661590463l_bool(collec1974731493e_bool(U_23))
      | ~ is_fun1661590463l_bool(U_23) ),
    inference(definitional_conversion,[status(esa)],[f_29_2]) ).

cnf(f_29_4,plain,
    ( is_fun1661590463l_bool(collec1974731493e_bool(U_23))
    | ~ is_fun1661590463l_bool(U_23) ),
    inference(clausify,[status(thm)],[f_29_3]) ).

fof(f_30_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_30_2,plain,
    ! [U_25,U_24] :
      ( is_fun_a_bool(image_a_a(U_25,U_24))
      | ~ is_fun_a_bool(U_24) ),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

fof(f_30_3,plain,
    ! [U_25,U_24] :
      ( is_fun_a_bool(image_a_a(U_25,U_24))
      | ~ is_fun_a_bool(U_24) ),
    inference(definitional_conversion,[status(esa)],[f_30_2]) ).

cnf(f_30_4,plain,
    ( is_fun_a_bool(image_a_a(U_25,U_24))
    | ~ is_fun_a_bool(U_24) ),
    inference(clausify,[status(thm)],[f_30_3]) ).

fof(f_31_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_31_2,plain,
    ! [U_27,U_26] :
      ( is_fun_pname_bool(image_a_pname(U_27,U_26))
      | ~ is_fun_a_bool(U_26) ),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

fof(f_31_3,plain,
    ! [U_27,U_26] :
      ( is_fun_pname_bool(image_a_pname(U_27,U_26))
      | ~ is_fun_a_bool(U_26) ),
    inference(definitional_conversion,[status(esa)],[f_31_2]) ).

cnf(f_31_4,plain,
    ( is_fun_pname_bool(image_a_pname(U_27,U_26))
    | ~ is_fun_a_bool(U_26) ),
    inference(clausify,[status(thm)],[f_31_3]) ).

fof(f_32_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_32_2,plain,
    ! [U_29,U_28] :
      ( is_fun949378684l_bool(image_a_fun_a_bool(U_29,U_28))
      | ~ is_fun_a_bool(U_28) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

fof(f_32_3,plain,
    ! [U_28,U_29] :
      ( is_fun949378684l_bool(image_a_fun_a_bool(U_29,U_28))
      | ~ is_fun_a_bool(U_28) ),
    inference(definitional_conversion,[status(esa)],[f_32_2]) ).

cnf(f_32_4,plain,
    ( is_fun949378684l_bool(image_a_fun_a_bool(U_29,U_28))
    | ~ is_fun_a_bool(U_28) ),
    inference(clausify,[status(thm)],[f_32_3]) ).

fof(f_33_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_33_2,plain,
    ! [U_31,U_30] :
      ( is_fun1661590463l_bool(image_819518260e_bool(U_31,U_30))
      | ~ is_fun_a_bool(U_30) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

fof(f_33_3,plain,
    ! [U_30,U_31] :
      ( is_fun1661590463l_bool(image_819518260e_bool(U_31,U_30))
      | ~ is_fun_a_bool(U_30) ),
    inference(definitional_conversion,[status(esa)],[f_33_2]) ).

cnf(f_33_4,plain,
    ( is_fun1661590463l_bool(image_819518260e_bool(U_31,U_30))
    | ~ is_fun_a_bool(U_30) ),
    inference(clausify,[status(thm)],[f_33_3]) ).

fof(f_34_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_34_2,plain,
    ! [U_33,U_32] :
      ( is_fun_a_bool(image_pname_a(U_33,U_32))
      | ~ is_fun_pname_bool(U_32) ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

fof(f_34_3,plain,
    ! [U_32,U_33] :
      ( is_fun_a_bool(image_pname_a(U_33,U_32))
      | ~ is_fun_pname_bool(U_32) ),
    inference(definitional_conversion,[status(esa)],[f_34_2]) ).

cnf(f_34_4,plain,
    ( is_fun_a_bool(image_pname_a(U_33,U_32))
    | ~ is_fun_pname_bool(U_32) ),
    inference(clausify,[status(thm)],[f_34_3]) ).

fof(f_35_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_35_2,plain,
    ! [U_35,U_34] :
      ( is_fun_pname_bool(image_pname_pname(U_35,U_34))
      | ~ is_fun_pname_bool(U_34) ),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

fof(f_35_3,plain,
    ! [U_34,U_35] :
      ( is_fun_pname_bool(image_pname_pname(U_35,U_34))
      | ~ is_fun_pname_bool(U_34) ),
    inference(definitional_conversion,[status(esa)],[f_35_2]) ).

cnf(f_35_4,plain,
    ( is_fun_pname_bool(image_pname_pname(U_35,U_34))
    | ~ is_fun_pname_bool(U_34) ),
    inference(clausify,[status(thm)],[f_35_3]) ).

fof(f_36_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_36_2,plain,
    ! [U_37,U_36] :
      ( is_fun949378684l_bool(image_112932426a_bool(U_37,U_36))
      | ~ is_fun_pname_bool(U_36) ),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

fof(f_36_3,plain,
    ! [U_36,U_37] :
      ( is_fun949378684l_bool(image_112932426a_bool(U_37,U_36))
      | ~ is_fun_pname_bool(U_36) ),
    inference(definitional_conversion,[status(esa)],[f_36_2]) ).

cnf(f_36_4,plain,
    ( is_fun949378684l_bool(image_112932426a_bool(U_37,U_36))
    | ~ is_fun_pname_bool(U_36) ),
    inference(clausify,[status(thm)],[f_36_3]) ).

fof(f_37_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_37_2,plain,
    ! [U_39,U_38] :
      ( is_fun1661590463l_bool(image_47868345e_bool(U_39,U_38))
      | ~ is_fun_pname_bool(U_38) ),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

fof(f_37_3,plain,
    ! [U_38,U_39] :
      ( is_fun1661590463l_bool(image_47868345e_bool(U_39,U_38))
      | ~ is_fun_pname_bool(U_38) ),
    inference(definitional_conversion,[status(esa)],[f_37_2]) ).

cnf(f_37_4,plain,
    ( is_fun1661590463l_bool(image_47868345e_bool(U_39,U_38))
    | ~ is_fun_pname_bool(U_38) ),
    inference(clausify,[status(thm)],[f_37_3]) ).

fof(f_38_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_38_2,plain,
    ! [U_41,U_40] : is_fun_a_bool(image_nat_a(U_41,U_40)),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

fof(f_38_3,plain,
    ! [U_40,U_41] : is_fun_a_bool(image_nat_a(U_41,U_40)),
    inference(definitional_conversion,[status(esa)],[f_38_2]) ).

cnf(f_38_4,plain,
    is_fun_a_bool(image_nat_a(U_41,U_40)),
    inference(clausify,[status(thm)],[f_38_3]) ).

fof(f_39_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_39_2,plain,
    ! [U_43,U_42] : is_fun_pname_bool(image_nat_pname(U_43,U_42)),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

fof(f_39_3,plain,
    ! [U_42,U_43] : is_fun_pname_bool(image_nat_pname(U_43,U_42)),
    inference(definitional_conversion,[status(esa)],[f_39_2]) ).

cnf(f_39_4,plain,
    is_fun_pname_bool(image_nat_pname(U_43,U_42)),
    inference(clausify,[status(thm)],[f_39_3]) ).

fof(f_40_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_40_2,plain,
    ! [U_45,U_44] : is_fun949378684l_bool(image_nat_fun_a_bool(U_45,U_44)),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

fof(f_40_3,plain,
    ! [U_44,U_45] : is_fun949378684l_bool(image_nat_fun_a_bool(U_45,U_44)),
    inference(definitional_conversion,[status(esa)],[f_40_2]) ).

cnf(f_40_4,plain,
    is_fun949378684l_bool(image_nat_fun_a_bool(U_45,U_44)),
    inference(clausify,[status(thm)],[f_40_3]) ).

fof(f_41_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_41_2,plain,
    ! [U_47,U_46] : is_fun1661590463l_bool(image_1655916159e_bool(U_47,U_46)),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

fof(f_41_3,plain,
    ! [U_46,U_47] : is_fun1661590463l_bool(image_1655916159e_bool(U_47,U_46)),
    inference(definitional_conversion,[status(esa)],[f_41_2]) ).

cnf(f_41_4,plain,
    is_fun1661590463l_bool(image_1655916159e_bool(U_47,U_46)),
    inference(clausify,[status(thm)],[f_41_3]) ).

fof(f_42_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_42_2,plain,
    ! [U_49,U_48] :
      ( is_fun_a_bool(image_fun_a_bool_a(U_49,U_48))
      | ~ is_fun949378684l_bool(U_48) ),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

fof(f_42_3,plain,
    ! [U_48,U_49] :
      ( is_fun_a_bool(image_fun_a_bool_a(U_49,U_48))
      | ~ is_fun949378684l_bool(U_48) ),
    inference(definitional_conversion,[status(esa)],[f_42_2]) ).

cnf(f_42_4,plain,
    ( is_fun_a_bool(image_fun_a_bool_a(U_49,U_48))
    | ~ is_fun949378684l_bool(U_48) ),
    inference(clausify,[status(thm)],[f_42_3]) ).

fof(f_43_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_43_2,plain,
    ! [U_51,U_50] :
      ( is_fun_pname_bool(image_1854862208_pname(U_51,U_50))
      | ~ is_fun949378684l_bool(U_50) ),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

fof(f_43_3,plain,
    ! [U_50,U_51] :
      ( is_fun_pname_bool(image_1854862208_pname(U_51,U_50))
      | ~ is_fun949378684l_bool(U_50) ),
    inference(definitional_conversion,[status(esa)],[f_43_2]) ).

cnf(f_43_4,plain,
    ( is_fun_pname_bool(image_1854862208_pname(U_51,U_50))
    | ~ is_fun949378684l_bool(U_50) ),
    inference(clausify,[status(thm)],[f_43_3]) ).

fof(f_44_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_44_2,plain,
    ! [U_53,U_52] :
      ( is_fun_a_bool(image_876012084bool_a(U_53,U_52))
      | ~ is_fun1661590463l_bool(U_52) ),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

fof(f_44_3,plain,
    ! [U_52,U_53] :
      ( is_fun_a_bool(image_876012084bool_a(U_53,U_52))
      | ~ is_fun1661590463l_bool(U_52) ),
    inference(definitional_conversion,[status(esa)],[f_44_2]) ).

cnf(f_44_4,plain,
    ( is_fun_a_bool(image_876012084bool_a(U_53,U_52))
    | ~ is_fun1661590463l_bool(U_52) ),
    inference(clausify,[status(thm)],[f_44_3]) ).

fof(f_45_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_45_2,plain,
    ! [U_55,U_54] :
      ( is_fun_pname_bool(image_1283814551_pname(U_55,U_54))
      | ~ is_fun1661590463l_bool(U_54) ),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

fof(f_45_3,plain,
    ! [U_54,U_55] :
      ( is_fun_pname_bool(image_1283814551_pname(U_55,U_54))
      | ~ is_fun1661590463l_bool(U_54) ),
    inference(definitional_conversion,[status(esa)],[f_45_2]) ).

cnf(f_45_4,plain,
    ( is_fun_pname_bool(image_1283814551_pname(U_55,U_54))
    | ~ is_fun1661590463l_bool(U_54) ),
    inference(clausify,[status(thm)],[f_45_3]) ).

fof(f_46_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_46_2,plain,
    ! [U_57,U_56] : is_fun_a_bool(image_fun_nat_bool_a(U_57,U_56)),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

fof(f_46_3,plain,
    ! [U_56,U_57] : is_fun_a_bool(image_fun_nat_bool_a(U_57,U_56)),
    inference(definitional_conversion,[status(esa)],[f_46_2]) ).

cnf(f_46_4,plain,
    is_fun_a_bool(image_fun_nat_bool_a(U_57,U_56)),
    inference(clausify,[status(thm)],[f_46_3]) ).

fof(f_47_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_47_2,plain,
    ! [U_59,U_58] : is_fun_pname_bool(image_1921560913_pname(U_59,U_58)),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

fof(f_47_3,plain,
    ! [U_58,U_59] : is_fun_pname_bool(image_1921560913_pname(U_59,U_58)),
    inference(definitional_conversion,[status(esa)],[f_47_2]) ).

cnf(f_47_4,plain,
    is_fun_pname_bool(image_1921560913_pname(U_59,U_58)),
    inference(clausify,[status(thm)],[f_47_3]) ).

fof(f_48_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(insert_a(B_1_1,B_2_1))
      | ~ is_fun_a_bool(B_2_1)
      | ~ is_a(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000t__a]) ).

fof(f_48_2,plain,
    ! [U_61,U_60] :
      ( is_fun_a_bool(insert_a(U_61,U_60))
      | ~ is_fun_a_bool(U_60)
      | ~ is_a(U_61) ),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

fof(f_48_3,plain,
    ! [U_61,U_60] :
      ( is_fun_a_bool(insert_a(U_61,U_60))
      | ~ is_fun_a_bool(U_60)
      | ~ is_a(U_61) ),
    inference(definitional_conversion,[status(esa)],[f_48_2]) ).

cnf(f_48_4,plain,
    ( is_fun_a_bool(insert_a(U_61,U_60))
    | ~ is_fun_a_bool(U_60)
    | ~ is_a(U_61) ),
    inference(clausify,[status(thm)],[f_48_3]) ).

fof(f_49_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(insert_pname(B_1_1,B_2_1))
      | ~ is_fun_pname_bool(B_2_1)
      | ~ is_pname(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000tc__Com__Opname]) ).

fof(f_49_2,plain,
    ! [U_63,U_62] :
      ( is_fun_pname_bool(insert_pname(U_63,U_62))
      | ~ is_fun_pname_bool(U_62)
      | ~ is_pname(U_63) ),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

fof(f_49_3,plain,
    ! [U_63,U_62] :
      ( is_fun_pname_bool(insert_pname(U_63,U_62))
      | ~ is_fun_pname_bool(U_62)
      | ~ is_pname(U_63) ),
    inference(definitional_conversion,[status(esa)],[f_49_2]) ).

cnf(f_49_4,plain,
    ( is_fun_pname_bool(insert_pname(U_63,U_62))
    | ~ is_fun_pname_bool(U_62)
    | ~ is_pname(U_63) ),
    inference(clausify,[status(thm)],[f_49_3]) ).

fof(f_50_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun949378684l_bool(insert_fun_a_bool(B_1_1,B_2_1))
      | ~ is_fun949378684l_bool(B_2_1)
      | ~ is_fun_a_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_50_2,plain,
    ! [U_65,U_64] :
      ( is_fun949378684l_bool(insert_fun_a_bool(U_65,U_64))
      | ~ is_fun949378684l_bool(U_64)
      | ~ is_fun_a_bool(U_65) ),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

fof(f_50_3,plain,
    ! [U_64,U_65] :
      ( is_fun949378684l_bool(insert_fun_a_bool(U_65,U_64))
      | ~ is_fun949378684l_bool(U_64)
      | ~ is_fun_a_bool(U_65) ),
    inference(definitional_conversion,[status(esa)],[f_50_2]) ).

cnf(f_50_4,plain,
    ( is_fun949378684l_bool(insert_fun_a_bool(U_65,U_64))
    | ~ is_fun949378684l_bool(U_64)
    | ~ is_fun_a_bool(U_65) ),
    inference(clausify,[status(thm)],[f_50_3]) ).

fof(f_51_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1661590463l_bool(insert1325755072e_bool(B_1_1,B_2_1))
      | ~ is_fun1661590463l_bool(B_2_1)
      | ~ is_fun_pname_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_51_2,plain,
    ! [U_67,U_66] :
      ( is_fun1661590463l_bool(insert1325755072e_bool(U_67,U_66))
      | ~ is_fun1661590463l_bool(U_66)
      | ~ is_fun_pname_bool(U_67) ),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

fof(f_51_3,plain,
    ! [U_67,U_66] :
      ( is_fun1661590463l_bool(insert1325755072e_bool(U_67,U_66))
      | ~ is_fun1661590463l_bool(U_66)
      | ~ is_fun_pname_bool(U_67) ),
    inference(definitional_conversion,[status(esa)],[f_51_2]) ).

cnf(f_51_4,plain,
    ( is_fun1661590463l_bool(insert1325755072e_bool(U_67,U_66))
    | ~ is_fun1661590463l_bool(U_66)
    | ~ is_fun_pname_bool(U_67) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

fof(f_52_1,plain,
    is_bool(fFalse),
    inference(fof_nnf,[status(thm)],[gsy_c_fFalse]) ).

fof(f_52_2,plain,
    is_bool(fFalse),
    inference(definitional_conversion,[status(esa)],[f_52_1]) ).

cnf(f_52_3,plain,
    is_bool(fFalse),
    inference(clausify,[status(thm)],[f_52_2]) ).

fof(f_53_1,plain,
    is_bool(fTrue),
    inference(fof_nnf,[status(thm)],[gsy_c_fTrue]) ).

fof(f_53_2,plain,
    is_bool(fTrue),
    inference(definitional_conversion,[status(esa)],[f_53_1]) ).

cnf(f_53_3,plain,
    is_bool(fTrue),
    inference(clausify,[status(thm)],[f_53_2]) ).

fof(f_54_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_54_2,plain,
    ! [U_69,U_68] :
      ( is_a(hAPP_a_a(U_69,U_68))
      | ~ is_a(U_68) ),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

fof(f_54_3,plain,
    ! [U_69,U_68] :
      ( is_a(hAPP_a_a(U_69,U_68))
      | ~ is_a(U_68) ),
    inference(definitional_conversion,[status(esa)],[f_54_2]) ).

cnf(f_54_4,plain,
    ( is_a(hAPP_a_a(U_69,U_68))
    | ~ is_a(U_68) ),
    inference(clausify,[status(thm)],[f_54_3]) ).

fof(f_55_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_pname(hAPP_a_pname(B_1_1,B_2_1))
      | ~ is_a(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__Com__Opname]) ).

fof(f_55_2,plain,
    ! [U_71,U_70] :
      ( is_pname(hAPP_a_pname(U_71,U_70))
      | ~ is_a(U_70) ),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

fof(f_55_3,plain,
    ! [U_71,U_70] :
      ( is_pname(hAPP_a_pname(U_71,U_70))
      | ~ is_a(U_70) ),
    inference(definitional_conversion,[status(esa)],[f_55_2]) ).

cnf(f_55_4,plain,
    ( is_pname(hAPP_a_pname(U_71,U_70))
    | ~ is_a(U_70) ),
    inference(clausify,[status(thm)],[f_55_3]) ).

fof(f_56_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_56_2,plain,
    ! [U_73,U_72] :
      ( is_bool(hAPP_a_bool(U_73,U_72))
      | ~ is_a(U_72)
      | ~ is_fun_a_bool(U_73) ),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

fof(f_56_3,plain,
    ! [U_73,U_72] :
      ( is_bool(hAPP_a_bool(U_73,U_72))
      | ~ is_a(U_72)
      | ~ is_fun_a_bool(U_73) ),
    inference(definitional_conversion,[status(esa)],[f_56_2]) ).

cnf(f_56_4,plain,
    ( is_bool(hAPP_a_bool(U_73,U_72))
    | ~ is_a(U_72)
    | ~ is_fun_a_bool(U_73) ),
    inference(clausify,[status(thm)],[f_56_3]) ).

fof(f_57_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_57_2,plain,
    ! [U_75,U_74] :
      ( is_fun_a_bool(hAPP_a_fun_a_bool(U_75,U_74))
      | ~ is_a(U_74) ),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

fof(f_57_3,plain,
    ! [U_75,U_74] :
      ( is_fun_a_bool(hAPP_a_fun_a_bool(U_75,U_74))
      | ~ is_a(U_74) ),
    inference(definitional_conversion,[status(esa)],[f_57_2]) ).

cnf(f_57_4,plain,
    ( is_fun_a_bool(hAPP_a_fun_a_bool(U_75,U_74))
    | ~ is_a(U_74) ),
    inference(clausify,[status(thm)],[f_57_3]) ).

fof(f_58_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_58_2,plain,
    ! [U_77,U_76] :
      ( is_fun_pname_bool(hAPP_a93125764e_bool(U_77,U_76))
      | ~ is_a(U_76) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

fof(f_58_3,plain,
    ! [U_76,U_77] :
      ( is_fun_pname_bool(hAPP_a93125764e_bool(U_77,U_76))
      | ~ is_a(U_76) ),
    inference(definitional_conversion,[status(esa)],[f_58_2]) ).

cnf(f_58_4,plain,
    ( is_fun_pname_bool(hAPP_a93125764e_bool(U_77,U_76))
    | ~ is_a(U_76) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

fof(f_59_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_59_2,plain,
    ! [U_79,U_78] :
      ( is_fun949378684l_bool(hAPP_a85458249l_bool(U_79,U_78))
      | ~ is_a(U_78) ),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

fof(f_59_3,plain,
    ! [U_78,U_79] :
      ( is_fun949378684l_bool(hAPP_a85458249l_bool(U_79,U_78))
      | ~ is_a(U_78) ),
    inference(definitional_conversion,[status(esa)],[f_59_2]) ).

cnf(f_59_4,plain,
    ( is_fun949378684l_bool(hAPP_a85458249l_bool(U_79,U_78))
    | ~ is_a(U_78) ),
    inference(clausify,[status(thm)],[f_59_3]) ).

fof(f_60_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1661590463l_bool(hAPP_a217006258l_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_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H]) ).

fof(f_60_2,plain,
    ! [U_81,U_80] :
      ( is_fun1661590463l_bool(hAPP_a217006258l_bool(U_81,U_80))
      | ~ is_a(U_80) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

fof(f_60_3,plain,
    ! [U_80,U_81] :
      ( is_fun1661590463l_bool(hAPP_a217006258l_bool(U_81,U_80))
      | ~ is_a(U_80) ),
    inference(definitional_conversion,[status(esa)],[f_60_2]) ).

cnf(f_60_4,plain,
    ( is_fun1661590463l_bool(hAPP_a217006258l_bool(U_81,U_80))
    | ~ is_a(U_80) ),
    inference(clausify,[status(thm)],[f_60_3]) ).

fof(f_61_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_61_2,plain,
    ! [U_83,U_82] :
      ( is_a(hAPP_pname_a(U_83,U_82))
      | ~ is_pname(U_82) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

fof(f_61_3,plain,
    ! [U_83,U_82] :
      ( is_a(hAPP_pname_a(U_83,U_82))
      | ~ is_pname(U_82) ),
    inference(definitional_conversion,[status(esa)],[f_61_2]) ).

cnf(f_61_4,plain,
    ( is_a(hAPP_pname_a(U_83,U_82))
    | ~ is_pname(U_82) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

fof(f_62_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_62_2,plain,
    ! [U_85,U_84] :
      ( is_pname(hAPP_pname_pname(U_85,U_84))
      | ~ is_pname(U_84) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

fof(f_62_3,plain,
    ! [U_84,U_85] :
      ( is_pname(hAPP_pname_pname(U_85,U_84))
      | ~ is_pname(U_84) ),
    inference(definitional_conversion,[status(esa)],[f_62_2]) ).

cnf(f_62_4,plain,
    ( is_pname(hAPP_pname_pname(U_85,U_84))
    | ~ is_pname(U_84) ),
    inference(clausify,[status(thm)],[f_62_3]) ).

fof(f_63_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_63_2,plain,
    ! [U_87,U_86] :
      ( is_bool(hAPP_pname_bool(U_87,U_86))
      | ~ is_pname(U_86)
      | ~ is_fun_pname_bool(U_87) ),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

fof(f_63_3,plain,
    ! [U_86,U_87] :
      ( is_bool(hAPP_pname_bool(U_87,U_86))
      | ~ is_pname(U_86)
      | ~ is_fun_pname_bool(U_87) ),
    inference(definitional_conversion,[status(esa)],[f_63_2]) ).

cnf(f_63_4,plain,
    ( is_bool(hAPP_pname_bool(U_87,U_86))
    | ~ is_pname(U_86)
    | ~ is_fun_pname_bool(U_87) ),
    inference(clausify,[status(thm)],[f_63_3]) ).

fof(f_64_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_64_2,plain,
    ! [U_89,U_88] :
      ( is_fun_a_bool(hAPP_p1534023578a_bool(U_89,U_88))
      | ~ is_pname(U_88) ),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

fof(f_64_3,plain,
    ! [U_88,U_89] :
      ( is_fun_a_bool(hAPP_p1534023578a_bool(U_89,U_88))
      | ~ is_pname(U_88) ),
    inference(definitional_conversion,[status(esa)],[f_64_2]) ).

cnf(f_64_4,plain,
    ( is_fun_a_bool(hAPP_p1534023578a_bool(U_89,U_88))
    | ~ is_pname(U_88) ),
    inference(clausify,[status(thm)],[f_64_3]) ).

fof(f_65_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_65_2,plain,
    ! [U_91,U_90] :
      ( is_fun_pname_bool(hAPP_p61793385e_bool(U_91,U_90))
      | ~ is_pname(U_90) ),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

fof(f_65_3,plain,
    ! [U_90,U_91] :
      ( is_fun_pname_bool(hAPP_p61793385e_bool(U_91,U_90))
      | ~ is_pname(U_90) ),
    inference(definitional_conversion,[status(esa)],[f_65_2]) ).

cnf(f_65_4,plain,
    ( is_fun_pname_bool(hAPP_p61793385e_bool(U_91,U_90))
    | ~ is_pname(U_90) ),
    inference(clausify,[status(thm)],[f_65_3]) ).

fof(f_66_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun949378684l_bool(hAPP_p1824510254l_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_It__a_Mtc__HOL__Obool_J_Mtc__H]) ).

fof(f_66_2,plain,
    ! [U_93,U_92] :
      ( is_fun949378684l_bool(hAPP_p1824510254l_bool(U_93,U_92))
      | ~ is_pname(U_92) ),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

fof(f_66_3,plain,
    ! [U_93,U_92] :
      ( is_fun949378684l_bool(hAPP_p1824510254l_bool(U_93,U_92))
      | ~ is_pname(U_92) ),
    inference(definitional_conversion,[status(esa)],[f_66_2]) ).

cnf(f_66_4,plain,
    ( is_fun949378684l_bool(hAPP_p1824510254l_bool(U_93,U_92))
    | ~ is_pname(U_92) ),
    inference(clausify,[status(thm)],[f_66_3]) ).

fof(f_67_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_67_2,plain,
    ! [U_95,U_94] :
      ( is_fun1661590463l_bool(hAPP_p338031245l_bool(U_95,U_94))
      | ~ is_pname(U_94) ),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

fof(f_67_3,plain,
    ! [U_94,U_95] :
      ( is_fun1661590463l_bool(hAPP_p338031245l_bool(U_95,U_94))
      | ~ is_pname(U_94) ),
    inference(definitional_conversion,[status(esa)],[f_67_2]) ).

cnf(f_67_4,plain,
    ( is_fun1661590463l_bool(hAPP_p338031245l_bool(U_95,U_94))
    | ~ is_pname(U_94) ),
    inference(clausify,[status(thm)],[f_67_3]) ).

fof(f_68_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_68_2,plain,
    ! [U_97,U_96] :
      ( is_bool(hAPP_bool_bool(U_97,U_96))
      | ~ is_bool(U_96) ),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

fof(f_68_3,plain,
    ! [U_96,U_97] :
      ( is_bool(hAPP_bool_bool(U_97,U_96))
      | ~ is_bool(U_96) ),
    inference(definitional_conversion,[status(esa)],[f_68_2]) ).

cnf(f_68_4,plain,
    ( is_bool(hAPP_bool_bool(U_97,U_96))
    | ~ is_bool(U_96) ),
    inference(clausify,[status(thm)],[f_68_3]) ).

fof(f_69_1,plain,
    ! [B_1_1,B_2_1] : is_a(hAPP_nat_a(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000t__a]) ).

fof(f_69_2,plain,
    ! [U_99,U_98] : is_a(hAPP_nat_a(U_99,U_98)),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

fof(f_69_3,plain,
    ! [U_98,U_99] : is_a(hAPP_nat_a(U_99,U_98)),
    inference(definitional_conversion,[status(esa)],[f_69_2]) ).

cnf(f_69_4,plain,
    is_a(hAPP_nat_a(U_99,U_98)),
    inference(clausify,[status(thm)],[f_69_3]) ).

fof(f_70_1,plain,
    ! [B_1_1,B_2_1] : is_pname(hAPP_nat_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Com__Opname]) ).

fof(f_70_2,plain,
    ! [U_101,U_100] : is_pname(hAPP_nat_pname(U_101,U_100)),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

fof(f_70_3,plain,
    ! [U_100,U_101] : is_pname(hAPP_nat_pname(U_101,U_100)),
    inference(definitional_conversion,[status(esa)],[f_70_2]) ).

cnf(f_70_4,plain,
    is_pname(hAPP_nat_pname(U_101,U_100)),
    inference(clausify,[status(thm)],[f_70_3]) ).

fof(f_71_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_71_2,plain,
    ! [U_103,U_102] : is_bool(hAPP_nat_bool(U_103,U_102)),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

fof(f_71_3,plain,
    ! [U_102,U_103] : is_bool(hAPP_nat_bool(U_103,U_102)),
    inference(definitional_conversion,[status(esa)],[f_71_2]) ).

cnf(f_71_4,plain,
    is_bool(hAPP_nat_bool(U_103,U_102)),
    inference(clausify,[status(thm)],[f_71_3]) ).

fof(f_72_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_72_2,plain,
    ! [U_105,U_104] : is_fun_a_bool(hAPP_nat_fun_a_bool(U_105,U_104)),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

fof(f_72_3,plain,
    ! [U_104,U_105] : is_fun_a_bool(hAPP_nat_fun_a_bool(U_105,U_104)),
    inference(definitional_conversion,[status(esa)],[f_72_2]) ).

cnf(f_72_4,plain,
    is_fun_a_bool(hAPP_nat_fun_a_bool(U_105,U_104)),
    inference(clausify,[status(thm)],[f_72_3]) ).

fof(f_73_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_73_2,plain,
    ! [U_107,U_106] : is_fun_pname_bool(hAPP_n1025906991e_bool(U_107,U_106)),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

fof(f_73_3,plain,
    ! [U_106,U_107] : is_fun_pname_bool(hAPP_n1025906991e_bool(U_107,U_106)),
    inference(definitional_conversion,[status(esa)],[f_73_2]) ).

cnf(f_73_4,plain,
    is_fun_pname_bool(hAPP_n1025906991e_bool(U_107,U_106)),
    inference(clausify,[status(thm)],[f_73_3]) ).

fof(f_74_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_74_2,plain,
    ! [U_109,U_108] : is_fun949378684l_bool(hAPP_n1414589940l_bool(U_109,U_108)),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

fof(f_74_3,plain,
    ! [U_108,U_109] : is_fun949378684l_bool(hAPP_n1414589940l_bool(U_109,U_108)),
    inference(definitional_conversion,[status(esa)],[f_74_2]) ).

cnf(f_74_4,plain,
    is_fun949378684l_bool(hAPP_n1414589940l_bool(U_109,U_108)),
    inference(clausify,[status(thm)],[f_74_3]) ).

fof(f_75_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_75_2,plain,
    ! [U_111,U_110] : is_fun1661590463l_bool(hAPP_n850744903l_bool(U_111,U_110)),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

fof(f_75_3,plain,
    ! [U_110,U_111] : is_fun1661590463l_bool(hAPP_n850744903l_bool(U_111,U_110)),
    inference(definitional_conversion,[status(esa)],[f_75_2]) ).

cnf(f_75_4,plain,
    is_fun1661590463l_bool(hAPP_n850744903l_bool(U_111,U_110)),
    inference(clausify,[status(thm)],[f_75_3]) ).

fof(f_76_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_pname(hAPP_f1128469712_pname(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__Com__Opname]) ).

fof(f_76_2,plain,
    ! [U_113,U_112] :
      ( is_pname(hAPP_f1128469712_pname(U_113,U_112))
      | ~ is_fun_a_bool(U_112) ),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

fof(f_76_3,plain,
    ! [U_112,U_113] :
      ( is_pname(hAPP_f1128469712_pname(U_113,U_112))
      | ~ is_fun_a_bool(U_112) ),
    inference(definitional_conversion,[status(esa)],[f_76_2]) ).

cnf(f_76_4,plain,
    ( is_pname(hAPP_f1128469712_pname(U_113,U_112))
    | ~ is_fun_a_bool(U_112) ),
    inference(clausify,[status(thm)],[f_76_3]) ).

fof(f_77_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_77_2,plain,
    ! [U_115,U_114] :
      ( is_bool(hAPP_fun_a_bool_bool(U_115,U_114))
      | ~ is_fun_a_bool(U_114)
      | ~ is_fun949378684l_bool(U_115) ),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ! [U_114,U_115] :
      ( is_bool(hAPP_fun_a_bool_bool(U_115,U_114))
      | ~ is_fun_a_bool(U_114)
      | ~ is_fun949378684l_bool(U_115) ),
    inference(definitional_conversion,[status(esa)],[f_77_2]) ).

cnf(f_77_4,plain,
    ( is_bool(hAPP_fun_a_bool_bool(U_115,U_114))
    | ~ is_fun_a_bool(U_114)
    | ~ is_fun949378684l_bool(U_115) ),
    inference(clausify,[status(thm)],[f_77_3]) ).

fof(f_78_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_78_2,plain,
    ! [U_117,U_116] :
      ( is_fun_a_bool(hAPP_f2050579477a_bool(U_117,U_116))
      | ~ is_fun_a_bool(U_116) ),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

fof(f_78_3,plain,
    ! [U_117,U_116] :
      ( is_fun_a_bool(hAPP_f2050579477a_bool(U_117,U_116))
      | ~ is_fun_a_bool(U_116) ),
    inference(definitional_conversion,[status(esa)],[f_78_2]) ).

cnf(f_78_4,plain,
    ( is_fun_a_bool(hAPP_f2050579477a_bool(U_117,U_116))
    | ~ is_fun_a_bool(U_116) ),
    inference(clausify,[status(thm)],[f_78_3]) ).

fof(f_79_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(hAPP_f1794073134e_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__Com__Opname_Mtc__H]) ).

fof(f_79_2,plain,
    ! [U_119,U_118] :
      ( is_fun_pname_bool(hAPP_f1794073134e_bool(U_119,U_118))
      | ~ is_fun_a_bool(U_118) ),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

fof(f_79_3,plain,
    ! [U_118,U_119] :
      ( is_fun_pname_bool(hAPP_f1794073134e_bool(U_119,U_118))
      | ~ is_fun_a_bool(U_118) ),
    inference(definitional_conversion,[status(esa)],[f_79_2]) ).

cnf(f_79_4,plain,
    ( is_fun_pname_bool(hAPP_f1794073134e_bool(U_119,U_118))
    | ~ is_fun_a_bool(U_118) ),
    inference(clausify,[status(thm)],[f_79_3]) ).

fof(f_80_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_80_2,plain,
    ! [U_121,U_120] :
      ( is_fun949378684l_bool(hAPP_f1631501043l_bool(U_121,U_120))
      | ~ is_fun_a_bool(U_120) ),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

fof(f_80_3,plain,
    ! [U_120,U_121] :
      ( is_fun949378684l_bool(hAPP_f1631501043l_bool(U_121,U_120))
      | ~ is_fun_a_bool(U_120) ),
    inference(definitional_conversion,[status(esa)],[f_80_2]) ).

cnf(f_80_4,plain,
    ( is_fun949378684l_bool(hAPP_f1631501043l_bool(U_121,U_120))
    | ~ is_fun_a_bool(U_120) ),
    inference(clausify,[status(thm)],[f_80_3]) ).

fof(f_81_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_81_2,plain,
    ! [U_123,U_122] :
      ( is_pname(hAPP_f1297739591_pname(U_123,U_122))
      | ~ is_fun_pname_bool(U_122) ),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

fof(f_81_3,plain,
    ! [U_122,U_123] :
      ( is_pname(hAPP_f1297739591_pname(U_123,U_122))
      | ~ is_fun_pname_bool(U_122) ),
    inference(definitional_conversion,[status(esa)],[f_81_2]) ).

cnf(f_81_4,plain,
    ( is_pname(hAPP_f1297739591_pname(U_123,U_122))
    | ~ is_fun_pname_bool(U_122) ),
    inference(clausify,[status(thm)],[f_81_3]) ).

fof(f_82_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_82_2,plain,
    ! [U_125,U_124] :
      ( is_bool(hAPP_f1664156314l_bool(U_125,U_124))
      | ~ is_fun_pname_bool(U_124)
      | ~ is_fun1661590463l_bool(U_125) ),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

fof(f_82_3,plain,
    ! [U_124,U_125] :
      ( is_bool(hAPP_f1664156314l_bool(U_125,U_124))
      | ~ is_fun_pname_bool(U_124)
      | ~ is_fun1661590463l_bool(U_125) ),
    inference(definitional_conversion,[status(esa)],[f_82_2]) ).

cnf(f_82_4,plain,
    ( is_bool(hAPP_f1664156314l_bool(U_125,U_124))
    | ~ is_fun_pname_bool(U_124)
    | ~ is_fun1661590463l_bool(U_125) ),
    inference(clausify,[status(thm)],[f_82_3]) ).

fof(f_83_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(hAPP_f1051908748a_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_It__a_Mtc__H]) ).

fof(f_83_2,plain,
    ! [U_127,U_126] :
      ( is_fun_a_bool(hAPP_f1051908748a_bool(U_127,U_126))
      | ~ is_fun_pname_bool(U_126) ),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

fof(f_83_3,plain,
    ! [U_127,U_126] :
      ( is_fun_a_bool(hAPP_f1051908748a_bool(U_127,U_126))
      | ~ is_fun_pname_bool(U_126) ),
    inference(definitional_conversion,[status(esa)],[f_83_2]) ).

cnf(f_83_4,plain,
    ( is_fun_a_bool(hAPP_f1051908748a_bool(U_127,U_126))
    | ~ is_fun_pname_bool(U_126) ),
    inference(clausify,[status(thm)],[f_83_3]) ).

fof(f_84_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_84_2,plain,
    ! [U_129,U_128] :
      ( is_fun_pname_bool(hAPP_f759274231e_bool(U_129,U_128))
      | ~ is_fun_pname_bool(U_128) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

fof(f_84_3,plain,
    ! [U_128,U_129] :
      ( is_fun_pname_bool(hAPP_f759274231e_bool(U_129,U_128))
      | ~ is_fun_pname_bool(U_128) ),
    inference(definitional_conversion,[status(esa)],[f_84_2]) ).

cnf(f_84_4,plain,
    ( is_fun_pname_bool(hAPP_f759274231e_bool(U_129,U_128))
    | ~ is_fun_pname_bool(U_128) ),
    inference(clausify,[status(thm)],[f_84_3]) ).

fof(f_85_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_85_2,plain,
    ! [U_131,U_130] :
      ( is_fun1661590463l_bool(hAPP_f434788991l_bool(U_131,U_130))
      | ~ is_fun_pname_bool(U_130) ),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

fof(f_85_3,plain,
    ! [U_130,U_131] :
      ( is_fun1661590463l_bool(hAPP_f434788991l_bool(U_131,U_130))
      | ~ is_fun_pname_bool(U_130) ),
    inference(definitional_conversion,[status(esa)],[f_85_2]) ).

cnf(f_85_4,plain,
    ( is_fun1661590463l_bool(hAPP_f434788991l_bool(U_131,U_130))
    | ~ is_fun_pname_bool(U_130) ),
    inference(clausify,[status(thm)],[f_85_3]) ).

fof(f_86_1,plain,
    ! [B_1_1,B_2_1] : is_pname(hAPP_f1291551745_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname]) ).

fof(f_86_2,plain,
    ! [U_133,U_132] : is_pname(hAPP_f1291551745_pname(U_133,U_132)),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

fof(f_86_3,plain,
    ! [U_132,U_133] : is_pname(hAPP_f1291551745_pname(U_133,U_132)),
    inference(definitional_conversion,[status(esa)],[f_86_2]) ).

cnf(f_86_4,plain,
    is_pname(hAPP_f1291551745_pname(U_133,U_132)),
    inference(clausify,[status(thm)],[f_86_3]) ).

fof(f_87_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_87_2,plain,
    ! [U_135,U_134] : is_bool(hAPP_f54304608l_bool(U_135,U_134)),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

fof(f_87_3,plain,
    ! [U_134,U_135] : is_bool(hAPP_f54304608l_bool(U_135,U_134)),
    inference(definitional_conversion,[status(esa)],[f_87_2]) ).

cnf(f_87_4,plain,
    is_bool(hAPP_f54304608l_bool(U_135,U_134)),
    inference(clausify,[status(thm)],[f_87_3]) ).

fof(f_88_1,plain,
    ! [B_1_1,B_2_1] : is_fun_a_bool(hAPP_f1549043526a_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__fun_It__a_Mtc__HOL]) ).

fof(f_88_2,plain,
    ! [U_137,U_136] : is_fun_a_bool(hAPP_f1549043526a_bool(U_137,U_136)),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

fof(f_88_3,plain,
    ! [U_136,U_137] : is_fun_a_bool(hAPP_f1549043526a_bool(U_137,U_136)),
    inference(definitional_conversion,[status(esa)],[f_88_2]) ).

cnf(f_88_4,plain,
    is_fun_a_bool(hAPP_f1549043526a_bool(U_137,U_136)),
    inference(clausify,[status(thm)],[f_88_3]) ).

fof(f_89_1,plain,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_f654413245e_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__fun_Itc__Com__Opna]) ).

fof(f_89_2,plain,
    ! [U_139,U_138] : is_fun_pname_bool(hAPP_f654413245e_bool(U_139,U_138)),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

fof(f_89_3,plain,
    ! [U_138,U_139] : is_fun_pname_bool(hAPP_f654413245e_bool(U_139,U_138)),
    inference(definitional_conversion,[status(esa)],[f_89_2]) ).

cnf(f_89_4,plain,
    is_fun_pname_bool(hAPP_f654413245e_bool(U_139,U_138)),
    inference(clausify,[status(thm)],[f_89_3]) ).

fof(f_90_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_90_2,plain,
    ! [U_141,U_140] :
      ( is_bool(hAPP_f621171935l_bool(U_141,U_140))
      | ~ is_fun949378684l_bool(U_140) ),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

fof(f_90_3,plain,
    ! [U_140,U_141] :
      ( is_bool(hAPP_f621171935l_bool(U_141,U_140))
      | ~ is_fun949378684l_bool(U_140) ),
    inference(definitional_conversion,[status(esa)],[f_90_2]) ).

cnf(f_90_4,plain,
    ( is_bool(hAPP_f621171935l_bool(U_141,U_140))
    | ~ is_fun949378684l_bool(U_140) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

fof(f_91_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_91_2,plain,
    ! [U_143,U_142] :
      ( is_fun949378684l_bool(hAPP_f2117159681l_bool(U_143,U_142))
      | ~ is_fun949378684l_bool(U_142) ),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

fof(f_91_3,plain,
    ! [U_142,U_143] :
      ( is_fun949378684l_bool(hAPP_f2117159681l_bool(U_143,U_142))
      | ~ is_fun949378684l_bool(U_142) ),
    inference(definitional_conversion,[status(esa)],[f_91_2]) ).

cnf(f_91_4,plain,
    ( is_fun949378684l_bool(hAPP_f2117159681l_bool(U_143,U_142))
    | ~ is_fun949378684l_bool(U_142) ),
    inference(clausify,[status(thm)],[f_91_3]) ).

fof(f_92_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_92_2,plain,
    ! [U_145,U_144] :
      ( is_bool(hAPP_f1935102916l_bool(U_145,U_144))
      | ~ is_fun1661590463l_bool(U_144) ),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

fof(f_92_3,plain,
    ! [U_144,U_145] :
      ( is_bool(hAPP_f1935102916l_bool(U_145,U_144))
      | ~ is_fun1661590463l_bool(U_144) ),
    inference(definitional_conversion,[status(esa)],[f_92_2]) ).

cnf(f_92_4,plain,
    ( is_bool(hAPP_f1935102916l_bool(U_145,U_144))
    | ~ is_fun1661590463l_bool(U_144) ),
    inference(clausify,[status(thm)],[f_92_3]) ).

fof(f_93_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_93_2,plain,
    ! [U_147,U_146] :
      ( is_fun1661590463l_bool(hAPP_f559147733l_bool(U_147,U_146))
      | ~ is_fun1661590463l_bool(U_146) ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

fof(f_93_3,plain,
    ! [U_146,U_147] :
      ( is_fun1661590463l_bool(hAPP_f559147733l_bool(U_147,U_146))
      | ~ is_fun1661590463l_bool(U_146) ),
    inference(definitional_conversion,[status(esa)],[f_93_2]) ).

cnf(f_93_4,plain,
    ( is_fun1661590463l_bool(hAPP_f559147733l_bool(U_147,U_146))
    | ~ is_fun1661590463l_bool(U_146) ),
    inference(clausify,[status(thm)],[f_93_3]) ).

fof(f_94_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_94_2,plain,
    ! [U_149,U_148] : is_bool(hAPP_f1637334154l_bool(U_149,U_148)),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

fof(f_94_3,plain,
    ! [U_148,U_149] : is_bool(hAPP_f1637334154l_bool(U_149,U_148)),
    inference(definitional_conversion,[status(esa)],[f_94_2]) ).

cnf(f_94_4,plain,
    is_bool(hAPP_f1637334154l_bool(U_149,U_148)),
    inference(clausify,[status(thm)],[f_94_3]) ).

fof(f_95_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_95_2,plain,
    ! [U_151,U_150] : is_bool(hAPP_f292226953l_bool(U_151,U_150)),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

fof(f_95_3,plain,
    ! [U_150,U_151] : is_bool(hAPP_f292226953l_bool(U_151,U_150)),
    inference(definitional_conversion,[status(esa)],[f_95_2]) ).

cnf(f_95_4,plain,
    is_bool(hAPP_f292226953l_bool(U_151,U_150)),
    inference(clausify,[status(thm)],[f_95_3]) ).

fof(f_96_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_96_2,plain,
    ! [U_153,U_152] : is_bool(hAPP_f389811538l_bool(U_153,U_152)),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ! [U_152,U_153] : is_bool(hAPP_f389811538l_bool(U_153,U_152)),
    inference(definitional_conversion,[status(esa)],[f_96_2]) ).

cnf(f_96_4,plain,
    is_bool(hAPP_f389811538l_bool(U_153,U_152)),
    inference(clausify,[status(thm)],[f_96_3]) ).

fof(f_97_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_97_2,plain,
    ! [U_155,U_154] : is_bool(hAPP_f937997336l_bool(U_155,U_154)),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

fof(f_97_3,plain,
    ! [U_154,U_155] : is_bool(hAPP_f937997336l_bool(U_155,U_154)),
    inference(definitional_conversion,[status(esa)],[f_97_2]) ).

cnf(f_97_4,plain,
    is_bool(hAPP_f937997336l_bool(U_155,U_154)),
    inference(clausify,[status(thm)],[f_97_3]) ).

fof(f_98_1,plain,
    is_fun_a_bool(g),
    inference(fof_nnf,[status(thm)],[gsy_v_G]) ).

fof(f_98_2,plain,
    is_fun_a_bool(g),
    inference(definitional_conversion,[status(esa)],[f_98_1]) ).

cnf(f_98_3,plain,
    is_fun_a_bool(g),
    inference(clausify,[status(thm)],[f_98_2]) ).

fof(f_99_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_99_2,plain,
    ! [U_156] :
      ( is_fun949378684l_bool(p(U_156))
      | ~ is_fun_a_bool(U_156) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

fof(f_99_3,plain,
    ! [U_156] :
      ( is_fun949378684l_bool(p(U_156))
      | ~ is_fun_a_bool(U_156) ),
    inference(definitional_conversion,[status(esa)],[f_99_2]) ).

cnf(f_99_4,plain,
    ( is_fun949378684l_bool(p(U_156))
    | ~ is_fun_a_bool(U_156) ),
    inference(clausify,[status(thm)],[f_99_3]) ).

fof(f_100_1,plain,
    is_fun_pname_bool(u),
    inference(fof_nnf,[status(thm)],[gsy_v_U]) ).

fof(f_100_2,plain,
    is_fun_pname_bool(u),
    inference(definitional_conversion,[status(esa)],[f_100_1]) ).

cnf(f_100_3,plain,
    is_fun_pname_bool(u),
    inference(clausify,[status(thm)],[f_100_2]) ).

fof(f_101_1,plain,
    ! [B_1_1] : is_a(mgt(B_1_1)),
    inference(fof_nnf,[status(thm)],[gsy_v_mgt]) ).

fof(f_101_2,plain,
    ! [U_157] : is_a(mgt(U_157)),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

fof(f_101_3,plain,
    ! [U_157] : is_a(mgt(U_157)),
    inference(definitional_conversion,[status(esa)],[f_101_2]) ).

cnf(f_101_4,plain,
    is_a(mgt(U_157)),
    inference(clausify,[status(thm)],[f_101_3]) ).

fof(f_102_1,plain,
    is_pname(pn),
    inference(fof_nnf,[status(thm)],[gsy_v_pn]) ).

fof(f_102_2,plain,
    is_pname(pn),
    inference(definitional_conversion,[status(esa)],[f_102_1]) ).

cnf(f_102_3,plain,
    is_pname(pn),
    inference(clausify,[status(thm)],[f_102_2]) ).

fof(f_103_1,plain,
    ! [B_1_1] : is_bool(wt(B_1_1)),
    inference(fof_nnf,[status(thm)],[gsy_v_wt]) ).

fof(f_103_2,plain,
    ! [U_158] : is_bool(wt(U_158)),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

fof(f_103_3,plain,
    ! [U_158] : is_bool(wt(U_158)),
    inference(definitional_conversion,[status(esa)],[f_103_2]) ).

cnf(f_103_4,plain,
    is_bool(wt(U_158)),
    inference(clausify,[status(thm)],[f_103_3]) ).

fof(f_104_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_104_2,plain,
    ! [U_160,U_159] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_159),U_160))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_160),U_159)) ),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

fof(f_104_3,plain,
    ! [U_159,U_160] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_159),U_160))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_160),U_159)) ),
    inference(definitional_conversion,[status(esa)],[f_104_2]) ).

cnf(f_104_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(p(U_159),U_160))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_160),U_159)) ),
    inference(clausify,[status(thm)],[f_104_3]) ).

fof(f_105_1,plain,
    ! [A_1] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),A_1))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1_finite__Collect__subsets]) ).

fof(f_105_2,plain,
    ! [U_161] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),U_161))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_161)) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

fof(f_105_3,plain,
    ! [U_161] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),U_161))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_161)) ),
    inference(definitional_conversion,[status(esa)],[f_105_2]) ).

cnf(f_105_4,plain,
    ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),U_161))))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_161)) ),
    inference(clausify,[status(thm)],[f_105_3]) ).

fof(f_106_1,plain,
    ! [A_1] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A_1))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_2_finite__Collect__subsets]) ).

fof(f_106_2,plain,
    ! [U_162] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),U_162))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_162)) ),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

fof(f_106_3,plain,
    ! [U_162] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),U_162))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_162)) ),
    inference(definitional_conversion,[status(esa)],[f_106_2]) ).

cnf(f_106_4,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),U_162))))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_162)) ),
    inference(clausify,[status(thm)],[f_106_3]) ).

fof(f_107_1,plain,
    ! [A_1] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),A_1))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_3_finite__Collect__subsets]) ).

fof(f_107_2,plain,
    ! [U_163] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),U_163))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_163)) ),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

fof(f_107_3,plain,
    ! [U_163] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),U_163))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_163)) ),
    inference(definitional_conversion,[status(esa)],[f_107_2]) ).

cnf(f_107_4,plain,
    ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),U_163))))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_163)) ),
    inference(clausify,[status(thm)],[f_107_3]) ).

fof(f_108_1,plain,
    ! [A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),A_1))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_4_finite__Collect__subsets]) ).

fof(f_108_2,plain,
    ! [U_164] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),U_164))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_164)) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

fof(f_108_3,plain,
    ! [U_164] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),U_164))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_164)) ),
    inference(definitional_conversion,[status(esa)],[f_108_2]) ).

cnf(f_108_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),U_164))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_164)) ),
    inference(clausify,[status(thm)],[f_108_3]) ).

fof(f_109_1,plain,
    ! [A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A_1))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_5_finite__Collect__subsets]) ).

fof(f_109_2,plain,
    ! [U_165] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),U_165))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_165)) ),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

fof(f_109_3,plain,
    ! [U_165] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),U_165))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_165)) ),
    inference(definitional_conversion,[status(esa)],[f_109_2]) ).

cnf(f_109_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),U_165))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_165)) ),
    inference(clausify,[status(thm)],[f_109_3]) ).

fof(f_110_1,plain,
    ! [A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),A_1))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_6_finite__Collect__subsets]) ).

fof(f_110_2,plain,
    ! [U_166] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),U_166))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_166)) ),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

fof(f_110_3,plain,
    ! [U_166] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),U_166))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_166)) ),
    inference(definitional_conversion,[status(esa)],[f_110_2]) ).

cnf(f_110_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),U_166))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_166)) ),
    inference(clausify,[status(thm)],[f_110_3]) ).

fof(f_111_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_7_finite__imageI]) ).

fof(f_111_2,plain,
    ! [U_168,U_167] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(U_168,U_167)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_167)) ),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

fof(f_111_3,plain,
    ! [U_167,U_168] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(U_168,U_167)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_167)) ),
    inference(definitional_conversion,[status(esa)],[f_111_2]) ).

cnf(f_111_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(U_168,U_167)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_167)) ),
    inference(clausify,[status(thm)],[f_111_3]) ).

fof(f_112_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_8_finite__imageI]) ).

fof(f_112_2,plain,
    ! [U_170,U_169] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_170,U_169)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_169)) ),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

fof(f_112_3,plain,
    ! [U_169,U_170] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_170,U_169)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_169)) ),
    inference(definitional_conversion,[status(esa)],[f_112_2]) ).

cnf(f_112_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_170,U_169)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_169)) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

fof(f_113_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_9_finite__imageI]) ).

fof(f_113_2,plain,
    ! [U_172,U_171] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(U_172,U_171)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_171)) ),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

fof(f_113_3,plain,
    ! [U_171,U_172] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(U_172,U_171)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_171)) ),
    inference(definitional_conversion,[status(esa)],[f_113_2]) ).

cnf(f_113_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(U_172,U_171)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_171)) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

fof(f_114_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_10_finite__imageI]) ).

fof(f_114_2,plain,
    ! [U_174,U_173] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(U_174,U_173)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_173)) ),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

fof(f_114_3,plain,
    ! [U_173,U_174] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(U_174,U_173)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_173)) ),
    inference(definitional_conversion,[status(esa)],[f_114_2]) ).

cnf(f_114_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(U_174,U_173)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_173)) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

fof(f_115_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_11_finite__imageI]) ).

fof(f_115_2,plain,
    ! [U_176,U_175] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_176,U_175)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_175)) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

fof(f_115_3,plain,
    ! [U_175,U_176] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_176,U_175)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_175)) ),
    inference(definitional_conversion,[status(esa)],[f_115_2]) ).

cnf(f_115_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_176,U_175)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_175)) ),
    inference(clausify,[status(thm)],[f_115_3]) ).

fof(f_116_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_12_finite__imageI]) ).

fof(f_116_2,plain,
    ! [U_178,U_177] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_178,U_177)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_177)) ),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

fof(f_116_3,plain,
    ! [U_177,U_178] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_178,U_177)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_177)) ),
    inference(definitional_conversion,[status(esa)],[f_116_2]) ).

cnf(f_116_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_178,U_177)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_177)) ),
    inference(clausify,[status(thm)],[f_116_3]) ).

fof(f_117_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_13_finite__imageI]) ).

fof(f_117_2,plain,
    ! [U_180,U_179] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_180,U_179)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_179)) ),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

fof(f_117_3,plain,
    ! [U_179,U_180] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_180,U_179)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_179)) ),
    inference(definitional_conversion,[status(esa)],[f_117_2]) ).

cnf(f_117_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_180,U_179)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_179)) ),
    inference(clausify,[status(thm)],[f_117_3]) ).

fof(f_118_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_14_finite__imageI]) ).

fof(f_118_2,plain,
    ! [U_182,U_181] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(U_182,U_181)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_181)) ),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

fof(f_118_3,plain,
    ! [U_181,U_182] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(U_182,U_181)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_181)) ),
    inference(definitional_conversion,[status(esa)],[f_118_2]) ).

cnf(f_118_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(U_182,U_181)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_181)) ),
    inference(clausify,[status(thm)],[f_118_3]) ).

fof(f_119_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_15_finite__imageI]) ).

fof(f_119_2,plain,
    ! [U_184,U_183] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(U_184,U_183)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_183)) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

fof(f_119_3,plain,
    ! [U_183,U_184] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(U_184,U_183)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_183)) ),
    inference(definitional_conversion,[status(esa)],[f_119_2]) ).

cnf(f_119_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(U_184,U_183)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_183)) ),
    inference(clausify,[status(thm)],[f_119_3]) ).

fof(f_120_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_16_finite__imageI]) ).

fof(f_120_2,plain,
    ! [U_186,U_185] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_186,U_185)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_185)) ),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

fof(f_120_3,plain,
    ! [U_185,U_186] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_186,U_185)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_185)) ),
    inference(definitional_conversion,[status(esa)],[f_120_2]) ).

cnf(f_120_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_186,U_185)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_185)) ),
    inference(clausify,[status(thm)],[f_120_3]) ).

fof(f_121_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_17_finite__imageI]) ).

fof(f_121_2,plain,
    ! [U_188,U_187] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(U_188,U_187)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_187)) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

fof(f_121_3,plain,
    ! [U_187,U_188] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(U_188,U_187)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_187)) ),
    inference(definitional_conversion,[status(esa)],[f_121_2]) ).

cnf(f_121_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(U_188,U_187)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_187)) ),
    inference(clausify,[status(thm)],[f_121_3]) ).

fof(f_122_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_18_finite__imageI]) ).

fof(f_122_2,plain,
    ! [U_190,U_189] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(U_190,U_189)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_189)) ),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

fof(f_122_3,plain,
    ! [U_189,U_190] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(U_190,U_189)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_189)) ),
    inference(definitional_conversion,[status(esa)],[f_122_2]) ).

cnf(f_122_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(U_190,U_189)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_189)) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

fof(f_123_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_19_finite__imageI]) ).

fof(f_123_2,plain,
    ! [U_192,U_191] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(U_192,U_191)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_191)) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

fof(f_123_3,plain,
    ! [U_191,U_192] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(U_192,U_191)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_191)) ),
    inference(definitional_conversion,[status(esa)],[f_123_2]) ).

cnf(f_123_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(U_192,U_191)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_191)) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

fof(f_124_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_20_finite__imageI]) ).

fof(f_124_2,plain,
    ! [U_194,U_193] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(U_194,U_193)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_193)) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ! [U_193,U_194] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(U_194,U_193)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_193)) ),
    inference(definitional_conversion,[status(esa)],[f_124_2]) ).

cnf(f_124_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(U_194,U_193)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_193)) ),
    inference(clausify,[status(thm)],[f_124_3]) ).

fof(f_125_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_21_finite__imageI]) ).

fof(f_125_2,plain,
    ! [U_196,U_195] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(U_196,U_195)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_195)) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ! [U_195,U_196] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(U_196,U_195)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_195)) ),
    inference(definitional_conversion,[status(esa)],[f_125_2]) ).

cnf(f_125_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(U_196,U_195)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_195)) ),
    inference(clausify,[status(thm)],[f_125_3]) ).

fof(f_126_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_22_finite__imageI]) ).

fof(f_126_2,plain,
    ! [U_198,U_197] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_198,U_197)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_197)) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ! [U_197,U_198] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_198,U_197)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_197)) ),
    inference(definitional_conversion,[status(esa)],[f_126_2]) ).

cnf(f_126_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_198,U_197)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_197)) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

fof(f_127_1,plain,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_3,A_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_23_finite_OinsertI]) ).

fof(f_127_2,plain,
    ! [U_200,U_199] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_200,U_199)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_199)) ),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

fof(f_127_3,plain,
    ! [U_199,U_200] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_200,U_199)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_199)) ),
    inference(definitional_conversion,[status(esa)],[f_127_2]) ).

cnf(f_127_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_200,U_199)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_199)) ),
    inference(clausify,[status(thm)],[f_127_3]) ).

fof(f_128_1,plain,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_3,A_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_24_finite_OinsertI]) ).

fof(f_128_2,plain,
    ! [U_202,U_201] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_202,U_201)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_201)) ),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

fof(f_128_3,plain,
    ! [U_201,U_202] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_202,U_201)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_201)) ),
    inference(definitional_conversion,[status(esa)],[f_128_2]) ).

cnf(f_128_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_202,U_201)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_201)) ),
    inference(clausify,[status(thm)],[f_128_3]) ).

fof(f_129_1,plain,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_3,A_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_25_finite_OinsertI]) ).

fof(f_129_2,plain,
    ! [U_204,U_203] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_204,U_203)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_203)) ),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

fof(f_129_3,plain,
    ! [U_203,U_204] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_204,U_203)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_203)) ),
    inference(definitional_conversion,[status(esa)],[f_129_2]) ).

cnf(f_129_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_204,U_203)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_203)) ),
    inference(clausify,[status(thm)],[f_129_3]) ).

fof(f_130_1,plain,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_3,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_26_finite_OinsertI]) ).

fof(f_130_2,plain,
    ! [U_206,U_205] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_206,U_205)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_205)) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

fof(f_130_3,plain,
    ! [U_205,U_206] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_206,U_205)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_205)) ),
    inference(definitional_conversion,[status(esa)],[f_130_2]) ).

cnf(f_130_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_206,U_205)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_205)) ),
    inference(clausify,[status(thm)],[f_130_3]) ).

fof(f_131_1,plain,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_3,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_27_finite_OinsertI]) ).

fof(f_131_2,plain,
    ! [U_208,U_207] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_208,U_207)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_207)) ),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

fof(f_131_3,plain,
    ! [U_207,U_208] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_208,U_207)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_207)) ),
    inference(definitional_conversion,[status(esa)],[f_131_2]) ).

cnf(f_131_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_208,U_207)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_207)) ),
    inference(clausify,[status(thm)],[f_131_3]) ).

fof(f_132_1,plain,
    ! [A_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_3,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_28_finite_OinsertI]) ).

fof(f_132_2,plain,
    ! [U_210,U_209] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_210,U_209)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_209)) ),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

fof(f_132_3,plain,
    ! [U_209,U_210] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_210,U_209)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_209)) ),
    inference(definitional_conversion,[status(esa)],[f_132_2]) ).

cnf(f_132_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_210,U_209)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_209)) ),
    inference(clausify,[status(thm)],[f_132_3]) ).

fof(f_133_1,plain,
    ! [F,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(F,A_1))),hAPP_f921600141ol_nat(finite_card_pname,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_29_card__image__le]) ).

fof(f_133_2,plain,
    ! [U_212,U_211] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(U_212,U_211))),hAPP_f921600141ol_nat(finite_card_pname,U_211)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_211)) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

fof(f_133_3,plain,
    ! [U_211,U_212] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(U_212,U_211))),hAPP_f921600141ol_nat(finite_card_pname,U_211)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_211)) ),
    inference(definitional_conversion,[status(esa)],[f_133_2]) ).

cnf(f_133_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(U_212,U_211))),hAPP_f921600141ol_nat(finite_card_pname,U_211)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_211)) ),
    inference(clausify,[status(thm)],[f_133_3]) ).

fof(f_134_1,plain,
    ! [F,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(F,A_1))),hAPP_fun_a_bool_nat(finite_card_a,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_30_card__image__le]) ).

fof(f_134_2,plain,
    ! [U_214,U_213] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(U_214,U_213))),hAPP_fun_a_bool_nat(finite_card_a,U_213)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_213)) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

fof(f_134_3,plain,
    ! [U_213,U_214] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(U_214,U_213))),hAPP_fun_a_bool_nat(finite_card_a,U_213)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_213)) ),
    inference(definitional_conversion,[status(esa)],[f_134_2]) ).

cnf(f_134_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_214,U_213))),hAPP_fun_a_bool_nat(finite_card_a,U_213)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_213)) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

fof(f_135_1,plain,
    ! [F,A_1] :
      ( 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_1))),hAPP_f696928925ol_nat(finite346522414t_bool,A_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_31_card__image__le]) ).

fof(f_135_2,plain,
    ! [U_216,U_215] :
      ( 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_216,U_215))),hAPP_f696928925ol_nat(finite346522414t_bool,U_215)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_215)) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

fof(f_135_3,plain,
    ! [U_215,U_216] :
      ( 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_216,U_215))),hAPP_f696928925ol_nat(finite346522414t_bool,U_215)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_215)) ),
    inference(definitional_conversion,[status(esa)],[f_135_2]) ).

cnf(f_135_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_216,U_215))),hAPP_f696928925ol_nat(finite346522414t_bool,U_215)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_215)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

fof(f_136_1,plain,
    ! [F,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(F,A_1))),hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_32_card__image__le]) ).

fof(f_136_2,plain,
    ! [U_218,U_217] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(U_218,U_217))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_217)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_217)) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

fof(f_136_3,plain,
    ! [U_217,U_218] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(U_218,U_217))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_217)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_217)) ),
    inference(definitional_conversion,[status(esa)],[f_136_2]) ).

cnf(f_136_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_218,U_217))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_217)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_217)) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

fof(f_137_1,plain,
    ! [F,A_1] :
      ( 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_1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_33_card__image__le]) ).

fof(f_137_2,plain,
    ! [U_220,U_219] :
      ( 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_220,U_219))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_219)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_219)) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

fof(f_137_3,plain,
    ! [U_219,U_220] :
      ( 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_220,U_219))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_219)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_219)) ),
    inference(definitional_conversion,[status(esa)],[f_137_2]) ).

cnf(f_137_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_220,U_219))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_219)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_219)) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

fof(f_138_1,plain,
    ! [F,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(F,A_1))),hAPP_f921600141ol_nat(finite_card_pname,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_34_card__image__le]) ).

fof(f_138_2,plain,
    ! [U_222,U_221] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(U_222,U_221))),hAPP_f921600141ol_nat(finite_card_pname,U_221)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_221)) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

fof(f_138_3,plain,
    ! [U_221,U_222] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(U_222,U_221))),hAPP_f921600141ol_nat(finite_card_pname,U_221)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_221)) ),
    inference(definitional_conversion,[status(esa)],[f_138_2]) ).

cnf(f_138_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(U_222,U_221))),hAPP_f921600141ol_nat(finite_card_pname,U_221)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_221)) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

fof(f_139_1,plain,
    ! [F,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(F,A_1))),hAPP_fun_a_bool_nat(finite_card_a,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_35_card__image__le]) ).

fof(f_139_2,plain,
    ! [U_224,U_223] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(U_224,U_223))),hAPP_fun_a_bool_nat(finite_card_a,U_223)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_223)) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

fof(f_139_3,plain,
    ! [U_223,U_224] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(U_224,U_223))),hAPP_fun_a_bool_nat(finite_card_a,U_223)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_223)) ),
    inference(definitional_conversion,[status(esa)],[f_139_2]) ).

cnf(f_139_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(U_224,U_223))),hAPP_fun_a_bool_nat(finite_card_a,U_223)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_223)) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

fof(f_140_1,plain,
    ! [F,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(F,A_1))),hAPP_f696928925ol_nat(finite346522414t_bool,A_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_36_card__image__le]) ).

fof(f_140_2,plain,
    ! [U_226,U_225] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(U_226,U_225))),hAPP_f696928925ol_nat(finite346522414t_bool,U_225)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_225)) ),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

fof(f_140_3,plain,
    ! [U_225,U_226] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(U_226,U_225))),hAPP_f696928925ol_nat(finite346522414t_bool,U_225)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_225)) ),
    inference(definitional_conversion,[status(esa)],[f_140_2]) ).

cnf(f_140_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(U_226,U_225))),hAPP_f696928925ol_nat(finite346522414t_bool,U_225)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_225)) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

fof(f_141_1,plain,
    ! [F,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(F,A_1))),hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_37_card__image__le]) ).

fof(f_141_2,plain,
    ! [U_228,U_227] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(U_228,U_227))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_227)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_227)) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

fof(f_141_3,plain,
    ! [U_227,U_228] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(U_228,U_227))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_227)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_227)) ),
    inference(definitional_conversion,[status(esa)],[f_141_2]) ).

cnf(f_141_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(U_228,U_227))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_227)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_227)) ),
    inference(clausify,[status(thm)],[f_141_3]) ).

fof(f_142_1,plain,
    ! [F,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(F,A_1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_38_card__image__le]) ).

fof(f_142_2,plain,
    ! [U_230,U_229] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(U_230,U_229))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_229)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_229)) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

fof(f_142_3,plain,
    ! [U_229,U_230] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(U_230,U_229))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_229)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_229)) ),
    inference(definitional_conversion,[status(esa)],[f_142_2]) ).

cnf(f_142_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_230,U_229))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_229)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_229)) ),
    inference(clausify,[status(thm)],[f_142_3]) ).

fof(f_143_1,plain,
    ! [F,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(F,A_1))),hAPP_fun_a_bool_nat(finite_card_a,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_39_card__image__le]) ).

fof(f_143_2,plain,
    ! [U_232,U_231] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(U_232,U_231))),hAPP_fun_a_bool_nat(finite_card_a,U_231)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_231)) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

fof(f_143_3,plain,
    ! [U_231,U_232] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(U_232,U_231))),hAPP_fun_a_bool_nat(finite_card_a,U_231)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_231)) ),
    inference(definitional_conversion,[status(esa)],[f_143_2]) ).

cnf(f_143_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(U_232,U_231))),hAPP_fun_a_bool_nat(finite_card_a,U_231)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_231)) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

fof(f_144_1,plain,
    ! [F,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(F,A_1))),hAPP_f22106695ol_nat(finite_card_nat,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_40_card__image__le]) ).

fof(f_144_2,plain,
    ! [U_234,U_233] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(U_234,U_233))),hAPP_f22106695ol_nat(finite_card_nat,U_233)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_233)) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ! [U_233,U_234] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(U_234,U_233))),hAPP_f22106695ol_nat(finite_card_nat,U_233)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_233)) ),
    inference(definitional_conversion,[status(esa)],[f_144_2]) ).

cnf(f_144_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(U_234,U_233))),hAPP_f22106695ol_nat(finite_card_nat,U_233)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_233)) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_1,plain,
    ! [F,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(F,A_1))),hAPP_f921600141ol_nat(finite_card_pname,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_41_card__image__le]) ).

fof(f_145_2,plain,
    ! [U_236,U_235] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(U_236,U_235))),hAPP_f921600141ol_nat(finite_card_pname,U_235)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_235)) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

fof(f_145_3,plain,
    ! [U_235,U_236] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(U_236,U_235))),hAPP_f921600141ol_nat(finite_card_pname,U_235)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_235)) ),
    inference(definitional_conversion,[status(esa)],[f_145_2]) ).

cnf(f_145_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_236,U_235))),hAPP_f921600141ol_nat(finite_card_pname,U_235)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_235)) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

fof(f_146_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A_1)),hAPP_f696928925ol_nat(finite346522414t_bool,B_6)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_42_card__mono]) ).

fof(f_146_2,plain,
    ! [U_238,U_237] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_238)),hAPP_f696928925ol_nat(finite346522414t_bool,U_237)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_238),U_237))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_237)) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

fof(f_146_3,plain,
    ! [U_237,U_238] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_238)),hAPP_f696928925ol_nat(finite346522414t_bool,U_237)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_238),U_237))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_237)) ),
    inference(definitional_conversion,[status(esa)],[f_146_2]) ).

cnf(f_146_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_238)),hAPP_f696928925ol_nat(finite346522414t_bool,U_237)))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_238),U_237))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_237)) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

fof(f_147_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)),hAPP_f55526627ol_nat(finite1340463720e_bool,B_6)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_43_card__mono]) ).

fof(f_147_2,plain,
    ! [U_240,U_239] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_240)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_239)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_240),U_239))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_239)) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

fof(f_147_3,plain,
    ! [U_239,U_240] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_240)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_239)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_240),U_239))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_239)) ),
    inference(definitional_conversion,[status(esa)],[f_147_2]) ).

cnf(f_147_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_240)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_239)))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_240),U_239))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_239)) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

fof(f_148_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,B_6)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_44_card__mono]) ).

fof(f_148_2,plain,
    ! [U_242,U_241] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_242)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_241)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_242),U_241))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_241)) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

fof(f_148_3,plain,
    ! [U_241,U_242] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_242)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_241)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_242),U_241))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_241)) ),
    inference(definitional_conversion,[status(esa)],[f_148_2]) ).

cnf(f_148_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_242)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_241)))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_242),U_241))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_241)) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

fof(f_149_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A_1)),hAPP_f921600141ol_nat(finite_card_pname,B_6)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_45_card__mono]) ).

fof(f_149_2,plain,
    ! [U_244,U_243] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_244)),hAPP_f921600141ol_nat(finite_card_pname,U_243)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_244),U_243))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_243)) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

fof(f_149_3,plain,
    ! [U_243,U_244] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_244)),hAPP_f921600141ol_nat(finite_card_pname,U_243)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_244),U_243))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_243)) ),
    inference(definitional_conversion,[status(esa)],[f_149_2]) ).

cnf(f_149_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_244)),hAPP_f921600141ol_nat(finite_card_pname,U_243)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_244),U_243))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_243)) ),
    inference(clausify,[status(thm)],[f_149_3]) ).

fof(f_150_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A_1)),hAPP_fun_a_bool_nat(finite_card_a,B_6)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_46_card__mono]) ).

fof(f_150_2,plain,
    ! [U_246,U_245] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_246)),hAPP_fun_a_bool_nat(finite_card_a,U_245)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_246),U_245))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_245)) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

fof(f_150_3,plain,
    ! [U_246,U_245] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_246)),hAPP_fun_a_bool_nat(finite_card_a,U_245)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_246),U_245))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_245)) ),
    inference(definitional_conversion,[status(esa)],[f_150_2]) ).

cnf(f_150_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_246)),hAPP_fun_a_bool_nat(finite_card_a,U_245)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_246),U_245))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_245)) ),
    inference(clausify,[status(thm)],[f_150_3]) ).

fof(f_151_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A_1)),hAPP_f22106695ol_nat(finite_card_nat,B_6)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_47_card__mono]) ).

fof(f_151_2,plain,
    ! [U_248,U_247] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_248)),hAPP_f22106695ol_nat(finite_card_nat,U_247)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_248),U_247))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_247)) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

fof(f_151_3,plain,
    ! [U_247,U_248] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_248)),hAPP_f22106695ol_nat(finite_card_nat,U_247)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_248),U_247))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_247)) ),
    inference(definitional_conversion,[status(esa)],[f_151_2]) ).

cnf(f_151_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_248)),hAPP_f22106695ol_nat(finite_card_nat,U_247)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_248),U_247))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_247)) ),
    inference(clausify,[status(thm)],[f_151_3]) ).

fof(f_152_1,plain,
    ! [A_1,B_6] :
      ( A_1 = B_6
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,B_6)),hAPP_f696928925ol_nat(finite346522414t_bool,A_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_48_card__seteq]) ).

fof(f_152_2,plain,
    ! [U_250,U_249] :
      ( U_250 = U_249
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_249)),hAPP_f696928925ol_nat(finite346522414t_bool,U_250)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_250),U_249))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_249)) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ! [U_249,U_250] :
      ( U_250 = U_249
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_249)),hAPP_f696928925ol_nat(finite346522414t_bool,U_250)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_250),U_249))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_249)) ),
    inference(definitional_conversion,[status(esa)],[f_152_2]) ).

cnf(f_152_4,plain,
    ( U_250 = U_249
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_249)),hAPP_f696928925ol_nat(finite346522414t_bool,U_250)))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_250),U_249))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_249)) ),
    inference(clausify,[status(thm)],[f_152_3]) ).

fof(f_153_1,plain,
    ! [A_1,B_6] :
      ( A_1 = B_6
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,B_6)),hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
      | ~ is_fun1661590463l_bool(B_6)
      | ~ is_fun1661590463l_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_49_card__seteq]) ).

fof(f_153_2,plain,
    ! [U_252,U_251] :
      ( U_252 = U_251
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_251)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_252)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_252),U_251))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_251))
      | ~ is_fun1661590463l_bool(U_251)
      | ~ is_fun1661590463l_bool(U_252) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

fof(f_153_3,plain,
    ! [U_251,U_252] :
      ( U_252 = U_251
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_251)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_252)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_252),U_251))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_251))
      | ~ is_fun1661590463l_bool(U_251)
      | ~ is_fun1661590463l_bool(U_252) ),
    inference(definitional_conversion,[status(esa)],[f_153_2]) ).

cnf(f_153_4,plain,
    ( U_252 = U_251
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_251)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_252)))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_252),U_251))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_251))
    | ~ is_fun1661590463l_bool(U_251)
    | ~ is_fun1661590463l_bool(U_252) ),
    inference(clausify,[status(thm)],[f_153_3]) ).

fof(f_154_1,plain,
    ! [A_1,B_6] :
      ( A_1 = B_6
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,B_6)),hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
      | ~ is_fun949378684l_bool(B_6)
      | ~ is_fun949378684l_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_50_card__seteq]) ).

fof(f_154_2,plain,
    ! [U_254,U_253] :
      ( U_254 = U_253
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_253)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_254)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_254),U_253))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_253))
      | ~ is_fun949378684l_bool(U_253)
      | ~ is_fun949378684l_bool(U_254) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

fof(f_154_3,plain,
    ! [U_254,U_253] :
      ( U_254 = U_253
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_253)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_254)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_254),U_253))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_253))
      | ~ is_fun949378684l_bool(U_253)
      | ~ is_fun949378684l_bool(U_254) ),
    inference(definitional_conversion,[status(esa)],[f_154_2]) ).

cnf(f_154_4,plain,
    ( U_254 = U_253
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_253)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_254)))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_254),U_253))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_253))
    | ~ is_fun949378684l_bool(U_253)
    | ~ is_fun949378684l_bool(U_254) ),
    inference(clausify,[status(thm)],[f_154_3]) ).

fof(f_155_1,plain,
    ! [A_1,B_6] :
      ( A_1 = B_6
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,B_6)),hAPP_f921600141ol_nat(finite_card_pname,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ is_fun_pname_bool(B_6)
      | ~ is_fun_pname_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_51_card__seteq]) ).

fof(f_155_2,plain,
    ! [U_256,U_255] :
      ( U_256 = U_255
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_255)),hAPP_f921600141ol_nat(finite_card_pname,U_256)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_256),U_255))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_255))
      | ~ is_fun_pname_bool(U_255)
      | ~ is_fun_pname_bool(U_256) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

fof(f_155_3,plain,
    ! [U_255,U_256] :
      ( U_256 = U_255
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_255)),hAPP_f921600141ol_nat(finite_card_pname,U_256)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_256),U_255))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_255))
      | ~ is_fun_pname_bool(U_255)
      | ~ is_fun_pname_bool(U_256) ),
    inference(definitional_conversion,[status(esa)],[f_155_2]) ).

cnf(f_155_4,plain,
    ( U_256 = U_255
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_255)),hAPP_f921600141ol_nat(finite_card_pname,U_256)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_256),U_255))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_255))
    | ~ is_fun_pname_bool(U_255)
    | ~ is_fun_pname_bool(U_256) ),
    inference(clausify,[status(thm)],[f_155_3]) ).

fof(f_156_1,plain,
    ! [A_1,B_6] :
      ( A_1 = B_6
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,B_6)),hAPP_fun_a_bool_nat(finite_card_a,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ is_fun_a_bool(B_6)
      | ~ is_fun_a_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_52_card__seteq]) ).

fof(f_156_2,plain,
    ! [U_258,U_257] :
      ( U_258 = U_257
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_257)),hAPP_fun_a_bool_nat(finite_card_a,U_258)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_258),U_257))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_257))
      | ~ is_fun_a_bool(U_257)
      | ~ is_fun_a_bool(U_258) ),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

fof(f_156_3,plain,
    ! [U_257,U_258] :
      ( U_258 = U_257
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_257)),hAPP_fun_a_bool_nat(finite_card_a,U_258)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_258),U_257))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_257))
      | ~ is_fun_a_bool(U_257)
      | ~ is_fun_a_bool(U_258) ),
    inference(definitional_conversion,[status(esa)],[f_156_2]) ).

cnf(f_156_4,plain,
    ( U_258 = U_257
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_257)),hAPP_fun_a_bool_nat(finite_card_a,U_258)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_258),U_257))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_257))
    | ~ is_fun_a_bool(U_257)
    | ~ is_fun_a_bool(U_258) ),
    inference(clausify,[status(thm)],[f_156_3]) ).

fof(f_157_1,plain,
    ! [A_1,B_6] :
      ( A_1 = B_6
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,B_6)),hAPP_f22106695ol_nat(finite_card_nat,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_53_card__seteq]) ).

fof(f_157_2,plain,
    ! [U_260,U_259] :
      ( U_260 = U_259
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_259)),hAPP_f22106695ol_nat(finite_card_nat,U_260)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_260),U_259))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_259)) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

fof(f_157_3,plain,
    ! [U_260,U_259] :
      ( U_260 = U_259
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_259)),hAPP_f22106695ol_nat(finite_card_nat,U_260)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_260),U_259))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_259)) ),
    inference(definitional_conversion,[status(esa)],[f_157_2]) ).

cnf(f_157_4,plain,
    ( U_260 = U_259
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_259)),hAPP_f22106695ol_nat(finite_card_nat,U_260)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_260),U_259))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_259)) ),
    inference(clausify,[status(thm)],[f_157_3]) ).

fof(f_158_1,plain,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A_1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_54_card__insert__le]) ).

fof(f_158_2,plain,
    ! [U_262,U_261] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_261)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_262,U_261))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_261)) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

fof(f_158_3,plain,
    ! [U_261,U_262] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_261)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_262,U_261))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_261)) ),
    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_f696928925ol_nat(finite346522414t_bool,U_261)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_262,U_261))))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_261)) ),
    inference(clausify,[status(thm)],[f_158_3]) ).

fof(f_159_1,plain,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_55_card__insert__le]) ).

fof(f_159_2,plain,
    ! [U_264,U_263] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_263)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_264,U_263))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_263)) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

fof(f_159_3,plain,
    ! [U_263,U_264] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_263)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_264,U_263))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_263)) ),
    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_f55526627ol_nat(finite1340463720e_bool,U_263)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_264,U_263))))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_263)) ),
    inference(clausify,[status(thm)],[f_159_3]) ).

fof(f_160_1,plain,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_56_card__insert__le]) ).

fof(f_160_2,plain,
    ! [U_266,U_265] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_265)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_266,U_265))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_265)) ),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

fof(f_160_3,plain,
    ! [U_265,U_266] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_265)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_266,U_265))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_265)) ),
    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_f2009550088ol_nat(finite1306199131a_bool,U_265)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_266,U_265))))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_265)) ),
    inference(clausify,[status(thm)],[f_160_3]) ).

fof(f_161_1,plain,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A_1)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_57_card__insert__le]) ).

fof(f_161_2,plain,
    ! [U_268,U_267] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_267)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_268,U_267))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_267)) ),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

fof(f_161_3,plain,
    ! [U_267,U_268] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_267)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_268,U_267))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_267)) ),
    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_f921600141ol_nat(finite_card_pname,U_267)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_268,U_267))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_267)) ),
    inference(clausify,[status(thm)],[f_161_3]) ).

fof(f_162_1,plain,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A_1)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_58_card__insert__le]) ).

fof(f_162_2,plain,
    ! [U_270,U_269] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_269)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_270,U_269))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_269)) ),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

fof(f_162_3,plain,
    ! [U_269,U_270] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_269)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_270,U_269))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_269)) ),
    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,U_269)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_270,U_269))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_269)) ),
    inference(clausify,[status(thm)],[f_162_3]) ).

fof(f_163_1,plain,
    ! [X_3,A_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A_1)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_59_card__insert__le]) ).

fof(f_163_2,plain,
    ! [U_272,U_271] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_271)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_272,U_271))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_271)) ),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

fof(f_163_3,plain,
    ! [U_271,U_272] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_271)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_272,U_271))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_271)) ),
    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_fun_a_bool_nat(finite_card_a,U_271)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_272,U_271))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_271)) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

fof(f_164_1,plain,
    ! [X_3,A_1] :
      ( ( ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A_1))
          | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_3),A_1)) )
        & ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)) = hAPP_f696928925ol_nat(finite346522414t_bool,A_1)
          | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_3),A_1)) ) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_60_card__insert__if]) ).

fof(f_164_2,plain,
    ! [U_274,U_273] :
      ( ( ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_274,U_273)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_273))
          | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_274),U_273)) )
        & ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_274,U_273)) = hAPP_f696928925ol_nat(finite346522414t_bool,U_273)
          | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_274),U_273)) ) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_273)) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

fof(f_164_3,plain,
    ( ! [U_274,U_273] :
        ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_274,U_273)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_273))
        | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_274),U_273))
        | ~ sP0(U_274,U_273) )
    & ! [U_274,U_273] :
        ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_274,U_273)) = hAPP_f696928925ol_nat(finite346522414t_bool,U_273)
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_274),U_273))
        | ~ sP0(U_274,U_273) )
    & ! [U_274,U_273] :
        ( sP0(U_274,U_273)
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_273)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_164_2]) ).

cnf(f_164_4,plain,
    ( sP0(U_274,U_273)
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_273)) ),
    inference(clausify,[status(thm)],[f_164_3]) ).

cnf(f_164_5,plain,
    ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_274,U_273)) = hAPP_f696928925ol_nat(finite346522414t_bool,U_273)
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_274),U_273))
    | ~ sP0(U_274,U_273) ),
    inference(clausify,[status(thm)],[f_164_3]) ).

cnf(f_164_6,plain,
    ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_274,U_273)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_273))
    | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_274),U_273))
    | ~ sP0(U_274,U_273) ),
    inference(clausify,[status(thm)],[f_164_3]) ).

fof(f_165_1,plain,
    ! [X_3,A_1] :
      ( ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1))
          | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_3),A_1)) )
        & ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)) = hAPP_f55526627ol_nat(finite1340463720e_bool,A_1)
          | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_3),A_1)) ) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_61_card__insert__if]) ).

fof(f_165_2,plain,
    ! [U_276,U_275] :
      ( ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_276,U_275)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_275))
          | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_276),U_275)) )
        & ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_276,U_275)) = hAPP_f55526627ol_nat(finite1340463720e_bool,U_275)
          | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_276),U_275)) ) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_275)) ),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

fof(f_165_3,plain,
    ( ! [U_276,U_275] :
        ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_276,U_275)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_275))
        | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_276),U_275))
        | ~ sP1(U_276,U_275) )
    & ! [U_276,U_275] :
        ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_276,U_275)) = hAPP_f55526627ol_nat(finite1340463720e_bool,U_275)
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_276),U_275))
        | ~ sP1(U_276,U_275) )
    & ! [U_276,U_275] :
        ( sP1(U_276,U_275)
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_275)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_165_2]) ).

cnf(f_165_4,plain,
    ( sP1(U_276,U_275)
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_275)) ),
    inference(clausify,[status(thm)],[f_165_3]) ).

cnf(f_165_5,plain,
    ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_276,U_275)) = hAPP_f55526627ol_nat(finite1340463720e_bool,U_275)
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_276),U_275))
    | ~ sP1(U_276,U_275) ),
    inference(clausify,[status(thm)],[f_165_3]) ).

cnf(f_165_6,plain,
    ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_276,U_275)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_275))
    | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_276),U_275))
    | ~ sP1(U_276,U_275) ),
    inference(clausify,[status(thm)],[f_165_3]) ).

fof(f_166_1,plain,
    ! [X_3,A_1] :
      ( ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1))
          | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_3),A_1)) )
        & ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1)
          | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_3),A_1)) ) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_62_card__insert__if]) ).

fof(f_166_2,plain,
    ! [U_278,U_277] :
      ( ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_278,U_277)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_277))
          | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_278),U_277)) )
        & ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_278,U_277)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,U_277)
          | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_278),U_277)) ) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_277)) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

fof(f_166_3,plain,
    ( ! [U_278,U_277] :
        ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_278,U_277)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_277))
        | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_278),U_277))
        | ~ sP2(U_278,U_277) )
    & ! [U_278,U_277] :
        ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_278,U_277)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,U_277)
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_278),U_277))
        | ~ sP2(U_278,U_277) )
    & ! [U_278,U_277] :
        ( sP2(U_278,U_277)
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_277)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_166_2]) ).

cnf(f_166_4,plain,
    ( sP2(U_278,U_277)
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_277)) ),
    inference(clausify,[status(thm)],[f_166_3]) ).

cnf(f_166_5,plain,
    ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_278,U_277)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,U_277)
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_278),U_277))
    | ~ sP2(U_278,U_277) ),
    inference(clausify,[status(thm)],[f_166_3]) ).

cnf(f_166_6,plain,
    ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_278,U_277)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_277))
    | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_278),U_277))
    | ~ sP2(U_278,U_277) ),
    inference(clausify,[status(thm)],[f_166_3]) ).

fof(f_167_1,plain,
    ! [X_3,A_1] :
      ( ( ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A_1))
          | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) )
        & ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)) = hAPP_f22106695ol_nat(finite_card_nat,A_1)
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_63_card__insert__if]) ).

fof(f_167_2,plain,
    ! [U_280,U_279] :
      ( ( ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_280,U_279)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_279))
          | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_280),U_279)) )
        & ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_280,U_279)) = hAPP_f22106695ol_nat(finite_card_nat,U_279)
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_280),U_279)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_279)) ),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

fof(f_167_3,plain,
    ( ! [U_280,U_279] :
        ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_280,U_279)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_279))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_280),U_279))
        | ~ sP3(U_280,U_279) )
    & ! [U_280,U_279] :
        ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_280,U_279)) = hAPP_f22106695ol_nat(finite_card_nat,U_279)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_280),U_279))
        | ~ sP3(U_280,U_279) )
    & ! [U_280,U_279] :
        ( sP3(U_280,U_279)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_279)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_167_2]) ).

cnf(f_167_4,plain,
    ( sP3(U_280,U_279)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_279)) ),
    inference(clausify,[status(thm)],[f_167_3]) ).

cnf(f_167_5,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_280,U_279)) = hAPP_f22106695ol_nat(finite_card_nat,U_279)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_280),U_279))
    | ~ sP3(U_280,U_279) ),
    inference(clausify,[status(thm)],[f_167_3]) ).

cnf(f_167_6,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_280,U_279)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_279))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_280),U_279))
    | ~ sP3(U_280,U_279) ),
    inference(clausify,[status(thm)],[f_167_3]) ).

fof(f_168_1,plain,
    ! [X_3,A_1] :
      ( ( ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A_1))
          | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) )
        & ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)) = hAPP_f921600141ol_nat(finite_card_pname,A_1)
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_64_card__insert__if]) ).

fof(f_168_2,plain,
    ! [U_282,U_281] :
      ( ( ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_282,U_281)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_281))
          | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_282),U_281)) )
        & ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_282,U_281)) = hAPP_f921600141ol_nat(finite_card_pname,U_281)
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_282),U_281)) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_281)) ),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

fof(f_168_3,plain,
    ( ! [U_281,U_282] :
        ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_282,U_281)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_281))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_282),U_281))
        | ~ sP4(U_281,U_282) )
    & ! [U_281,U_282] :
        ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_282,U_281)) = hAPP_f921600141ol_nat(finite_card_pname,U_281)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_282),U_281))
        | ~ sP4(U_281,U_282) )
    & ! [U_281,U_282] :
        ( sP4(U_281,U_282)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_281)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_168_2]) ).

cnf(f_168_4,plain,
    ( sP4(U_281,U_282)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_281)) ),
    inference(clausify,[status(thm)],[f_168_3]) ).

cnf(f_168_5,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_282,U_281)) = hAPP_f921600141ol_nat(finite_card_pname,U_281)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_282),U_281))
    | ~ sP4(U_281,U_282) ),
    inference(clausify,[status(thm)],[f_168_3]) ).

cnf(f_168_6,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_282,U_281)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_281))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_282),U_281))
    | ~ sP4(U_281,U_282) ),
    inference(clausify,[status(thm)],[f_168_3]) ).

fof(f_169_1,plain,
    ! [X_3,A_1] :
      ( ( ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A_1))
          | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) )
        & ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)) = hAPP_fun_a_bool_nat(finite_card_a,A_1)
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_65_card__insert__if]) ).

fof(f_169_2,plain,
    ! [U_284,U_283] :
      ( ( ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_284,U_283)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_283))
          | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_284),U_283)) )
        & ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_284,U_283)) = hAPP_fun_a_bool_nat(finite_card_a,U_283)
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_284),U_283)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_283)) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

fof(f_169_3,plain,
    ( ! [U_283,U_284] :
        ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_284,U_283)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_283))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_284),U_283))
        | ~ sP5(U_283,U_284) )
    & ! [U_283,U_284] :
        ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_284,U_283)) = hAPP_fun_a_bool_nat(finite_card_a,U_283)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_284),U_283))
        | ~ sP5(U_283,U_284) )
    & ! [U_283,U_284] :
        ( sP5(U_283,U_284)
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_283)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_169_2]) ).

cnf(f_169_4,plain,
    ( sP5(U_283,U_284)
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_283)) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

cnf(f_169_5,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_284,U_283)) = hAPP_fun_a_bool_nat(finite_card_a,U_283)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_284),U_283))
    | ~ sP5(U_283,U_284) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

cnf(f_169_6,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_284,U_283)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_283))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_284),U_283))
    | ~ sP5(U_283,U_284) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

fof(f_170_1,plain,
    ! [X_3,A_1] :
      ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A_1))
      | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_3),A_1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_66_card__insert__disjoint]) ).

fof(f_170_2,plain,
    ! [U_286,U_285] :
      ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_286,U_285)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_285))
      | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_286),U_285))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_285)) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

fof(f_170_3,plain,
    ! [U_286,U_285] :
      ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_286,U_285)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_285))
      | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_286),U_285))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_285)) ),
    inference(definitional_conversion,[status(esa)],[f_170_2]) ).

cnf(f_170_4,plain,
    ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_286,U_285)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_285))
    | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_286),U_285))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_285)) ),
    inference(clausify,[status(thm)],[f_170_3]) ).

fof(f_171_1,plain,
    ! [X_3,A_1] :
      ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A_1))
      | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_3),A_1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_67_card__insert__disjoint]) ).

fof(f_171_2,plain,
    ! [U_288,U_287] :
      ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_288,U_287)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_287))
      | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_288),U_287))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_287)) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

fof(f_171_3,plain,
    ! [U_287,U_288] :
      ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_288,U_287)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_287))
      | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_288),U_287))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_287)) ),
    inference(definitional_conversion,[status(esa)],[f_171_2]) ).

cnf(f_171_4,plain,
    ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_288,U_287)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_287))
    | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_288),U_287))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_287)) ),
    inference(clausify,[status(thm)],[f_171_3]) ).

fof(f_172_1,plain,
    ! [X_3,A_1] :
      ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A_1))
      | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_3),A_1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_68_card__insert__disjoint]) ).

fof(f_172_2,plain,
    ! [U_290,U_289] :
      ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_290,U_289)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_289))
      | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_290),U_289))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_289)) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

fof(f_172_3,plain,
    ! [U_289,U_290] :
      ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_290,U_289)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_289))
      | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_290),U_289))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_289)) ),
    inference(definitional_conversion,[status(esa)],[f_172_2]) ).

cnf(f_172_4,plain,
    ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_290,U_289)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_289))
    | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_290),U_289))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_289)) ),
    inference(clausify,[status(thm)],[f_172_3]) ).

fof(f_173_1,plain,
    ! [X_3,A_1] :
      ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A_1))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_69_card__insert__disjoint]) ).

fof(f_173_2,plain,
    ! [U_292,U_291] :
      ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_292,U_291)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_291))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_292),U_291))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_291)) ),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

fof(f_173_3,plain,
    ! [U_291,U_292] :
      ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_292,U_291)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_291))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_292),U_291))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_291)) ),
    inference(definitional_conversion,[status(esa)],[f_173_2]) ).

cnf(f_173_4,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_292,U_291)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_291))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_292),U_291))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_291)) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

fof(f_174_1,plain,
    ! [X_3,A_1] :
      ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A_1))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_70_card__insert__disjoint]) ).

fof(f_174_2,plain,
    ! [U_294,U_293] :
      ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_294,U_293)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_293))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_294),U_293))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_293)) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

fof(f_174_3,plain,
    ! [U_293,U_294] :
      ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_294,U_293)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_293))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_294),U_293))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_293)) ),
    inference(definitional_conversion,[status(esa)],[f_174_2]) ).

cnf(f_174_4,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_294,U_293)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_293))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_294),U_293))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_293)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

fof(f_175_1,plain,
    ! [X_3,A_1] :
      ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_3,A_1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A_1))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_71_card__insert__disjoint]) ).

fof(f_175_2,plain,
    ! [U_296,U_295] :
      ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_296,U_295)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_295))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_296),U_295))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_295)) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

fof(f_175_3,plain,
    ! [U_295,U_296] :
      ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_296,U_295)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_295))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_296),U_295))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_295)) ),
    inference(definitional_conversion,[status(esa)],[f_175_2]) ).

cnf(f_175_4,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_296,U_295)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_295))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_296),U_295))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_295)) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

fof(f_176_1,plain,
    ! [Q_1,Pa] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,Pa),Q_1))))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_72_finite__Collect__conjI]) ).

fof(f_176_2,plain,
    ! [U_298,U_297] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,U_297),U_298))))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_298)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_297))) ) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

fof(f_176_3,plain,
    ( ! [U_297,U_298] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_298)))
        | ~ sP6(U_297,U_298) )
    & ! [U_297,U_298] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_297)))
        | ~ sP6(U_297,U_298) )
    & ! [U_297,U_298] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,U_297),U_298))))
        | sP6(U_297,U_298) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_176_2]) ).

cnf(f_176_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,U_297),U_298))))
    | sP6(U_297,U_298) ),
    inference(clausify,[status(thm)],[f_176_3]) ).

cnf(f_176_5,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_297)))
    | ~ sP6(U_297,U_298) ),
    inference(clausify,[status(thm)],[f_176_3]) ).

cnf(f_176_6,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_298)))
    | ~ sP6(U_297,U_298) ),
    inference(clausify,[status(thm)],[f_176_3]) ).

fof(f_177_1,plain,
    ! [Q_1,Pa] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,Pa),Q_1))))
      | ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1)))
        & ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_73_finite__Collect__conjI]) ).

fof(f_177_2,plain,
    ! [U_300,U_299] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,U_299),U_300))))
      | ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_300)))
        & ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_299))) ) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

fof(f_177_3,plain,
    ( ! [U_299,U_300] :
        ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_300)))
        | ~ sP7(U_299,U_300) )
    & ! [U_299,U_300] :
        ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_299)))
        | ~ sP7(U_299,U_300) )
    & ! [U_299,U_300] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,U_299),U_300))))
        | sP7(U_299,U_300) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_177_2]) ).

cnf(f_177_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,U_299),U_300))))
    | sP7(U_299,U_300) ),
    inference(clausify,[status(thm)],[f_177_3]) ).

cnf(f_177_5,plain,
    ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_299)))
    | ~ sP7(U_299,U_300) ),
    inference(clausify,[status(thm)],[f_177_3]) ).

cnf(f_177_6,plain,
    ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_300)))
    | ~ sP7(U_299,U_300) ),
    inference(clausify,[status(thm)],[f_177_3]) ).

fof(f_178_1,plain,
    ! [Q_1,Pa] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,Pa),Q_1))))
      | ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
        & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_74_finite__Collect__conjI]) ).

fof(f_178_2,plain,
    ! [U_302,U_301] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,U_301),U_302))))
      | ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_302)))
        & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_301))) ) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

fof(f_178_3,plain,
    ( ! [U_301,U_302] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_302)))
        | ~ sP8(U_301,U_302) )
    & ! [U_301,U_302] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_301)))
        | ~ sP8(U_301,U_302) )
    & ! [U_301,U_302] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,U_301),U_302))))
        | sP8(U_301,U_302) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_178_2]) ).

cnf(f_178_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,U_301),U_302))))
    | sP8(U_301,U_302) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

cnf(f_178_5,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_301)))
    | ~ sP8(U_301,U_302) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

cnf(f_178_6,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_302)))
    | ~ sP8(U_301,U_302) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

fof(f_179_1,plain,
    ! [Q_1,Pa] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,Pa),Q_1))))
      | ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1)))
        & ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_75_finite__Collect__conjI]) ).

fof(f_179_2,plain,
    ! [U_304,U_303] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,U_303),U_304))))
      | ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_304)))
        & ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_303))) ) ),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

fof(f_179_3,plain,
    ( ! [U_303,U_304] :
        ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_304)))
        | ~ sP9(U_303,U_304) )
    & ! [U_303,U_304] :
        ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_303)))
        | ~ sP9(U_303,U_304) )
    & ! [U_303,U_304] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,U_303),U_304))))
        | sP9(U_303,U_304) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_179_2]) ).

cnf(f_179_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,U_303),U_304))))
    | sP9(U_303,U_304) ),
    inference(clausify,[status(thm)],[f_179_3]) ).

cnf(f_179_5,plain,
    ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_303)))
    | ~ sP9(U_303,U_304) ),
    inference(clausify,[status(thm)],[f_179_3]) ).

cnf(f_179_6,plain,
    ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_304)))
    | ~ sP9(U_303,U_304) ),
    inference(clausify,[status(thm)],[f_179_3]) ).

fof(f_180_1,plain,
    ! [Q_1,Pa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,Pa),Q_1))))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
        & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_76_finite__Collect__conjI]) ).

fof(f_180_2,plain,
    ! [U_306,U_305] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,U_305),U_306))))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_306)))
        & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_305))) ) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

fof(f_180_3,plain,
    ( ! [U_305,U_306] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_306)))
        | ~ sP10(U_305,U_306) )
    & ! [U_305,U_306] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_305)))
        | ~ sP10(U_305,U_306) )
    & ! [U_305,U_306] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,U_305),U_306))))
        | sP10(U_305,U_306) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_180_2]) ).

cnf(f_180_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,U_305),U_306))))
    | sP10(U_305,U_306) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_5,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_305)))
    | ~ sP10(U_305,U_306) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

cnf(f_180_6,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_306)))
    | ~ sP10(U_305,U_306) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

fof(f_181_1,plain,
    ! [Q_1,Pa] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),Q_1))))
      | ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1)))
        & ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_77_finite__Collect__conjI]) ).

fof(f_181_2,plain,
    ! [U_308,U_307] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_307),U_308))))
      | ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_308)))
        & ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_307))) ) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

fof(f_181_3,plain,
    ( ! [U_307,U_308] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_308)))
        | ~ sP11(U_307,U_308) )
    & ! [U_307,U_308] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_307)))
        | ~ sP11(U_307,U_308) )
    & ! [U_307,U_308] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_307),U_308))))
        | sP11(U_307,U_308) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_181_2]) ).

cnf(f_181_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_307),U_308))))
    | sP11(U_307,U_308) ),
    inference(clausify,[status(thm)],[f_181_3]) ).

cnf(f_181_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_307)))
    | ~ sP11(U_307,U_308) ),
    inference(clausify,[status(thm)],[f_181_3]) ).

cnf(f_181_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_308)))
    | ~ sP11(U_307,U_308) ),
    inference(clausify,[status(thm)],[f_181_3]) ).

fof(f_182_1,plain,
    ! [N,M] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(M),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) ),
    inference(fof_nnf,[status(thm)],[fact_78_Suc__diff__le]) ).

fof(f_182_2,plain,
    ! [U_310,U_309] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_309)),U_310) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(U_309),U_310))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_310),U_309)) ),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

fof(f_182_3,plain,
    ! [U_309,U_310] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_309)),U_310) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(U_309),U_310))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_310),U_309)) ),
    inference(definitional_conversion,[status(esa)],[f_182_2]) ).

cnf(f_182_4,plain,
    ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_309)),U_310) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(U_309),U_310))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_310),U_309)) ),
    inference(clausify,[status(thm)],[f_182_3]) ).

fof(f_183_1,plain,
    ! [K_2] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),K_2)))),
    inference(fof_nnf,[status(thm)],[fact_79_finite__Collect__le__nat]) ).

fof(f_183_2,plain,
    ! [U_311] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_311)))),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

fof(f_183_3,plain,
    ! [U_311] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_311)))),
    inference(definitional_conversion,[status(esa)],[f_183_2]) ).

cnf(f_183_4,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_311)))),
    inference(clausify,[status(thm)],[f_183_3]) ).

fof(f_184_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_80_card__Collect__le__nat]) ).

fof(f_184_2,plain,
    ! [U_312] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_312))) = hAPP_nat_nat(suc,U_312),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

fof(f_184_3,plain,
    ! [U_312] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_312))) = hAPP_nat_nat(suc,U_312),
    inference(definitional_conversion,[status(esa)],[f_184_2]) ).

cnf(f_184_4,plain,
    hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_312))) = hAPP_nat_nat(suc,U_312),
    inference(clausify,[status(thm)],[f_184_3]) ).

fof(f_185_1,plain,
    ! [X,Y] :
      ( X = Y
      | hAPP_nat_nat(suc,X) != hAPP_nat_nat(suc,Y) ),
    inference(fof_nnf,[status(thm)],[fact_81_Suc__inject]) ).

fof(f_185_2,plain,
    ! [U_314,U_313] :
      ( U_314 = U_313
      | hAPP_nat_nat(suc,U_314) != hAPP_nat_nat(suc,U_313) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

fof(f_185_3,plain,
    ! [U_313,U_314] :
      ( U_314 = U_313
      | hAPP_nat_nat(suc,U_314) != hAPP_nat_nat(suc,U_313) ),
    inference(definitional_conversion,[status(esa)],[f_185_2]) ).

cnf(f_185_4,plain,
    ( U_314 = U_313
    | hAPP_nat_nat(suc,U_314) != hAPP_nat_nat(suc,U_313) ),
    inference(clausify,[status(thm)],[f_185_3]) ).

fof(f_186_1,plain,
    ! [Nat_3,Nat_2] :
      ( ( hAPP_nat_nat(suc,Nat_3) = hAPP_nat_nat(suc,Nat_2)
        | Nat_3 != Nat_2 )
      & ( Nat_3 = Nat_2
        | hAPP_nat_nat(suc,Nat_3) != hAPP_nat_nat(suc,Nat_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_82_nat_Oinject]) ).

fof(f_186_2,plain,
    ! [U_316,U_315] :
      ( ( hAPP_nat_nat(suc,U_316) = hAPP_nat_nat(suc,U_315)
        | U_316 != U_315 )
      & ( U_316 = U_315
        | hAPP_nat_nat(suc,U_316) != hAPP_nat_nat(suc,U_315) ) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

fof(f_186_3,plain,
    ( ! [U_320,U_318] :
        ( hAPP_nat_nat(suc,U_320) = hAPP_nat_nat(suc,U_318)
        | U_320 != U_318 )
    & ! [U_319,U_317] :
        ( U_319 = U_317
        | hAPP_nat_nat(suc,U_319) != hAPP_nat_nat(suc,U_317) ) ),
    inference(miniscope,[status(thm)],[f_186_2]) ).

fof(f_186_4,plain,
    ( ! [U_318,U_320] :
        ( hAPP_nat_nat(suc,U_320) = hAPP_nat_nat(suc,U_318)
        | U_320 != U_318 )
    & ! [U_319,U_317] :
        ( U_319 = U_317
        | hAPP_nat_nat(suc,U_319) != hAPP_nat_nat(suc,U_317) ) ),
    inference(definitional_conversion,[status(esa)],[f_186_3]) ).

cnf(f_186_5,plain,
    ( U_319 = U_317
    | hAPP_nat_nat(suc,U_319) != hAPP_nat_nat(suc,U_317) ),
    inference(clausify,[status(thm)],[f_186_4]) ).

cnf(f_186_6,plain,
    ( hAPP_nat_nat(suc,U_320) = hAPP_nat_nat(suc,U_318)
    | U_320 != U_318 ),
    inference(clausify,[status(thm)],[f_186_4]) ).

fof(f_187_1,plain,
    ! [N] : hAPP_nat_nat(suc,N) != N,
    inference(fof_nnf,[status(thm)],[fact_83_Suc__n__not__n]) ).

fof(f_187_2,plain,
    ! [U_321] : hAPP_nat_nat(suc,U_321) != U_321,
    inference(variable_rename,[status(thm)],[f_187_1]) ).

fof(f_187_3,plain,
    ! [U_321] : hAPP_nat_nat(suc,U_321) != U_321,
    inference(definitional_conversion,[status(esa)],[f_187_2]) ).

cnf(f_187_4,plain,
    hAPP_nat_nat(suc,U_321) != U_321,
    inference(clausify,[status(thm)],[f_187_3]) ).

fof(f_188_1,plain,
    ! [N] : N != hAPP_nat_nat(suc,N),
    inference(fof_nnf,[status(thm)],[fact_84_n__not__Suc__n]) ).

fof(f_188_2,plain,
    ! [U_322] : U_322 != hAPP_nat_nat(suc,U_322),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

fof(f_188_3,plain,
    ! [U_322] : U_322 != hAPP_nat_nat(suc,U_322),
    inference(definitional_conversion,[status(esa)],[f_188_2]) ).

cnf(f_188_4,plain,
    U_322 != hAPP_nat_nat(suc,U_322),
    inference(clausify,[status(thm)],[f_188_3]) ).

fof(f_189_1,plain,
    ! [M,N] :
      ( M = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_85_le__antisym]) ).

fof(f_189_2,plain,
    ! [U_324,U_323] :
      ( U_324 = U_323
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_323),U_324))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_324),U_323)) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

fof(f_189_3,plain,
    ! [U_323,U_324] :
      ( U_324 = U_323
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_323),U_324))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_324),U_323)) ),
    inference(definitional_conversion,[status(esa)],[f_189_2]) ).

cnf(f_189_4,plain,
    ( U_324 = U_323
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_323),U_324))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_324),U_323)) ),
    inference(clausify,[status(thm)],[f_189_3]) ).

fof(f_190_1,plain,
    ! [K,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),K))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_86_le__trans]) ).

fof(f_190_2,plain,
    ! [U_327,U_326,U_325] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_326),U_327))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_325),U_327))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_326),U_325)) ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

fof(f_190_3,plain,
    ! [U_325,U_326,U_327] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_326),U_327))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_325),U_327))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_326),U_325)) ),
    inference(definitional_conversion,[status(esa)],[f_190_2]) ).

cnf(f_190_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_326),U_327))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_325),U_327))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_326),U_325)) ),
    inference(clausify,[status(thm)],[f_190_3]) ).

fof(f_191_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
      | M != N ),
    inference(fof_nnf,[status(thm)],[fact_87_eq__imp__le]) ).

fof(f_191_2,plain,
    ! [U_329,U_328] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_329),U_328))
      | U_329 != U_328 ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

fof(f_191_3,plain,
    ! [U_329,U_328] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_329),U_328))
      | U_329 != U_328 ),
    inference(definitional_conversion,[status(esa)],[f_191_2]) ).

cnf(f_191_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_329),U_328))
    | U_329 != U_328 ),
    inference(clausify,[status(thm)],[f_191_3]) ).

fof(f_192_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_88_nat__le__linear]) ).

fof(f_192_2,plain,
    ! [U_331,U_330] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_330),U_331))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_331),U_330)) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

fof(f_192_3,plain,
    ! [U_330,U_331] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_330),U_331))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_331),U_330)) ),
    inference(definitional_conversion,[status(esa)],[f_192_2]) ).

cnf(f_192_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_330),U_331))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_331),U_330)) ),
    inference(clausify,[status(thm)],[f_192_3]) ).

fof(f_193_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N)),
    inference(fof_nnf,[status(thm)],[fact_89_le__refl]) ).

fof(f_193_2,plain,
    ! [U_332] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_332),U_332)),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

fof(f_193_3,plain,
    ! [U_332] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_332),U_332)),
    inference(definitional_conversion,[status(esa)],[f_193_2]) ).

cnf(f_193_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_332),U_332)),
    inference(clausify,[status(thm)],[f_193_3]) ).

fof(f_194_1,plain,
    ! [I,J_2,K] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J_2)),K) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),K)),J_2),
    inference(fof_nnf,[status(thm)],[fact_90_diff__commute]) ).

fof(f_194_2,plain,
    ! [U_335,U_334,U_333] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_335),U_334)),U_333) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_335),U_333)),U_334),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

fof(f_194_3,plain,
    ! [U_333,U_334,U_335] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_335),U_334)),U_333) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_335),U_333)),U_334),
    inference(definitional_conversion,[status(esa)],[f_194_2]) ).

cnf(f_194_4,plain,
    hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_335),U_334)),U_333) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_335),U_333)),U_334),
    inference(clausify,[status(thm)],[f_194_3]) ).

fof(f_195_1,plain,
    ! [Pa,Q_1] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,Pa),Q_1))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1)))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,Pa),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_91_finite__Collect__disjI]) ).

fof(f_195_2,plain,
    ! [U_337,U_336] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_337),U_336))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_336)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_337))) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_336)))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_337))) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_337),U_336)))) ) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

fof(f_195_3,plain,
    ( ! [U_341,U_339] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_341),U_339))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_339)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_341))) )
    & ! [U_340,U_338] :
        ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_338)))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_340))) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_340),U_338)))) ) ),
    inference(miniscope,[status(thm)],[f_195_2]) ).

fof(f_195_4,plain,
    ( ! [U_340,U_338] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_338)))
        | ~ sP12(U_340,U_338) )
    & ! [U_340,U_338] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_340)))
        | ~ sP12(U_340,U_338) )
    & ! [U_339,U_341] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_341),U_339))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_339)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_341))) )
    & ! [U_340,U_338] :
        ( sP12(U_340,U_338)
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_340),U_338)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_195_3]) ).

cnf(f_195_5,plain,
    ( sP12(U_340,U_338)
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_340),U_338)))) ),
    inference(clausify,[status(thm)],[f_195_4]) ).

cnf(f_195_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_341),U_339))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_339)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_341))) ),
    inference(clausify,[status(thm)],[f_195_4]) ).

cnf(f_195_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_340)))
    | ~ sP12(U_340,U_338) ),
    inference(clausify,[status(thm)],[f_195_4]) ).

cnf(f_195_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_338)))
    | ~ sP12(U_340,U_338) ),
    inference(clausify,[status(thm)],[f_195_4]) ).

fof(f_196_1,plain,
    ! [Pa,Q_1] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,Pa),Q_1))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) )
      & ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1)))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) )
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,Pa),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_92_finite__Collect__disjI]) ).

fof(f_196_2,plain,
    ! [U_343,U_342] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_343),U_342))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_342)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_343))) )
      & ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_342)))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_343))) )
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_343),U_342)))) ) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

fof(f_196_3,plain,
    ( ! [U_347,U_345] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_347),U_345))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_345)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_347))) )
    & ! [U_346,U_344] :
        ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_344)))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_346))) )
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_346),U_344)))) ) ),
    inference(miniscope,[status(thm)],[f_196_2]) ).

fof(f_196_4,plain,
    ( ! [U_344,U_346] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_344)))
        | ~ sP13(U_344,U_346) )
    & ! [U_344,U_346] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_346)))
        | ~ sP13(U_344,U_346) )
    & ! [U_345,U_347] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_347),U_345))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_345)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_347))) )
    & ! [U_344,U_346] :
        ( sP13(U_344,U_346)
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_346),U_344)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_196_3]) ).

cnf(f_196_5,plain,
    ( sP13(U_344,U_346)
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_346),U_344)))) ),
    inference(clausify,[status(thm)],[f_196_4]) ).

cnf(f_196_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_347),U_345))))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_345)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_347))) ),
    inference(clausify,[status(thm)],[f_196_4]) ).

cnf(f_196_7,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_346)))
    | ~ sP13(U_344,U_346) ),
    inference(clausify,[status(thm)],[f_196_4]) ).

cnf(f_196_8,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_344)))
    | ~ sP13(U_344,U_346) ),
    inference(clausify,[status(thm)],[f_196_4]) ).

fof(f_197_1,plain,
    ! [Pa,Q_1] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,Pa),Q_1))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) )
      & ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,Pa),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_93_finite__Collect__disjI]) ).

fof(f_197_2,plain,
    ! [U_349,U_348] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_349),U_348))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_348)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_349))) )
      & ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_348)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_349))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_349),U_348)))) ) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

fof(f_197_3,plain,
    ( ! [U_353,U_351] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_353),U_351))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_351)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_353))) )
    & ! [U_352,U_350] :
        ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_350)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_352))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_352),U_350)))) ) ),
    inference(miniscope,[status(thm)],[f_197_2]) ).

fof(f_197_4,plain,
    ( ! [U_352,U_350] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_350)))
        | ~ sP14(U_352,U_350) )
    & ! [U_352,U_350] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_352)))
        | ~ sP14(U_352,U_350) )
    & ! [U_351,U_353] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_353),U_351))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_351)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_353))) )
    & ! [U_352,U_350] :
        ( sP14(U_352,U_350)
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_352),U_350)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_197_3]) ).

cnf(f_197_5,plain,
    ( sP14(U_352,U_350)
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_352),U_350)))) ),
    inference(clausify,[status(thm)],[f_197_4]) ).

cnf(f_197_6,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_353),U_351))))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_351)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_353))) ),
    inference(clausify,[status(thm)],[f_197_4]) ).

cnf(f_197_7,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_352)))
    | ~ sP14(U_352,U_350) ),
    inference(clausify,[status(thm)],[f_197_4]) ).

cnf(f_197_8,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_350)))
    | ~ sP14(U_352,U_350) ),
    inference(clausify,[status(thm)],[f_197_4]) ).

fof(f_198_1,plain,
    ! [Pa,Q_1] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,Pa),Q_1))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) )
      & ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1)))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) )
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,Pa),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_94_finite__Collect__disjI]) ).

fof(f_198_2,plain,
    ! [U_355,U_354] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_355),U_354))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_354)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_355))) )
      & ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_354)))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_355))) )
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_355),U_354)))) ) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

fof(f_198_3,plain,
    ( ! [U_359,U_357] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_359),U_357))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_357)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_359))) )
    & ! [U_358,U_356] :
        ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_356)))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_358))) )
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_358),U_356)))) ) ),
    inference(miniscope,[status(thm)],[f_198_2]) ).

fof(f_198_4,plain,
    ( ! [U_358,U_356] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_356)))
        | ~ sP15(U_358,U_356) )
    & ! [U_358,U_356] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_358)))
        | ~ sP15(U_358,U_356) )
    & ! [U_357,U_359] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_359),U_357))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_357)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_359))) )
    & ! [U_358,U_356] :
        ( sP15(U_358,U_356)
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_358),U_356)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_198_3]) ).

cnf(f_198_5,plain,
    ( sP15(U_358,U_356)
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_358),U_356)))) ),
    inference(clausify,[status(thm)],[f_198_4]) ).

cnf(f_198_6,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_359),U_357))))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_357)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_359))) ),
    inference(clausify,[status(thm)],[f_198_4]) ).

cnf(f_198_7,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_358)))
    | ~ sP15(U_358,U_356) ),
    inference(clausify,[status(thm)],[f_198_4]) ).

cnf(f_198_8,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_356)))
    | ~ sP15(U_358,U_356) ),
    inference(clausify,[status(thm)],[f_198_4]) ).

fof(f_199_1,plain,
    ! [Pa,Q_1] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Q_1))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_95_finite__Collect__disjI]) ).

fof(f_199_2,plain,
    ! [U_361,U_360] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_361),U_360))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_360)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_361))) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_360)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_361))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_361),U_360)))) ) ),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

fof(f_199_3,plain,
    ( ! [U_365,U_363] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_365),U_363))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_363)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_365))) )
    & ! [U_364,U_362] :
        ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_362)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_364))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_364),U_362)))) ) ),
    inference(miniscope,[status(thm)],[f_199_2]) ).

fof(f_199_4,plain,
    ( ! [U_362,U_364] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_362)))
        | ~ sP16(U_362,U_364) )
    & ! [U_362,U_364] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_364)))
        | ~ sP16(U_362,U_364) )
    & ! [U_363,U_365] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_365),U_363))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_363)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_365))) )
    & ! [U_362,U_364] :
        ( sP16(U_362,U_364)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_364),U_362)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_199_3]) ).

cnf(f_199_5,plain,
    ( sP16(U_362,U_364)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_364),U_362)))) ),
    inference(clausify,[status(thm)],[f_199_4]) ).

cnf(f_199_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_365),U_363))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_363)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_365))) ),
    inference(clausify,[status(thm)],[f_199_4]) ).

cnf(f_199_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_364)))
    | ~ sP16(U_362,U_364) ),
    inference(clausify,[status(thm)],[f_199_4]) ).

cnf(f_199_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_362)))
    | ~ sP16(U_362,U_364) ),
    inference(clausify,[status(thm)],[f_199_4]) ).

fof(f_200_1,plain,
    ! [Pa,Q_1] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,Pa),Q_1))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) )
      & ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1)))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,Pa),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_96_finite__Collect__disjI]) ).

fof(f_200_2,plain,
    ! [U_367,U_366] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_367),U_366))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_366)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_367))) )
      & ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_366)))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_367))) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_367),U_366)))) ) ),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

fof(f_200_3,plain,
    ( ! [U_371,U_369] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_371),U_369))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_369)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_371))) )
    & ! [U_370,U_368] :
        ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_368)))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_370))) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_370),U_368)))) ) ),
    inference(miniscope,[status(thm)],[f_200_2]) ).

fof(f_200_4,plain,
    ( ! [U_370,U_368] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_368)))
        | ~ sP17(U_370,U_368) )
    & ! [U_370,U_368] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_370)))
        | ~ sP17(U_370,U_368) )
    & ! [U_371,U_369] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_371),U_369))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_369)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_371))) )
    & ! [U_370,U_368] :
        ( sP17(U_370,U_368)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_370),U_368)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_200_3]) ).

cnf(f_200_5,plain,
    ( sP17(U_370,U_368)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_370),U_368)))) ),
    inference(clausify,[status(thm)],[f_200_4]) ).

cnf(f_200_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_371),U_369))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_369)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_371))) ),
    inference(clausify,[status(thm)],[f_200_4]) ).

cnf(f_200_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_370)))
    | ~ sP17(U_370,U_368) ),
    inference(clausify,[status(thm)],[f_200_4]) ).

cnf(f_200_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_368)))
    | ~ sP17(U_370,U_368) ),
    inference(clausify,[status(thm)],[f_200_4]) ).

fof(f_201_1,plain,
    ! [A_3,A_1] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_3,A_1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) )
      & ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_3,A_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_97_finite__insert]) ).

fof(f_201_2,plain,
    ! [U_373,U_372] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_373,U_372)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_372)) )
      & ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_372))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_373,U_372))) ) ),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

fof(f_201_3,plain,
    ( ! [U_377,U_375] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_377,U_375)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_375)) )
    & ! [U_376,U_374] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_374))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_376,U_374))) ) ),
    inference(miniscope,[status(thm)],[f_201_2]) ).

fof(f_201_4,plain,
    ( ! [U_375,U_377] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_377,U_375)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_375)) )
    & ! [U_374,U_376] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_374))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_376,U_374))) ) ),
    inference(definitional_conversion,[status(esa)],[f_201_3]) ).

cnf(f_201_5,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_374))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_376,U_374))) ),
    inference(clausify,[status(thm)],[f_201_4]) ).

cnf(f_201_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_377,U_375)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_375)) ),
    inference(clausify,[status(thm)],[f_201_4]) ).

fof(f_202_1,plain,
    ! [A_3,A_1] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_3,A_1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) )
      & ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_3,A_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_98_finite__insert]) ).

fof(f_202_2,plain,
    ! [U_379,U_378] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_379,U_378)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_378)) )
      & ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_378))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_379,U_378))) ) ),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

fof(f_202_3,plain,
    ( ! [U_383,U_381] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_383,U_381)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_381)) )
    & ! [U_382,U_380] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_380))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_382,U_380))) ) ),
    inference(miniscope,[status(thm)],[f_202_2]) ).

fof(f_202_4,plain,
    ( ! [U_381,U_383] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_383,U_381)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_381)) )
    & ! [U_382,U_380] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_380))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_382,U_380))) ) ),
    inference(definitional_conversion,[status(esa)],[f_202_3]) ).

cnf(f_202_5,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_380))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_382,U_380))) ),
    inference(clausify,[status(thm)],[f_202_4]) ).

cnf(f_202_6,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_383,U_381)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_381)) ),
    inference(clausify,[status(thm)],[f_202_4]) ).

fof(f_203_1,plain,
    ! [A_3,A_1] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_3,A_1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) )
      & ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_3,A_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_99_finite__insert]) ).

fof(f_203_2,plain,
    ! [U_385,U_384] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_385,U_384)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_384)) )
      & ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_384))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_385,U_384))) ) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

fof(f_203_3,plain,
    ( ! [U_389,U_387] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_389,U_387)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_387)) )
    & ! [U_388,U_386] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_386))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_388,U_386))) ) ),
    inference(miniscope,[status(thm)],[f_203_2]) ).

fof(f_203_4,plain,
    ( ! [U_387,U_389] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_389,U_387)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_387)) )
    & ! [U_388,U_386] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_386))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_388,U_386))) ) ),
    inference(definitional_conversion,[status(esa)],[f_203_3]) ).

cnf(f_203_5,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_386))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_388,U_386))) ),
    inference(clausify,[status(thm)],[f_203_4]) ).

cnf(f_203_6,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_389,U_387)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_387)) ),
    inference(clausify,[status(thm)],[f_203_4]) ).

fof(f_204_1,plain,
    ! [A_3,A_1] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_3,A_1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) )
      & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_3,A_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_100_finite__insert]) ).

fof(f_204_2,plain,
    ! [U_391,U_390] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_391,U_390)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_390)) )
      & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_390))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_391,U_390))) ) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

fof(f_204_3,plain,
    ( ! [U_395,U_393] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_395,U_393)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_393)) )
    & ! [U_394,U_392] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_392))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_394,U_392))) ) ),
    inference(miniscope,[status(thm)],[f_204_2]) ).

fof(f_204_4,plain,
    ( ! [U_393,U_395] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_395,U_393)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_393)) )
    & ! [U_394,U_392] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_392))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_394,U_392))) ) ),
    inference(definitional_conversion,[status(esa)],[f_204_3]) ).

cnf(f_204_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_392))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_394,U_392))) ),
    inference(clausify,[status(thm)],[f_204_4]) ).

cnf(f_204_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_395,U_393)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_393)) ),
    inference(clausify,[status(thm)],[f_204_4]) ).

fof(f_205_1,plain,
    ! [A_3,A_1] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_3,A_1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) )
      & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_3,A_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_101_finite__insert]) ).

fof(f_205_2,plain,
    ! [U_397,U_396] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_397,U_396)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_396)) )
      & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_396))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_397,U_396))) ) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

fof(f_205_3,plain,
    ( ! [U_401,U_399] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_401,U_399)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_399)) )
    & ! [U_400,U_398] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_398))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_400,U_398))) ) ),
    inference(miniscope,[status(thm)],[f_205_2]) ).

fof(f_205_4,plain,
    ( ! [U_399,U_401] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_401,U_399)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_399)) )
    & ! [U_400,U_398] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_398))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_400,U_398))) ) ),
    inference(definitional_conversion,[status(esa)],[f_205_3]) ).

cnf(f_205_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_398))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_400,U_398))) ),
    inference(clausify,[status(thm)],[f_205_4]) ).

cnf(f_205_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_401,U_399)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_399)) ),
    inference(clausify,[status(thm)],[f_205_4]) ).

fof(f_206_1,plain,
    ! [A_3,A_1] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_3,A_1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) )
      & ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_3,A_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_102_finite__insert]) ).

fof(f_206_2,plain,
    ! [U_403,U_402] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_403,U_402)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_402)) )
      & ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_402))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_403,U_402))) ) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

fof(f_206_3,plain,
    ( ! [U_407,U_405] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_407,U_405)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_405)) )
    & ! [U_406,U_404] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_404))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_406,U_404))) ) ),
    inference(miniscope,[status(thm)],[f_206_2]) ).

fof(f_206_4,plain,
    ( ! [U_405,U_407] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_407,U_405)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_405)) )
    & ! [U_406,U_404] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_404))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_406,U_404))) ) ),
    inference(definitional_conversion,[status(esa)],[f_206_3]) ).

cnf(f_206_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_404))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_406,U_404))) ),
    inference(clausify,[status(thm)],[f_206_4]) ).

cnf(f_206_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_407,U_405)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_405)) ),
    inference(clausify,[status(thm)],[f_206_4]) ).

fof(f_207_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_103_finite__subset]) ).

fof(f_207_2,plain,
    ! [U_409,U_408] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_409))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_408))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_409),U_408)) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

fof(f_207_3,plain,
    ! [U_408,U_409] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_409))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_408))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_409),U_408)) ),
    inference(definitional_conversion,[status(esa)],[f_207_2]) ).

cnf(f_207_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_409))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_408))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_409),U_408)) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

fof(f_208_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_104_finite__subset]) ).

fof(f_208_2,plain,
    ! [U_411,U_410] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_411))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_410))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_411),U_410)) ),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

fof(f_208_3,plain,
    ! [U_411,U_410] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_411))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_410))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_411),U_410)) ),
    inference(definitional_conversion,[status(esa)],[f_208_2]) ).

cnf(f_208_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_411))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_410))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_411),U_410)) ),
    inference(clausify,[status(thm)],[f_208_3]) ).

fof(f_209_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_105_finite__subset]) ).

fof(f_209_2,plain,
    ! [U_413,U_412] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_413))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_412))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_413),U_412)) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

fof(f_209_3,plain,
    ! [U_413,U_412] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_413))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_412))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_413),U_412)) ),
    inference(definitional_conversion,[status(esa)],[f_209_2]) ).

cnf(f_209_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_413))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_412))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_413),U_412)) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

fof(f_210_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_106_finite__subset]) ).

fof(f_210_2,plain,
    ! [U_415,U_414] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_415))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_414))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_415),U_414)) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

fof(f_210_3,plain,
    ! [U_415,U_414] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_415))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_414))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_415),U_414)) ),
    inference(definitional_conversion,[status(esa)],[f_210_2]) ).

cnf(f_210_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_415))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_414))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_415),U_414)) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

fof(f_211_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_107_finite__subset]) ).

fof(f_211_2,plain,
    ! [U_417,U_416] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_417))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_416))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_417),U_416)) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

fof(f_211_3,plain,
    ! [U_417,U_416] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_417))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_416))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_417),U_416)) ),
    inference(definitional_conversion,[status(esa)],[f_211_2]) ).

cnf(f_211_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_417))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_416))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_417),U_416)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

fof(f_212_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_108_finite__subset]) ).

fof(f_212_2,plain,
    ! [U_419,U_418] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_419))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_418))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_419),U_418)) ),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

fof(f_212_3,plain,
    ! [U_419,U_418] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_419))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_418))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_419),U_418)) ),
    inference(definitional_conversion,[status(esa)],[f_212_2]) ).

cnf(f_212_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_419))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_418))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_419),U_418)) ),
    inference(clausify,[status(thm)],[f_212_3]) ).

fof(f_213_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_109_rev__finite__subset]) ).

fof(f_213_2,plain,
    ! [U_421,U_420] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_421))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_421),U_420))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_420)) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

fof(f_213_3,plain,
    ! [U_420,U_421] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_421))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_421),U_420))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_420)) ),
    inference(definitional_conversion,[status(esa)],[f_213_2]) ).

cnf(f_213_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_421))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_421),U_420))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_420)) ),
    inference(clausify,[status(thm)],[f_213_3]) ).

fof(f_214_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_110_rev__finite__subset]) ).

fof(f_214_2,plain,
    ! [U_423,U_422] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_423))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_423),U_422))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_422)) ),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

fof(f_214_3,plain,
    ! [U_423,U_422] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_423))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_423),U_422))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_422)) ),
    inference(definitional_conversion,[status(esa)],[f_214_2]) ).

cnf(f_214_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_423))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_423),U_422))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_422)) ),
    inference(clausify,[status(thm)],[f_214_3]) ).

fof(f_215_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_111_rev__finite__subset]) ).

fof(f_215_2,plain,
    ! [U_425,U_424] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_425))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_425),U_424))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_424)) ),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

fof(f_215_3,plain,
    ! [U_424,U_425] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_425))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_425),U_424))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_424)) ),
    inference(definitional_conversion,[status(esa)],[f_215_2]) ).

cnf(f_215_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_425))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_425),U_424))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_424)) ),
    inference(clausify,[status(thm)],[f_215_3]) ).

fof(f_216_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_112_rev__finite__subset]) ).

fof(f_216_2,plain,
    ! [U_427,U_426] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_427))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_427),U_426))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_426)) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

fof(f_216_3,plain,
    ! [U_426,U_427] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_427))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_427),U_426))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_426)) ),
    inference(definitional_conversion,[status(esa)],[f_216_2]) ).

cnf(f_216_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_427))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_427),U_426))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_426)) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

fof(f_217_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_113_rev__finite__subset]) ).

fof(f_217_2,plain,
    ! [U_429,U_428] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_429))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_429),U_428))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_428)) ),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

fof(f_217_3,plain,
    ! [U_428,U_429] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_429))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_429),U_428))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_428)) ),
    inference(definitional_conversion,[status(esa)],[f_217_2]) ).

cnf(f_217_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_429))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_429),U_428))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_428)) ),
    inference(clausify,[status(thm)],[f_217_3]) ).

fof(f_218_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_114_rev__finite__subset]) ).

fof(f_218_2,plain,
    ! [U_431,U_430] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_431))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_431),U_430))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_430)) ),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

fof(f_218_3,plain,
    ! [U_430,U_431] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_431))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_431),U_430))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_430)) ),
    inference(definitional_conversion,[status(esa)],[f_218_2]) ).

cnf(f_218_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_431))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_431),U_430))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_430)) ),
    inference(clausify,[status(thm)],[f_218_3]) ).

fof(f_219_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_115_Suc__leD]) ).

fof(f_219_2,plain,
    ! [U_433,U_432] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_433),U_432))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_433)),U_432)) ),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

fof(f_219_3,plain,
    ! [U_432,U_433] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_433),U_432))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_433)),U_432)) ),
    inference(definitional_conversion,[status(esa)],[f_219_2]) ).

cnf(f_219_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_433),U_432))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_433)),U_432)) ),
    inference(clausify,[status(thm)],[f_219_3]) ).

fof(f_220_1,plain,
    ! [M,N] :
      ( M = hAPP_nat_nat(suc,N)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_116_le__SucE]) ).

fof(f_220_2,plain,
    ! [U_435,U_434] :
      ( U_435 = hAPP_nat_nat(suc,U_434)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_435),U_434))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_435),hAPP_nat_nat(suc,U_434))) ),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

fof(f_220_3,plain,
    ! [U_434,U_435] :
      ( U_435 = hAPP_nat_nat(suc,U_434)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_435),U_434))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_435),hAPP_nat_nat(suc,U_434))) ),
    inference(definitional_conversion,[status(esa)],[f_220_2]) ).

cnf(f_220_4,plain,
    ( U_435 = hAPP_nat_nat(suc,U_434)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_435),U_434))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_435),hAPP_nat_nat(suc,U_434))) ),
    inference(clausify,[status(thm)],[f_220_3]) ).

fof(f_221_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_117_le__SucI]) ).

fof(f_221_2,plain,
    ! [U_437,U_436] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_437),hAPP_nat_nat(suc,U_436)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_437),U_436)) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

fof(f_221_3,plain,
    ! [U_437,U_436] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_437),hAPP_nat_nat(suc,U_436)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_437),U_436)) ),
    inference(definitional_conversion,[status(esa)],[f_221_2]) ).

cnf(f_221_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_437),hAPP_nat_nat(suc,U_436)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_437),U_436)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

fof(f_222_1,plain,
    ! [Na,M_1] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_118_Suc__le__mono]) ).

fof(f_222_2,plain,
    ! [U_439,U_438] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_439)),hAPP_nat_nat(suc,U_438)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_439),U_438)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_439),U_438))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_439)),hAPP_nat_nat(suc,U_438))) ) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

fof(f_222_3,plain,
    ( ! [U_443,U_441] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_443)),hAPP_nat_nat(suc,U_441)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_443),U_441)) )
    & ! [U_442,U_440] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_442),U_440))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_442)),hAPP_nat_nat(suc,U_440))) ) ),
    inference(miniscope,[status(thm)],[f_222_2]) ).

fof(f_222_4,plain,
    ( ! [U_441,U_443] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_443)),hAPP_nat_nat(suc,U_441)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_443),U_441)) )
    & ! [U_442,U_440] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_442),U_440))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_442)),hAPP_nat_nat(suc,U_440))) ) ),
    inference(definitional_conversion,[status(esa)],[f_222_3]) ).

cnf(f_222_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_442),U_440))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_442)),hAPP_nat_nat(suc,U_440))) ),
    inference(clausify,[status(thm)],[f_222_4]) ).

cnf(f_222_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_443)),hAPP_nat_nat(suc,U_441)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_443),U_441)) ),
    inference(clausify,[status(thm)],[f_222_4]) ).

fof(f_223_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,Na)))
        | ( M_1 != hAPP_nat_nat(suc,Na)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) )
      & ( M_1 = hAPP_nat_nat(suc,Na)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_119_le__Suc__eq]) ).

fof(f_223_2,plain,
    ! [U_445,U_444] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_445),hAPP_nat_nat(suc,U_444)))
        | ( U_445 != hAPP_nat_nat(suc,U_444)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_445),U_444)) ) )
      & ( U_445 = hAPP_nat_nat(suc,U_444)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_445),U_444))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_445),hAPP_nat_nat(suc,U_444))) ) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

fof(f_223_3,plain,
    ( ! [U_449,U_447] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_449),hAPP_nat_nat(suc,U_447)))
        | ( U_449 != hAPP_nat_nat(suc,U_447)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_449),U_447)) ) )
    & ! [U_448,U_446] :
        ( U_448 = hAPP_nat_nat(suc,U_446)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_448),U_446))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_448),hAPP_nat_nat(suc,U_446))) ) ),
    inference(miniscope,[status(thm)],[f_223_2]) ).

fof(f_223_4,plain,
    ( ! [U_447,U_449] :
        ( U_449 != hAPP_nat_nat(suc,U_447)
        | ~ sP18(U_447,U_449) )
    & ! [U_447,U_449] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_449),U_447))
        | ~ sP18(U_447,U_449) )
    & ! [U_447,U_449] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_449),hAPP_nat_nat(suc,U_447)))
        | sP18(U_447,U_449) )
    & ! [U_448,U_446] :
        ( U_448 = hAPP_nat_nat(suc,U_446)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_448),U_446))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_448),hAPP_nat_nat(suc,U_446))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_223_3]) ).

cnf(f_223_5,plain,
    ( U_448 = hAPP_nat_nat(suc,U_446)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_448),U_446))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_448),hAPP_nat_nat(suc,U_446))) ),
    inference(clausify,[status(thm)],[f_223_4]) ).

cnf(f_223_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_449),hAPP_nat_nat(suc,U_447)))
    | sP18(U_447,U_449) ),
    inference(clausify,[status(thm)],[f_223_4]) ).

cnf(f_223_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_449),U_447))
    | ~ sP18(U_447,U_449) ),
    inference(clausify,[status(thm)],[f_223_4]) ).

cnf(f_223_8,plain,
    ( U_449 != hAPP_nat_nat(suc,U_447)
    | ~ sP18(U_447,U_449) ),
    inference(clausify,[status(thm)],[f_223_4]) ).

fof(f_224_1,plain,
    ! [M_1,Na] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_120_not__less__eq__eq]) ).

fof(f_224_2,plain,
    ! [U_451,U_450] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_451),U_450))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_450)),U_451)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_450)),U_451))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_451),U_450)) ) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

fof(f_224_3,plain,
    ( ! [U_455,U_453] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_455),U_453))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_453)),U_455)) )
    & ! [U_454,U_452] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_452)),U_454))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_454),U_452)) ) ),
    inference(miniscope,[status(thm)],[f_224_2]) ).

fof(f_224_4,plain,
    ( ! [U_453,U_455] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_455),U_453))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_453)),U_455)) )
    & ! [U_452,U_454] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_452)),U_454))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_454),U_452)) ) ),
    inference(definitional_conversion,[status(esa)],[f_224_3]) ).

cnf(f_224_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_452)),U_454))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_454),U_452)) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

cnf(f_224_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_455),U_453))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_453)),U_455)) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

fof(f_225_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_121_Suc__n__not__le__n]) ).

fof(f_225_2,plain,
    ! [U_456] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_456)),U_456)),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

fof(f_225_3,plain,
    ! [U_456] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_456)),U_456)),
    inference(definitional_conversion,[status(esa)],[f_225_2]) ).

cnf(f_225_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_456)),U_456)),
    inference(clausify,[status(thm)],[f_225_3]) ).

fof(f_226_1,plain,
    ! [M,N,K] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),N)),hAPP_nat_nat(suc,K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),N)),K),
    inference(fof_nnf,[status(thm)],[fact_122_Suc__diff__diff]) ).

fof(f_226_2,plain,
    ! [U_459,U_458,U_457] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_459)),U_458)),hAPP_nat_nat(suc,U_457)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_459),U_458)),U_457),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

fof(f_226_3,plain,
    ! [U_459,U_458,U_457] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_459)),U_458)),hAPP_nat_nat(suc,U_457)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_459),U_458)),U_457),
    inference(definitional_conversion,[status(esa)],[f_226_2]) ).

cnf(f_226_4,plain,
    hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_459)),U_458)),hAPP_nat_nat(suc,U_457)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_459),U_458)),U_457),
    inference(clausify,[status(thm)],[f_226_3]) ).

fof(f_227_1,plain,
    ! [M,N] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(minus_minus_nat(M),N),
    inference(fof_nnf,[status(thm)],[fact_123_diff__Suc__Suc]) ).

fof(f_227_2,plain,
    ! [U_461,U_460] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_461)),hAPP_nat_nat(suc,U_460)) = hAPP_nat_nat(minus_minus_nat(U_461),U_460),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

fof(f_227_3,plain,
    ! [U_460,U_461] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_461)),hAPP_nat_nat(suc,U_460)) = hAPP_nat_nat(minus_minus_nat(U_461),U_460),
    inference(definitional_conversion,[status(esa)],[f_227_2]) ).

cnf(f_227_4,plain,
    hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_461)),hAPP_nat_nat(suc,U_460)) = hAPP_nat_nat(minus_minus_nat(U_461),U_460),
    inference(clausify,[status(thm)],[f_227_3]) ).

fof(f_228_1,plain,
    ! [Na,K_2,M_1] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_1),K_2)),hAPP_nat_nat(minus_minus_nat(Na),K_2)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_1),K_2)),hAPP_nat_nat(minus_minus_nat(Na),K_2))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_124_le__diff__iff]) ).

fof(f_228_2,plain,
    ! [U_464,U_463,U_462] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_462),U_463)),hAPP_nat_nat(minus_minus_nat(U_464),U_463)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_462),U_464)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_462),U_464))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_462),U_463)),hAPP_nat_nat(minus_minus_nat(U_464),U_463))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_463),U_464))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_463),U_462)) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

fof(f_228_3,plain,
    ( ! [U_462,U_463,U_464] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_462),U_463)),hAPP_nat_nat(minus_minus_nat(U_464),U_463)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_462),U_464))
        | ~ sP19(U_462,U_463,U_464) )
    & ! [U_462,U_463,U_464] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_462),U_464))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_462),U_463)),hAPP_nat_nat(minus_minus_nat(U_464),U_463)))
        | ~ sP19(U_462,U_463,U_464) )
    & ! [U_462,U_463,U_464] :
        ( sP19(U_462,U_463,U_464)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_463),U_464))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_463),U_462)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_228_2]) ).

cnf(f_228_4,plain,
    ( sP19(U_462,U_463,U_464)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_463),U_464))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_463),U_462)) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_462),U_464))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_462),U_463)),hAPP_nat_nat(minus_minus_nat(U_464),U_463)))
    | ~ sP19(U_462,U_463,U_464) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_462),U_463)),hAPP_nat_nat(minus_minus_nat(U_464),U_463)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_462),U_464))
    | ~ sP19(U_462,U_463,U_464) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

fof(f_229_1,plain,
    ! [N,K,M] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),K)),hAPP_nat_nat(minus_minus_nat(N),K)) = hAPP_nat_nat(minus_minus_nat(M),N)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M)) ),
    inference(fof_nnf,[status(thm)],[fact_125_Nat_Odiff__diff__eq]) ).

fof(f_229_2,plain,
    ! [U_467,U_466,U_465] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_465),U_466)),hAPP_nat_nat(minus_minus_nat(U_467),U_466)) = hAPP_nat_nat(minus_minus_nat(U_465),U_467)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_466),U_467))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_466),U_465)) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

fof(f_229_3,plain,
    ! [U_465,U_466,U_467] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_465),U_466)),hAPP_nat_nat(minus_minus_nat(U_467),U_466)) = hAPP_nat_nat(minus_minus_nat(U_465),U_467)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_466),U_467))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_466),U_465)) ),
    inference(definitional_conversion,[status(esa)],[f_229_2]) ).

cnf(f_229_4,plain,
    ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_465),U_466)),hAPP_nat_nat(minus_minus_nat(U_467),U_466)) = hAPP_nat_nat(minus_minus_nat(U_465),U_467)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_466),U_467))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_466),U_465)) ),
    inference(clausify,[status(thm)],[f_229_3]) ).

fof(f_230_1,plain,
    ! [Na,K_2,M_1] :
      ( ( ( hAPP_nat_nat(minus_minus_nat(M_1),K_2) = hAPP_nat_nat(minus_minus_nat(Na),K_2)
          | M_1 != Na )
        & ( M_1 = Na
          | hAPP_nat_nat(minus_minus_nat(M_1),K_2) != hAPP_nat_nat(minus_minus_nat(Na),K_2) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_126_eq__diff__iff]) ).

fof(f_230_2,plain,
    ! [U_470,U_469,U_468] :
      ( ( ( hAPP_nat_nat(minus_minus_nat(U_468),U_469) = hAPP_nat_nat(minus_minus_nat(U_470),U_469)
          | U_468 != U_470 )
        & ( U_468 = U_470
          | hAPP_nat_nat(minus_minus_nat(U_468),U_469) != hAPP_nat_nat(minus_minus_nat(U_470),U_469) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_469),U_470))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_469),U_468)) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

fof(f_230_3,plain,
    ( ! [U_468,U_469,U_470] :
        ( hAPP_nat_nat(minus_minus_nat(U_468),U_469) = hAPP_nat_nat(minus_minus_nat(U_470),U_469)
        | U_468 != U_470
        | ~ sP20(U_468,U_469,U_470) )
    & ! [U_468,U_469,U_470] :
        ( U_468 = U_470
        | hAPP_nat_nat(minus_minus_nat(U_468),U_469) != hAPP_nat_nat(minus_minus_nat(U_470),U_469)
        | ~ sP20(U_468,U_469,U_470) )
    & ! [U_468,U_469,U_470] :
        ( sP20(U_468,U_469,U_470)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_469),U_470))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_469),U_468)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_230_2]) ).

cnf(f_230_4,plain,
    ( sP20(U_468,U_469,U_470)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_469),U_470))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_469),U_468)) ),
    inference(clausify,[status(thm)],[f_230_3]) ).

cnf(f_230_5,plain,
    ( U_468 = U_470
    | hAPP_nat_nat(minus_minus_nat(U_468),U_469) != hAPP_nat_nat(minus_minus_nat(U_470),U_469)
    | ~ sP20(U_468,U_469,U_470) ),
    inference(clausify,[status(thm)],[f_230_3]) ).

cnf(f_230_6,plain,
    ( hAPP_nat_nat(minus_minus_nat(U_468),U_469) = hAPP_nat_nat(minus_minus_nat(U_470),U_469)
    | U_468 != U_470
    | ~ sP20(U_468,U_469,U_470) ),
    inference(clausify,[status(thm)],[f_230_3]) ).

fof(f_231_1,plain,
    ! [I,N] :
      ( hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(minus_minus_nat(N),I)) = I
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N)) ),
    inference(fof_nnf,[status(thm)],[fact_127_diff__diff__cancel]) ).

fof(f_231_2,plain,
    ! [U_472,U_471] :
      ( hAPP_nat_nat(minus_minus_nat(U_471),hAPP_nat_nat(minus_minus_nat(U_471),U_472)) = U_472
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_472),U_471)) ),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

fof(f_231_3,plain,
    ! [U_472,U_471] :
      ( hAPP_nat_nat(minus_minus_nat(U_471),hAPP_nat_nat(minus_minus_nat(U_471),U_472)) = U_472
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_472),U_471)) ),
    inference(definitional_conversion,[status(esa)],[f_231_2]) ).

cnf(f_231_4,plain,
    ( hAPP_nat_nat(minus_minus_nat(U_471),hAPP_nat_nat(minus_minus_nat(U_471),U_472)) = U_472
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_472),U_471)) ),
    inference(clausify,[status(thm)],[f_231_3]) ).

fof(f_232_1,plain,
    ! [L,M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),L)),hAPP_nat_nat(minus_minus_nat(N),L)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_128_diff__le__mono]) ).

fof(f_232_2,plain,
    ! [U_475,U_474,U_473] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_474),U_475)),hAPP_nat_nat(minus_minus_nat(U_473),U_475)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_474),U_473)) ),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

fof(f_232_3,plain,
    ! [U_474,U_473,U_475] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_474),U_475)),hAPP_nat_nat(minus_minus_nat(U_473),U_475)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_474),U_473)) ),
    inference(definitional_conversion,[status(esa)],[f_232_2]) ).

cnf(f_232_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_474),U_475)),hAPP_nat_nat(minus_minus_nat(U_473),U_475)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_474),U_473)) ),
    inference(clausify,[status(thm)],[f_232_3]) ).

fof(f_233_1,plain,
    ! [L,M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L),N)),hAPP_nat_nat(minus_minus_nat(L),M)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_129_diff__le__mono2]) ).

fof(f_233_2,plain,
    ! [U_478,U_477,U_476] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_478),U_476)),hAPP_nat_nat(minus_minus_nat(U_478),U_477)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_477),U_476)) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

fof(f_233_3,plain,
    ! [U_476,U_477,U_478] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_478),U_476)),hAPP_nat_nat(minus_minus_nat(U_478),U_477)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_477),U_476)) ),
    inference(definitional_conversion,[status(esa)],[f_233_2]) ).

cnf(f_233_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_478),U_476)),hAPP_nat_nat(minus_minus_nat(U_478),U_477)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_477),U_476)) ),
    inference(clausify,[status(thm)],[f_233_3]) ).

fof(f_234_1,plain,
    ! [M,N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),N)),M)),
    inference(fof_nnf,[status(thm)],[fact_130_diff__le__self]) ).

fof(f_234_2,plain,
    ! [U_480,U_479] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_480),U_479)),U_480)),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

fof(f_234_3,plain,
    ! [U_479,U_480] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_480),U_479)),U_480)),
    inference(definitional_conversion,[status(esa)],[f_234_2]) ).

cnf(f_234_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_480),U_479)),U_480)),
    inference(clausify,[status(thm)],[f_234_3]) ).

fof(f_235_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_a_a(F,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_131_finite__surj]) ).

fof(f_235_2,plain,
    ! [U_483,U_482,U_481] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_483))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_483),image_a_a(U_482,U_481)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_481)) ),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

fof(f_235_3,plain,
    ! [U_481,U_482,U_483] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_483))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_483),image_a_a(U_482,U_481)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_481)) ),
    inference(definitional_conversion,[status(esa)],[f_235_2]) ).

cnf(f_235_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_483))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_483),image_a_a(U_482,U_481)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_481)) ),
    inference(clausify,[status(thm)],[f_235_3]) ).

fof(f_236_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_nat_bool_a(F,A_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_132_finite__surj]) ).

fof(f_236_2,plain,
    ! [U_486,U_485,U_484] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_486))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_486),image_fun_nat_bool_a(U_485,U_484)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_484)) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

fof(f_236_3,plain,
    ! [U_485,U_484,U_486] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_486))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_486),image_fun_nat_bool_a(U_485,U_484)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_484)) ),
    inference(definitional_conversion,[status(esa)],[f_236_2]) ).

cnf(f_236_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_486))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_486),image_fun_nat_bool_a(U_485,U_484)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_484)) ),
    inference(clausify,[status(thm)],[f_236_3]) ).

fof(f_237_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_876012084bool_a(F,A_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_133_finite__surj]) ).

fof(f_237_2,plain,
    ! [U_489,U_488,U_487] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_489))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_489),image_876012084bool_a(U_488,U_487)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_487)) ),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

fof(f_237_3,plain,
    ! [U_487,U_488,U_489] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_489))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_489),image_876012084bool_a(U_488,U_487)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_487)) ),
    inference(definitional_conversion,[status(esa)],[f_237_2]) ).

cnf(f_237_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_489))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_489),image_876012084bool_a(U_488,U_487)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_487)) ),
    inference(clausify,[status(thm)],[f_237_3]) ).

fof(f_238_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_a_bool_a(F,A_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_134_finite__surj]) ).

fof(f_238_2,plain,
    ! [U_492,U_491,U_490] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_492))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_492),image_fun_a_bool_a(U_491,U_490)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_490)) ),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

fof(f_238_3,plain,
    ! [U_490,U_491,U_492] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_492))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_492),image_fun_a_bool_a(U_491,U_490)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_490)) ),
    inference(definitional_conversion,[status(esa)],[f_238_2]) ).

cnf(f_238_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_492))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_492),image_fun_a_bool_a(U_491,U_490)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_490)) ),
    inference(clausify,[status(thm)],[f_238_3]) ).

fof(f_239_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_2129980159t_bool(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_135_finite__surj]) ).

fof(f_239_2,plain,
    ! [U_495,U_494,U_493] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_495))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_495),image_2129980159t_bool(U_494,U_493)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_493)) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

fof(f_239_3,plain,
    ! [U_493,U_494,U_495] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_495))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_495),image_2129980159t_bool(U_494,U_493)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_493)) ),
    inference(definitional_conversion,[status(esa)],[f_239_2]) ).

cnf(f_239_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_495))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_495),image_2129980159t_bool(U_494,U_493)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_493)) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

fof(f_240_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_47868345e_bool(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_136_finite__surj]) ).

fof(f_240_2,plain,
    ! [U_498,U_497,U_496] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_498))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_498),image_47868345e_bool(U_497,U_496)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_496)) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

fof(f_240_3,plain,
    ! [U_497,U_496,U_498] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_498))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_498),image_47868345e_bool(U_497,U_496)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_496)) ),
    inference(definitional_conversion,[status(esa)],[f_240_2]) ).

cnf(f_240_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_498))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_498),image_47868345e_bool(U_497,U_496)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_496)) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

fof(f_241_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_112932426a_bool(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_137_finite__surj]) ).

fof(f_241_2,plain,
    ! [U_501,U_500,U_499] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_501))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_501),image_112932426a_bool(U_500,U_499)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_499)) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

fof(f_241_3,plain,
    ! [U_499,U_500,U_501] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_501))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_501),image_112932426a_bool(U_500,U_499)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_499)) ),
    inference(definitional_conversion,[status(esa)],[f_241_2]) ).

cnf(f_241_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_501))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_501),image_112932426a_bool(U_500,U_499)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_499)) ),
    inference(clausify,[status(thm)],[f_241_3]) ).

fof(f_242_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_pname_pname(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_138_finite__surj]) ).

fof(f_242_2,plain,
    ! [U_504,U_503,U_502] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_504))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_504),image_pname_pname(U_503,U_502)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_502)) ),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

fof(f_242_3,plain,
    ! [U_502,U_503,U_504] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_504))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_504),image_pname_pname(U_503,U_502)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_502)) ),
    inference(definitional_conversion,[status(esa)],[f_242_2]) ).

cnf(f_242_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_504))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_504),image_pname_pname(U_503,U_502)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_502)) ),
    inference(clausify,[status(thm)],[f_242_3]) ).

fof(f_243_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_pname_nat(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_139_finite__surj]) ).

fof(f_243_2,plain,
    ! [U_507,U_506,U_505] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_507))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_507),image_pname_nat(U_506,U_505)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_505)) ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

fof(f_243_3,plain,
    ! [U_505,U_506,U_507] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_507))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_507),image_pname_nat(U_506,U_505)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_505)) ),
    inference(definitional_conversion,[status(esa)],[f_243_2]) ).

cnf(f_243_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_507))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_507),image_pname_nat(U_506,U_505)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_505)) ),
    inference(clausify,[status(thm)],[f_243_3]) ).

fof(f_244_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_140_finite__surj]) ).

fof(f_244_2,plain,
    ! [U_510,U_509,U_508] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_510))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_510),image_nat_a(U_509,U_508)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_508)) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

fof(f_244_3,plain,
    ! [U_508,U_509,U_510] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_510))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_510),image_nat_a(U_509,U_508)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_508)) ),
    inference(definitional_conversion,[status(esa)],[f_244_2]) ).

cnf(f_244_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_510))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_510),image_nat_a(U_509,U_508)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_508)) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

fof(f_245_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_26036933t_bool(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_141_finite__surj]) ).

fof(f_245_2,plain,
    ! [U_513,U_512,U_511] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_513))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_513),image_26036933t_bool(U_512,U_511)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_511)) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ! [U_511,U_512,U_513] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_513))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_513),image_26036933t_bool(U_512,U_511)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_511)) ),
    inference(definitional_conversion,[status(esa)],[f_245_2]) ).

cnf(f_245_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_513))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_513),image_26036933t_bool(U_512,U_511)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_511)) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

fof(f_246_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_1655916159e_bool(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_142_finite__surj]) ).

fof(f_246_2,plain,
    ! [U_516,U_515,U_514] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_516))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_516),image_1655916159e_bool(U_515,U_514)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_514)) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

fof(f_246_3,plain,
    ! [U_514,U_515,U_516] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_516))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_516),image_1655916159e_bool(U_515,U_514)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_514)) ),
    inference(definitional_conversion,[status(esa)],[f_246_2]) ).

cnf(f_246_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_516))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_516),image_1655916159e_bool(U_515,U_514)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_514)) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

fof(f_247_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_nat_fun_a_bool(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_143_finite__surj]) ).

fof(f_247_2,plain,
    ! [U_519,U_518,U_517] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_519))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_519),image_nat_fun_a_bool(U_518,U_517)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_517)) ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

fof(f_247_3,plain,
    ! [U_517,U_518,U_519] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_519))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_519),image_nat_fun_a_bool(U_518,U_517)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_517)) ),
    inference(definitional_conversion,[status(esa)],[f_247_2]) ).

cnf(f_247_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_519))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_519),image_nat_fun_a_bool(U_518,U_517)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_517)) ),
    inference(clausify,[status(thm)],[f_247_3]) ).

fof(f_248_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_nat_pname(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_144_finite__surj]) ).

fof(f_248_2,plain,
    ! [U_522,U_521,U_520] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_522))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_522),image_nat_pname(U_521,U_520)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_520)) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

fof(f_248_3,plain,
    ! [U_520,U_521,U_522] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_522))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_522),image_nat_pname(U_521,U_520)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_520)) ),
    inference(definitional_conversion,[status(esa)],[f_248_2]) ).

cnf(f_248_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_522))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_522),image_nat_pname(U_521,U_520)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_520)) ),
    inference(clausify,[status(thm)],[f_248_3]) ).

fof(f_249_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_nat_nat(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_145_finite__surj]) ).

fof(f_249_2,plain,
    ! [U_525,U_524,U_523] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_525))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_525),image_nat_nat(U_524,U_523)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_523)) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

fof(f_249_3,plain,
    ! [U_523,U_524,U_525] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_525))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_525),image_nat_nat(U_524,U_523)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_523)) ),
    inference(definitional_conversion,[status(esa)],[f_249_2]) ).

cnf(f_249_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_525))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_525),image_nat_nat(U_524,U_523)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_523)) ),
    inference(clausify,[status(thm)],[f_249_3]) ).

fof(f_250_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_146_finite__surj]) ).

fof(f_250_2,plain,
    ! [U_528,U_527,U_526] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_528))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_528),image_a_pname(U_527,U_526)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_526)) ),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

fof(f_250_3,plain,
    ! [U_526,U_527,U_528] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_528))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_528),image_a_pname(U_527,U_526)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_526)) ),
    inference(definitional_conversion,[status(esa)],[f_250_2]) ).

cnf(f_250_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_528))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_528),image_a_pname(U_527,U_526)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_526)) ),
    inference(clausify,[status(thm)],[f_250_3]) ).

fof(f_251_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1921560913_pname(F,A_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_147_finite__surj]) ).

fof(f_251_2,plain,
    ! [U_531,U_530,U_529] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_531))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_531),image_1921560913_pname(U_530,U_529)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_529)) ),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

fof(f_251_3,plain,
    ! [U_530,U_529,U_531] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_531))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_531),image_1921560913_pname(U_530,U_529)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_529)) ),
    inference(definitional_conversion,[status(esa)],[f_251_2]) ).

cnf(f_251_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_531))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_531),image_1921560913_pname(U_530,U_529)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_529)) ),
    inference(clausify,[status(thm)],[f_251_3]) ).

fof(f_252_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1283814551_pname(F,A_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_148_finite__surj]) ).

fof(f_252_2,plain,
    ! [U_534,U_533,U_532] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_534))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_534),image_1283814551_pname(U_533,U_532)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_532)) ),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

fof(f_252_3,plain,
    ! [U_532,U_533,U_534] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_534))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_534),image_1283814551_pname(U_533,U_532)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_532)) ),
    inference(definitional_conversion,[status(esa)],[f_252_2]) ).

cnf(f_252_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_534))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_534),image_1283814551_pname(U_533,U_532)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_532)) ),
    inference(clausify,[status(thm)],[f_252_3]) ).

fof(f_253_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1854862208_pname(F,A_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_149_finite__surj]) ).

fof(f_253_2,plain,
    ! [U_537,U_536,U_535] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_537))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_537),image_1854862208_pname(U_536,U_535)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_535)) ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

fof(f_253_3,plain,
    ! [U_535,U_536,U_537] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_537))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_537),image_1854862208_pname(U_536,U_535)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_535)) ),
    inference(definitional_conversion,[status(esa)],[f_253_2]) ).

cnf(f_253_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_537))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_537),image_1854862208_pname(U_536,U_535)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_535)) ),
    inference(clausify,[status(thm)],[f_253_3]) ).

fof(f_254_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_150_finite__surj]) ).

fof(f_254_2,plain,
    ! [U_540,U_539,U_538] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_540))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_540),image_a_nat(U_539,U_538)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_538)) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

fof(f_254_3,plain,
    ! [U_538,U_539,U_540] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_540))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_540),image_a_nat(U_539,U_538)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_538)) ),
    inference(definitional_conversion,[status(esa)],[f_254_2]) ).

cnf(f_254_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_540))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_540),image_a_nat(U_539,U_538)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_538)) ),
    inference(clausify,[status(thm)],[f_254_3]) ).

fof(f_255_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_496248727ol_nat(F,A_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_151_finite__surj]) ).

fof(f_255_2,plain,
    ! [U_543,U_542,U_541] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_543))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_543),image_496248727ol_nat(U_542,U_541)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_541)) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

fof(f_255_3,plain,
    ! [U_542,U_541,U_543] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_543))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_543),image_496248727ol_nat(U_542,U_541)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_541)) ),
    inference(definitional_conversion,[status(esa)],[f_255_2]) ).

cnf(f_255_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_543))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_543),image_496248727ol_nat(U_542,U_541)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_541)) ),
    inference(clausify,[status(thm)],[f_255_3]) ).

fof(f_256_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_1551609309ol_nat(F,A_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_152_finite__surj]) ).

fof(f_256_2,plain,
    ! [U_546,U_545,U_544] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_546))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_546),image_1551609309ol_nat(U_545,U_544)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_544)) ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

fof(f_256_3,plain,
    ! [U_544,U_545,U_546] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_546))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_546),image_1551609309ol_nat(U_545,U_544)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_544)) ),
    inference(definitional_conversion,[status(esa)],[f_256_2]) ).

cnf(f_256_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_546))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_546),image_1551609309ol_nat(U_545,U_544)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_544)) ),
    inference(clausify,[status(thm)],[f_256_3]) ).

fof(f_257_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_fun_a_bool_nat(F,A_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_153_finite__surj]) ).

fof(f_257_2,plain,
    ! [U_549,U_548,U_547] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_549))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_549),image_fun_a_bool_nat(U_548,U_547)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_547)) ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

fof(f_257_3,plain,
    ! [U_547,U_548,U_549] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_549))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_549),image_fun_a_bool_nat(U_548,U_547)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_547)) ),
    inference(definitional_conversion,[status(esa)],[f_257_2]) ).

cnf(f_257_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_549))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_549),image_fun_a_bool_nat(U_548,U_547)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_547)) ),
    inference(clausify,[status(thm)],[f_257_3]) ).

fof(f_258_1,plain,
    ! [B_6,F,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_154_finite__surj]) ).

fof(f_258_2,plain,
    ! [U_552,U_551,U_550] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_552))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_552),image_pname_a(U_551,U_550)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_550)) ),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

fof(f_258_3,plain,
    ! [U_551,U_552,U_550] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_552))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_552),image_pname_a(U_551,U_550)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_550)) ),
    inference(definitional_conversion,[status(esa)],[f_258_2]) ).

cnf(f_258_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_552))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_552),image_pname_a(U_551,U_550)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_550)) ),
    inference(clausify,[status(thm)],[f_258_3]) ).

fof(f_259_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_fun_nat_bool_a(F,C_7)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_7))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_7),A_1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_nat_bool_a(F,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ is_fun_a_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_155_finite__subset__image]) ).

fof(f_259_2,plain,
    ! [U_556,U_555,U_554] :
      ( ? [U_553] :
          ( U_554 = image_fun_nat_bool_a(U_556,U_553)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_553))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_553),U_555)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_554),image_fun_nat_bool_a(U_556,U_555)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_554))
      | ~ is_fun_a_bool(U_554) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

fof(f_259_3,plain,
    ! [U_556,U_555,U_554] :
      ( ( U_554 = image_fun_nat_bool_a(U_556,sK1(U_556,U_555,U_554))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK1(U_556,U_555,U_554)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK1(U_556,U_555,U_554)),U_555)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_554),image_fun_nat_bool_a(U_556,U_555)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_554))
      | ~ is_fun_a_bool(U_554) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_553,sK1(U_556,U_555,U_554))],[f_259_2]) ).

fof(f_259_4,plain,
    ( ! [U_554,U_555,U_556] :
        ( U_554 = image_fun_nat_bool_a(U_556,sK1(U_556,U_555,U_554))
        | ~ sP21(U_554,U_555,U_556) )
    & ! [U_554,U_555,U_556] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK1(U_556,U_555,U_554)))
        | ~ sP21(U_554,U_555,U_556) )
    & ! [U_554,U_555,U_556] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK1(U_556,U_555,U_554)),U_555))
        | ~ sP21(U_554,U_555,U_556) )
    & ! [U_554,U_555,U_556] :
        ( sP21(U_554,U_555,U_556)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_554),image_fun_nat_bool_a(U_556,U_555)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_554))
        | ~ is_fun_a_bool(U_554) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_259_3]) ).

cnf(f_259_5,plain,
    ( sP21(U_554,U_555,U_556)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_554),image_fun_nat_bool_a(U_556,U_555)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_554))
    | ~ is_fun_a_bool(U_554) ),
    inference(clausify,[status(thm)],[f_259_4]) ).

cnf(f_259_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK1(U_556,U_555,U_554)),U_555))
    | ~ sP21(U_554,U_555,U_556) ),
    inference(clausify,[status(thm)],[f_259_4]) ).

cnf(f_259_7,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK1(U_556,U_555,U_554)))
    | ~ sP21(U_554,U_555,U_556) ),
    inference(clausify,[status(thm)],[f_259_4]) ).

cnf(f_259_8,plain,
    ( U_554 = image_fun_nat_bool_a(U_556,sK1(U_556,U_555,U_554))
    | ~ sP21(U_554,U_555,U_556) ),
    inference(clausify,[status(thm)],[f_259_4]) ).

fof(f_260_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_876012084bool_a(F,C_7)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_7))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_7),A_1))
          & is_fun1661590463l_bool(C_7) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_876012084bool_a(F,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ is_fun_a_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_156_finite__subset__image]) ).

fof(f_260_2,plain,
    ! [U_560,U_559,U_558] :
      ( ? [U_557] :
          ( U_558 = image_876012084bool_a(U_560,U_557)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_557))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_557),U_559))
          & is_fun1661590463l_bool(U_557) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_558),image_876012084bool_a(U_560,U_559)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_558))
      | ~ is_fun_a_bool(U_558) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

fof(f_260_3,plain,
    ! [U_560,U_559,U_558] :
      ( ( U_558 = image_876012084bool_a(U_560,sK2(U_560,U_559,U_558))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK2(U_560,U_559,U_558)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK2(U_560,U_559,U_558)),U_559))
        & is_fun1661590463l_bool(sK2(U_560,U_559,U_558)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_558),image_876012084bool_a(U_560,U_559)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_558))
      | ~ is_fun_a_bool(U_558) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_557,sK2(U_560,U_559,U_558))],[f_260_2]) ).

fof(f_260_4,plain,
    ( ! [U_558,U_560,U_559] :
        ( U_558 = image_876012084bool_a(U_560,sK2(U_560,U_559,U_558))
        | ~ sP22(U_558,U_560,U_559) )
    & ! [U_558,U_560,U_559] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK2(U_560,U_559,U_558)))
        | ~ sP22(U_558,U_560,U_559) )
    & ! [U_558,U_560,U_559] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK2(U_560,U_559,U_558)),U_559))
        | ~ sP22(U_558,U_560,U_559) )
    & ! [U_558,U_560,U_559] :
        ( is_fun1661590463l_bool(sK2(U_560,U_559,U_558))
        | ~ sP22(U_558,U_560,U_559) )
    & ! [U_558,U_560,U_559] :
        ( sP22(U_558,U_560,U_559)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_558),image_876012084bool_a(U_560,U_559)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_558))
        | ~ is_fun_a_bool(U_558) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_260_3]) ).

cnf(f_260_5,plain,
    ( sP22(U_558,U_560,U_559)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_558),image_876012084bool_a(U_560,U_559)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_558))
    | ~ is_fun_a_bool(U_558) ),
    inference(clausify,[status(thm)],[f_260_4]) ).

cnf(f_260_6,plain,
    ( is_fun1661590463l_bool(sK2(U_560,U_559,U_558))
    | ~ sP22(U_558,U_560,U_559) ),
    inference(clausify,[status(thm)],[f_260_4]) ).

cnf(f_260_7,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK2(U_560,U_559,U_558)),U_559))
    | ~ sP22(U_558,U_560,U_559) ),
    inference(clausify,[status(thm)],[f_260_4]) ).

cnf(f_260_8,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK2(U_560,U_559,U_558)))
    | ~ sP22(U_558,U_560,U_559) ),
    inference(clausify,[status(thm)],[f_260_4]) ).

cnf(f_260_9,plain,
    ( U_558 = image_876012084bool_a(U_560,sK2(U_560,U_559,U_558))
    | ~ sP22(U_558,U_560,U_559) ),
    inference(clausify,[status(thm)],[f_260_4]) ).

fof(f_261_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_fun_a_bool_a(F,C_7)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_7))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_7),A_1))
          & is_fun949378684l_bool(C_7) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_fun_a_bool_a(F,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ is_fun_a_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_157_finite__subset__image]) ).

fof(f_261_2,plain,
    ! [U_564,U_563,U_562] :
      ( ? [U_561] :
          ( U_562 = image_fun_a_bool_a(U_564,U_561)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_561))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_561),U_563))
          & is_fun949378684l_bool(U_561) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_562),image_fun_a_bool_a(U_564,U_563)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_562))
      | ~ is_fun_a_bool(U_562) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

fof(f_261_3,plain,
    ! [U_564,U_563,U_562] :
      ( ( U_562 = image_fun_a_bool_a(U_564,sK3(U_564,U_563,U_562))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK3(U_564,U_563,U_562)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK3(U_564,U_563,U_562)),U_563))
        & is_fun949378684l_bool(sK3(U_564,U_563,U_562)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_562),image_fun_a_bool_a(U_564,U_563)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_562))
      | ~ is_fun_a_bool(U_562) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_561,sK3(U_564,U_563,U_562))],[f_261_2]) ).

fof(f_261_4,plain,
    ( ! [U_563,U_562,U_564] :
        ( U_562 = image_fun_a_bool_a(U_564,sK3(U_564,U_563,U_562))
        | ~ sP23(U_563,U_562,U_564) )
    & ! [U_563,U_562,U_564] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK3(U_564,U_563,U_562)))
        | ~ sP23(U_563,U_562,U_564) )
    & ! [U_563,U_562,U_564] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK3(U_564,U_563,U_562)),U_563))
        | ~ sP23(U_563,U_562,U_564) )
    & ! [U_563,U_562,U_564] :
        ( is_fun949378684l_bool(sK3(U_564,U_563,U_562))
        | ~ sP23(U_563,U_562,U_564) )
    & ! [U_563,U_562,U_564] :
        ( sP23(U_563,U_562,U_564)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_562),image_fun_a_bool_a(U_564,U_563)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_562))
        | ~ is_fun_a_bool(U_562) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_261_3]) ).

cnf(f_261_5,plain,
    ( sP23(U_563,U_562,U_564)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_562),image_fun_a_bool_a(U_564,U_563)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_562))
    | ~ is_fun_a_bool(U_562) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_6,plain,
    ( is_fun949378684l_bool(sK3(U_564,U_563,U_562))
    | ~ sP23(U_563,U_562,U_564) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_7,plain,
    ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK3(U_564,U_563,U_562)),U_563))
    | ~ sP23(U_563,U_562,U_564) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_8,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK3(U_564,U_563,U_562)))
    | ~ sP23(U_563,U_562,U_564) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_9,plain,
    ( U_562 = image_fun_a_bool_a(U_564,sK3(U_564,U_563,U_562))
    | ~ sP23(U_563,U_562,U_564) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

fof(f_262_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_a_a(F,C_7)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1))
          & is_fun_a_bool(C_7) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_a_a(F,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ is_fun_a_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_158_finite__subset__image]) ).

fof(f_262_2,plain,
    ! [U_568,U_567,U_566] :
      ( ? [U_565] :
          ( U_566 = image_a_a(U_568,U_565)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_565))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_565),U_567))
          & is_fun_a_bool(U_565) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_566),image_a_a(U_568,U_567)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_566))
      | ~ is_fun_a_bool(U_566) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

fof(f_262_3,plain,
    ! [U_568,U_567,U_566] :
      ( ( U_566 = image_a_a(U_568,sK4(U_568,U_567,U_566))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK4(U_568,U_567,U_566)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK4(U_568,U_567,U_566)),U_567))
        & is_fun_a_bool(sK4(U_568,U_567,U_566)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_566),image_a_a(U_568,U_567)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_566))
      | ~ is_fun_a_bool(U_566) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_565,sK4(U_568,U_567,U_566))],[f_262_2]) ).

fof(f_262_4,plain,
    ( ! [U_566,U_567,U_568] :
        ( U_566 = image_a_a(U_568,sK4(U_568,U_567,U_566))
        | ~ sP24(U_566,U_567,U_568) )
    & ! [U_566,U_567,U_568] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK4(U_568,U_567,U_566)))
        | ~ sP24(U_566,U_567,U_568) )
    & ! [U_566,U_567,U_568] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK4(U_568,U_567,U_566)),U_567))
        | ~ sP24(U_566,U_567,U_568) )
    & ! [U_566,U_567,U_568] :
        ( is_fun_a_bool(sK4(U_568,U_567,U_566))
        | ~ sP24(U_566,U_567,U_568) )
    & ! [U_566,U_567,U_568] :
        ( sP24(U_566,U_567,U_568)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_566),image_a_a(U_568,U_567)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_566))
        | ~ is_fun_a_bool(U_566) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_262_3]) ).

cnf(f_262_5,plain,
    ( sP24(U_566,U_567,U_568)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_566),image_a_a(U_568,U_567)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_566))
    | ~ is_fun_a_bool(U_566) ),
    inference(clausify,[status(thm)],[f_262_4]) ).

cnf(f_262_6,plain,
    ( is_fun_a_bool(sK4(U_568,U_567,U_566))
    | ~ sP24(U_566,U_567,U_568) ),
    inference(clausify,[status(thm)],[f_262_4]) ).

cnf(f_262_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK4(U_568,U_567,U_566)),U_567))
    | ~ sP24(U_566,U_567,U_568) ),
    inference(clausify,[status(thm)],[f_262_4]) ).

cnf(f_262_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK4(U_568,U_567,U_566)))
    | ~ sP24(U_566,U_567,U_568) ),
    inference(clausify,[status(thm)],[f_262_4]) ).

cnf(f_262_9,plain,
    ( U_566 = image_a_a(U_568,sK4(U_568,U_567,U_566))
    | ~ sP24(U_566,U_567,U_568) ),
    inference(clausify,[status(thm)],[f_262_4]) ).

fof(f_263_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_a_fun_nat_bool(F,C_7)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1))
          & is_fun_a_bool(C_7) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_a_fun_nat_bool(F,A_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_159_finite__subset__image]) ).

fof(f_263_2,plain,
    ! [U_572,U_571,U_570] :
      ( ? [U_569] :
          ( U_570 = image_a_fun_nat_bool(U_572,U_569)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_569))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_569),U_571))
          & is_fun_a_bool(U_569) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_570),image_a_fun_nat_bool(U_572,U_571)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_570)) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

fof(f_263_3,plain,
    ! [U_572,U_571,U_570] :
      ( ( U_570 = image_a_fun_nat_bool(U_572,sK5(U_572,U_571,U_570))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK5(U_572,U_571,U_570)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK5(U_572,U_571,U_570)),U_571))
        & is_fun_a_bool(sK5(U_572,U_571,U_570)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_570),image_a_fun_nat_bool(U_572,U_571)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_570)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_569,sK5(U_572,U_571,U_570))],[f_263_2]) ).

fof(f_263_4,plain,
    ( ! [U_572,U_570,U_571] :
        ( U_570 = image_a_fun_nat_bool(U_572,sK5(U_572,U_571,U_570))
        | ~ sP25(U_572,U_570,U_571) )
    & ! [U_572,U_570,U_571] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK5(U_572,U_571,U_570)))
        | ~ sP25(U_572,U_570,U_571) )
    & ! [U_572,U_570,U_571] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK5(U_572,U_571,U_570)),U_571))
        | ~ sP25(U_572,U_570,U_571) )
    & ! [U_572,U_570,U_571] :
        ( is_fun_a_bool(sK5(U_572,U_571,U_570))
        | ~ sP25(U_572,U_570,U_571) )
    & ! [U_572,U_570,U_571] :
        ( sP25(U_572,U_570,U_571)
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_570),image_a_fun_nat_bool(U_572,U_571)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_570)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25])],[f_263_3]) ).

cnf(f_263_5,plain,
    ( sP25(U_572,U_570,U_571)
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_570),image_a_fun_nat_bool(U_572,U_571)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_570)) ),
    inference(clausify,[status(thm)],[f_263_4]) ).

cnf(f_263_6,plain,
    ( is_fun_a_bool(sK5(U_572,U_571,U_570))
    | ~ sP25(U_572,U_570,U_571) ),
    inference(clausify,[status(thm)],[f_263_4]) ).

cnf(f_263_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK5(U_572,U_571,U_570)),U_571))
    | ~ sP25(U_572,U_570,U_571) ),
    inference(clausify,[status(thm)],[f_263_4]) ).

cnf(f_263_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK5(U_572,U_571,U_570)))
    | ~ sP25(U_572,U_570,U_571) ),
    inference(clausify,[status(thm)],[f_263_4]) ).

cnf(f_263_9,plain,
    ( U_570 = image_a_fun_nat_bool(U_572,sK5(U_572,U_571,U_570))
    | ~ sP25(U_572,U_570,U_571) ),
    inference(clausify,[status(thm)],[f_263_4]) ).

fof(f_264_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_819518260e_bool(F,C_7)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1))
          & is_fun_a_bool(C_7) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_819518260e_bool(F,A_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
      | ~ is_fun1661590463l_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_160_finite__subset__image]) ).

fof(f_264_2,plain,
    ! [U_576,U_575,U_574] :
      ( ? [U_573] :
          ( U_574 = image_819518260e_bool(U_576,U_573)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_573))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_573),U_575))
          & is_fun_a_bool(U_573) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_574),image_819518260e_bool(U_576,U_575)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_574))
      | ~ is_fun1661590463l_bool(U_574) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

fof(f_264_3,plain,
    ! [U_576,U_575,U_574] :
      ( ( U_574 = image_819518260e_bool(U_576,sK6(U_576,U_575,U_574))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK6(U_576,U_575,U_574)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK6(U_576,U_575,U_574)),U_575))
        & is_fun_a_bool(sK6(U_576,U_575,U_574)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_574),image_819518260e_bool(U_576,U_575)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_574))
      | ~ is_fun1661590463l_bool(U_574) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_573,sK6(U_576,U_575,U_574))],[f_264_2]) ).

fof(f_264_4,plain,
    ( ! [U_576,U_575,U_574] :
        ( U_574 = image_819518260e_bool(U_576,sK6(U_576,U_575,U_574))
        | ~ sP26(U_576,U_575,U_574) )
    & ! [U_576,U_575,U_574] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK6(U_576,U_575,U_574)))
        | ~ sP26(U_576,U_575,U_574) )
    & ! [U_576,U_575,U_574] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK6(U_576,U_575,U_574)),U_575))
        | ~ sP26(U_576,U_575,U_574) )
    & ! [U_576,U_575,U_574] :
        ( is_fun_a_bool(sK6(U_576,U_575,U_574))
        | ~ sP26(U_576,U_575,U_574) )
    & ! [U_576,U_575,U_574] :
        ( sP26(U_576,U_575,U_574)
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_574),image_819518260e_bool(U_576,U_575)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_574))
        | ~ is_fun1661590463l_bool(U_574) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_264_3]) ).

cnf(f_264_5,plain,
    ( sP26(U_576,U_575,U_574)
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_574),image_819518260e_bool(U_576,U_575)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_574))
    | ~ is_fun1661590463l_bool(U_574) ),
    inference(clausify,[status(thm)],[f_264_4]) ).

cnf(f_264_6,plain,
    ( is_fun_a_bool(sK6(U_576,U_575,U_574))
    | ~ sP26(U_576,U_575,U_574) ),
    inference(clausify,[status(thm)],[f_264_4]) ).

cnf(f_264_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK6(U_576,U_575,U_574)),U_575))
    | ~ sP26(U_576,U_575,U_574) ),
    inference(clausify,[status(thm)],[f_264_4]) ).

cnf(f_264_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK6(U_576,U_575,U_574)))
    | ~ sP26(U_576,U_575,U_574) ),
    inference(clausify,[status(thm)],[f_264_4]) ).

cnf(f_264_9,plain,
    ( U_574 = image_819518260e_bool(U_576,sK6(U_576,U_575,U_574))
    | ~ sP26(U_576,U_575,U_574) ),
    inference(clausify,[status(thm)],[f_264_4]) ).

fof(f_265_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_a_fun_a_bool(F,C_7)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1))
          & is_fun_a_bool(C_7) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_a_fun_a_bool(F,A_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
      | ~ is_fun949378684l_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_161_finite__subset__image]) ).

fof(f_265_2,plain,
    ! [U_580,U_579,U_578] :
      ( ? [U_577] :
          ( U_578 = image_a_fun_a_bool(U_580,U_577)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_577))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_577),U_579))
          & is_fun_a_bool(U_577) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_578),image_a_fun_a_bool(U_580,U_579)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_578))
      | ~ is_fun949378684l_bool(U_578) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

fof(f_265_3,plain,
    ! [U_580,U_579,U_578] :
      ( ( U_578 = image_a_fun_a_bool(U_580,sK7(U_580,U_579,U_578))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK7(U_580,U_579,U_578)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK7(U_580,U_579,U_578)),U_579))
        & is_fun_a_bool(sK7(U_580,U_579,U_578)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_578),image_a_fun_a_bool(U_580,U_579)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_578))
      | ~ is_fun949378684l_bool(U_578) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_577,sK7(U_580,U_579,U_578))],[f_265_2]) ).

fof(f_265_4,plain,
    ( ! [U_578,U_579,U_580] :
        ( U_578 = image_a_fun_a_bool(U_580,sK7(U_580,U_579,U_578))
        | ~ sP27(U_578,U_579,U_580) )
    & ! [U_578,U_579,U_580] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK7(U_580,U_579,U_578)))
        | ~ sP27(U_578,U_579,U_580) )
    & ! [U_578,U_579,U_580] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK7(U_580,U_579,U_578)),U_579))
        | ~ sP27(U_578,U_579,U_580) )
    & ! [U_578,U_579,U_580] :
        ( is_fun_a_bool(sK7(U_580,U_579,U_578))
        | ~ sP27(U_578,U_579,U_580) )
    & ! [U_578,U_579,U_580] :
        ( sP27(U_578,U_579,U_580)
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_578),image_a_fun_a_bool(U_580,U_579)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_578))
        | ~ is_fun949378684l_bool(U_578) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27])],[f_265_3]) ).

cnf(f_265_5,plain,
    ( sP27(U_578,U_579,U_580)
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_578),image_a_fun_a_bool(U_580,U_579)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_578))
    | ~ is_fun949378684l_bool(U_578) ),
    inference(clausify,[status(thm)],[f_265_4]) ).

cnf(f_265_6,plain,
    ( is_fun_a_bool(sK7(U_580,U_579,U_578))
    | ~ sP27(U_578,U_579,U_580) ),
    inference(clausify,[status(thm)],[f_265_4]) ).

cnf(f_265_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK7(U_580,U_579,U_578)),U_579))
    | ~ sP27(U_578,U_579,U_580) ),
    inference(clausify,[status(thm)],[f_265_4]) ).

cnf(f_265_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK7(U_580,U_579,U_578)))
    | ~ sP27(U_578,U_579,U_580) ),
    inference(clausify,[status(thm)],[f_265_4]) ).

cnf(f_265_9,plain,
    ( U_578 = image_a_fun_a_bool(U_580,sK7(U_580,U_579,U_578))
    | ~ sP27(U_578,U_579,U_580) ),
    inference(clausify,[status(thm)],[f_265_4]) ).

fof(f_266_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_a_pname(F,C_7)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1))
          & is_fun_a_bool(C_7) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ is_fun_pname_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_162_finite__subset__image]) ).

fof(f_266_2,plain,
    ! [U_584,U_583,U_582] :
      ( ? [U_581] :
          ( U_582 = image_a_pname(U_584,U_581)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_581))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_581),U_583))
          & is_fun_a_bool(U_581) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_582),image_a_pname(U_584,U_583)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_582))
      | ~ is_fun_pname_bool(U_582) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

fof(f_266_3,plain,
    ! [U_584,U_583,U_582] :
      ( ( U_582 = image_a_pname(U_584,sK8(U_584,U_583,U_582))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK8(U_584,U_583,U_582)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK8(U_584,U_583,U_582)),U_583))
        & is_fun_a_bool(sK8(U_584,U_583,U_582)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_582),image_a_pname(U_584,U_583)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_582))
      | ~ is_fun_pname_bool(U_582) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_581,sK8(U_584,U_583,U_582))],[f_266_2]) ).

fof(f_266_4,plain,
    ( ! [U_584,U_582,U_583] :
        ( U_582 = image_a_pname(U_584,sK8(U_584,U_583,U_582))
        | ~ sP28(U_584,U_582,U_583) )
    & ! [U_584,U_582,U_583] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK8(U_584,U_583,U_582)))
        | ~ sP28(U_584,U_582,U_583) )
    & ! [U_584,U_582,U_583] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK8(U_584,U_583,U_582)),U_583))
        | ~ sP28(U_584,U_582,U_583) )
    & ! [U_584,U_582,U_583] :
        ( is_fun_a_bool(sK8(U_584,U_583,U_582))
        | ~ sP28(U_584,U_582,U_583) )
    & ! [U_584,U_582,U_583] :
        ( sP28(U_584,U_582,U_583)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_582),image_a_pname(U_584,U_583)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_582))
        | ~ is_fun_pname_bool(U_582) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28])],[f_266_3]) ).

cnf(f_266_5,plain,
    ( sP28(U_584,U_582,U_583)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_582),image_a_pname(U_584,U_583)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_582))
    | ~ is_fun_pname_bool(U_582) ),
    inference(clausify,[status(thm)],[f_266_4]) ).

cnf(f_266_6,plain,
    ( is_fun_a_bool(sK8(U_584,U_583,U_582))
    | ~ sP28(U_584,U_582,U_583) ),
    inference(clausify,[status(thm)],[f_266_4]) ).

cnf(f_266_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK8(U_584,U_583,U_582)),U_583))
    | ~ sP28(U_584,U_582,U_583) ),
    inference(clausify,[status(thm)],[f_266_4]) ).

cnf(f_266_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK8(U_584,U_583,U_582)))
    | ~ sP28(U_584,U_582,U_583) ),
    inference(clausify,[status(thm)],[f_266_4]) ).

cnf(f_266_9,plain,
    ( U_582 = image_a_pname(U_584,sK8(U_584,U_583,U_582))
    | ~ sP28(U_584,U_582,U_583) ),
    inference(clausify,[status(thm)],[f_266_4]) ).

fof(f_267_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_1921560913_pname(F,C_7)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_7))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_7),A_1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1921560913_pname(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ is_fun_pname_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_163_finite__subset__image]) ).

fof(f_267_2,plain,
    ! [U_588,U_587,U_586] :
      ( ? [U_585] :
          ( U_586 = image_1921560913_pname(U_588,U_585)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_585))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_585),U_587)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_586),image_1921560913_pname(U_588,U_587)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_586))
      | ~ is_fun_pname_bool(U_586) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

fof(f_267_3,plain,
    ! [U_588,U_587,U_586] :
      ( ( U_586 = image_1921560913_pname(U_588,sK9(U_588,U_587,U_586))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK9(U_588,U_587,U_586)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK9(U_588,U_587,U_586)),U_587)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_586),image_1921560913_pname(U_588,U_587)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_586))
      | ~ is_fun_pname_bool(U_586) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_585,sK9(U_588,U_587,U_586))],[f_267_2]) ).

fof(f_267_4,plain,
    ( ! [U_586,U_587,U_588] :
        ( U_586 = image_1921560913_pname(U_588,sK9(U_588,U_587,U_586))
        | ~ sP29(U_586,U_587,U_588) )
    & ! [U_586,U_587,U_588] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK9(U_588,U_587,U_586)))
        | ~ sP29(U_586,U_587,U_588) )
    & ! [U_586,U_587,U_588] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK9(U_588,U_587,U_586)),U_587))
        | ~ sP29(U_586,U_587,U_588) )
    & ! [U_586,U_587,U_588] :
        ( sP29(U_586,U_587,U_588)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_586),image_1921560913_pname(U_588,U_587)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_586))
        | ~ is_fun_pname_bool(U_586) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29])],[f_267_3]) ).

cnf(f_267_5,plain,
    ( sP29(U_586,U_587,U_588)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_586),image_1921560913_pname(U_588,U_587)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_586))
    | ~ is_fun_pname_bool(U_586) ),
    inference(clausify,[status(thm)],[f_267_4]) ).

cnf(f_267_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK9(U_588,U_587,U_586)),U_587))
    | ~ sP29(U_586,U_587,U_588) ),
    inference(clausify,[status(thm)],[f_267_4]) ).

cnf(f_267_7,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK9(U_588,U_587,U_586)))
    | ~ sP29(U_586,U_587,U_588) ),
    inference(clausify,[status(thm)],[f_267_4]) ).

cnf(f_267_8,plain,
    ( U_586 = image_1921560913_pname(U_588,sK9(U_588,U_587,U_586))
    | ~ sP29(U_586,U_587,U_588) ),
    inference(clausify,[status(thm)],[f_267_4]) ).

fof(f_268_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_1283814551_pname(F,C_7)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_7))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_7),A_1))
          & is_fun1661590463l_bool(C_7) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1283814551_pname(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ is_fun_pname_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_164_finite__subset__image]) ).

fof(f_268_2,plain,
    ! [U_592,U_591,U_590] :
      ( ? [U_589] :
          ( U_590 = image_1283814551_pname(U_592,U_589)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_589))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_589),U_591))
          & is_fun1661590463l_bool(U_589) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_590),image_1283814551_pname(U_592,U_591)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_590))
      | ~ is_fun_pname_bool(U_590) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

fof(f_268_3,plain,
    ! [U_592,U_591,U_590] :
      ( ( U_590 = image_1283814551_pname(U_592,sK10(U_592,U_591,U_590))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK10(U_592,U_591,U_590)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK10(U_592,U_591,U_590)),U_591))
        & is_fun1661590463l_bool(sK10(U_592,U_591,U_590)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_590),image_1283814551_pname(U_592,U_591)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_590))
      | ~ is_fun_pname_bool(U_590) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_589,sK10(U_592,U_591,U_590))],[f_268_2]) ).

fof(f_268_4,plain,
    ( ! [U_590,U_591,U_592] :
        ( U_590 = image_1283814551_pname(U_592,sK10(U_592,U_591,U_590))
        | ~ sP30(U_590,U_591,U_592) )
    & ! [U_590,U_591,U_592] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK10(U_592,U_591,U_590)))
        | ~ sP30(U_590,U_591,U_592) )
    & ! [U_590,U_591,U_592] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK10(U_592,U_591,U_590)),U_591))
        | ~ sP30(U_590,U_591,U_592) )
    & ! [U_590,U_591,U_592] :
        ( is_fun1661590463l_bool(sK10(U_592,U_591,U_590))
        | ~ sP30(U_590,U_591,U_592) )
    & ! [U_590,U_591,U_592] :
        ( sP30(U_590,U_591,U_592)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_590),image_1283814551_pname(U_592,U_591)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_590))
        | ~ is_fun_pname_bool(U_590) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30])],[f_268_3]) ).

cnf(f_268_5,plain,
    ( sP30(U_590,U_591,U_592)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_590),image_1283814551_pname(U_592,U_591)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_590))
    | ~ is_fun_pname_bool(U_590) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

cnf(f_268_6,plain,
    ( is_fun1661590463l_bool(sK10(U_592,U_591,U_590))
    | ~ sP30(U_590,U_591,U_592) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

cnf(f_268_7,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK10(U_592,U_591,U_590)),U_591))
    | ~ sP30(U_590,U_591,U_592) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

cnf(f_268_8,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK10(U_592,U_591,U_590)))
    | ~ sP30(U_590,U_591,U_592) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

cnf(f_268_9,plain,
    ( U_590 = image_1283814551_pname(U_592,sK10(U_592,U_591,U_590))
    | ~ sP30(U_590,U_591,U_592) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

fof(f_269_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_1854862208_pname(F,C_7)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_7))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_7),A_1))
          & is_fun949378684l_bool(C_7) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_1854862208_pname(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ is_fun_pname_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_165_finite__subset__image]) ).

fof(f_269_2,plain,
    ! [U_596,U_595,U_594] :
      ( ? [U_593] :
          ( U_594 = image_1854862208_pname(U_596,U_593)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_593))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_593),U_595))
          & is_fun949378684l_bool(U_593) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_594),image_1854862208_pname(U_596,U_595)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_594))
      | ~ is_fun_pname_bool(U_594) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

fof(f_269_3,plain,
    ! [U_596,U_595,U_594] :
      ( ( U_594 = image_1854862208_pname(U_596,sK11(U_596,U_595,U_594))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK11(U_596,U_595,U_594)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK11(U_596,U_595,U_594)),U_595))
        & is_fun949378684l_bool(sK11(U_596,U_595,U_594)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_594),image_1854862208_pname(U_596,U_595)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_594))
      | ~ is_fun_pname_bool(U_594) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_593,sK11(U_596,U_595,U_594))],[f_269_2]) ).

fof(f_269_4,plain,
    ( ! [U_594,U_595,U_596] :
        ( U_594 = image_1854862208_pname(U_596,sK11(U_596,U_595,U_594))
        | ~ sP31(U_594,U_595,U_596) )
    & ! [U_594,U_595,U_596] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK11(U_596,U_595,U_594)))
        | ~ sP31(U_594,U_595,U_596) )
    & ! [U_594,U_595,U_596] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK11(U_596,U_595,U_594)),U_595))
        | ~ sP31(U_594,U_595,U_596) )
    & ! [U_594,U_595,U_596] :
        ( is_fun949378684l_bool(sK11(U_596,U_595,U_594))
        | ~ sP31(U_594,U_595,U_596) )
    & ! [U_594,U_595,U_596] :
        ( sP31(U_594,U_595,U_596)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_594),image_1854862208_pname(U_596,U_595)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_594))
        | ~ is_fun_pname_bool(U_594) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31])],[f_269_3]) ).

cnf(f_269_5,plain,
    ( sP31(U_594,U_595,U_596)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_594),image_1854862208_pname(U_596,U_595)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_594))
    | ~ is_fun_pname_bool(U_594) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

cnf(f_269_6,plain,
    ( is_fun949378684l_bool(sK11(U_596,U_595,U_594))
    | ~ sP31(U_594,U_595,U_596) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

cnf(f_269_7,plain,
    ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK11(U_596,U_595,U_594)),U_595))
    | ~ sP31(U_594,U_595,U_596) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

cnf(f_269_8,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK11(U_596,U_595,U_594)))
    | ~ sP31(U_594,U_595,U_596) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

cnf(f_269_9,plain,
    ( U_594 = image_1854862208_pname(U_596,sK11(U_596,U_595,U_594))
    | ~ sP31(U_594,U_595,U_596) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

fof(f_270_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_a_nat(F,C_7)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_7))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_7),A_1))
          & is_fun_a_bool(C_7) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_166_finite__subset__image]) ).

fof(f_270_2,plain,
    ! [U_600,U_599,U_598] :
      ( ? [U_597] :
          ( U_598 = image_a_nat(U_600,U_597)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_597))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_597),U_599))
          & is_fun_a_bool(U_597) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_598),image_a_nat(U_600,U_599)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_598)) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ! [U_600,U_599,U_598] :
      ( ( U_598 = image_a_nat(U_600,sK12(U_600,U_599,U_598))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK12(U_600,U_599,U_598)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK12(U_600,U_599,U_598)),U_599))
        & is_fun_a_bool(sK12(U_600,U_599,U_598)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_598),image_a_nat(U_600,U_599)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_598)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_597,sK12(U_600,U_599,U_598))],[f_270_2]) ).

fof(f_270_4,plain,
    ( ! [U_600,U_598,U_599] :
        ( U_598 = image_a_nat(U_600,sK12(U_600,U_599,U_598))
        | ~ sP32(U_600,U_598,U_599) )
    & ! [U_600,U_598,U_599] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK12(U_600,U_599,U_598)))
        | ~ sP32(U_600,U_598,U_599) )
    & ! [U_600,U_598,U_599] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK12(U_600,U_599,U_598)),U_599))
        | ~ sP32(U_600,U_598,U_599) )
    & ! [U_600,U_598,U_599] :
        ( is_fun_a_bool(sK12(U_600,U_599,U_598))
        | ~ sP32(U_600,U_598,U_599) )
    & ! [U_600,U_598,U_599] :
        ( sP32(U_600,U_598,U_599)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_598),image_a_nat(U_600,U_599)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_598)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32])],[f_270_3]) ).

cnf(f_270_5,plain,
    ( sP32(U_600,U_598,U_599)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_598),image_a_nat(U_600,U_599)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_598)) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_6,plain,
    ( is_fun_a_bool(sK12(U_600,U_599,U_598))
    | ~ sP32(U_600,U_598,U_599) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK12(U_600,U_599,U_598)),U_599))
    | ~ sP32(U_600,U_598,U_599) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK12(U_600,U_599,U_598)))
    | ~ sP32(U_600,U_598,U_599) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_9,plain,
    ( U_598 = image_a_nat(U_600,sK12(U_600,U_599,U_598))
    | ~ sP32(U_600,U_598,U_599) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

fof(f_271_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_496248727ol_nat(F,C_7)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_7))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_7),A_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_496248727ol_nat(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_167_finite__subset__image]) ).

fof(f_271_2,plain,
    ! [U_604,U_603,U_602] :
      ( ? [U_601] :
          ( U_602 = image_496248727ol_nat(U_604,U_601)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_601))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_601),U_603)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_602),image_496248727ol_nat(U_604,U_603)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_602)) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

fof(f_271_3,plain,
    ! [U_604,U_603,U_602] :
      ( ( U_602 = image_496248727ol_nat(U_604,sK13(U_604,U_603,U_602))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK13(U_604,U_603,U_602)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK13(U_604,U_603,U_602)),U_603)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_602),image_496248727ol_nat(U_604,U_603)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_602)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_601,sK13(U_604,U_603,U_602))],[f_271_2]) ).

fof(f_271_4,plain,
    ( ! [U_603,U_602,U_604] :
        ( U_602 = image_496248727ol_nat(U_604,sK13(U_604,U_603,U_602))
        | ~ sP33(U_603,U_602,U_604) )
    & ! [U_603,U_602,U_604] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK13(U_604,U_603,U_602)))
        | ~ sP33(U_603,U_602,U_604) )
    & ! [U_603,U_602,U_604] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK13(U_604,U_603,U_602)),U_603))
        | ~ sP33(U_603,U_602,U_604) )
    & ! [U_603,U_602,U_604] :
        ( sP33(U_603,U_602,U_604)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_602),image_496248727ol_nat(U_604,U_603)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_602)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33])],[f_271_3]) ).

cnf(f_271_5,plain,
    ( sP33(U_603,U_602,U_604)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_602),image_496248727ol_nat(U_604,U_603)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_602)) ),
    inference(clausify,[status(thm)],[f_271_4]) ).

cnf(f_271_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK13(U_604,U_603,U_602)),U_603))
    | ~ sP33(U_603,U_602,U_604) ),
    inference(clausify,[status(thm)],[f_271_4]) ).

cnf(f_271_7,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK13(U_604,U_603,U_602)))
    | ~ sP33(U_603,U_602,U_604) ),
    inference(clausify,[status(thm)],[f_271_4]) ).

cnf(f_271_8,plain,
    ( U_602 = image_496248727ol_nat(U_604,sK13(U_604,U_603,U_602))
    | ~ sP33(U_603,U_602,U_604) ),
    inference(clausify,[status(thm)],[f_271_4]) ).

fof(f_272_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_1551609309ol_nat(F,C_7)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_7))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_7),A_1))
          & is_fun1661590463l_bool(C_7) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_1551609309ol_nat(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_168_finite__subset__image]) ).

fof(f_272_2,plain,
    ! [U_608,U_607,U_606] :
      ( ? [U_605] :
          ( U_606 = image_1551609309ol_nat(U_608,U_605)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_605))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_605),U_607))
          & is_fun1661590463l_bool(U_605) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_606),image_1551609309ol_nat(U_608,U_607)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_606)) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

fof(f_272_3,plain,
    ! [U_608,U_607,U_606] :
      ( ( U_606 = image_1551609309ol_nat(U_608,sK14(U_608,U_607,U_606))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK14(U_608,U_607,U_606)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK14(U_608,U_607,U_606)),U_607))
        & is_fun1661590463l_bool(sK14(U_608,U_607,U_606)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_606),image_1551609309ol_nat(U_608,U_607)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_606)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_605,sK14(U_608,U_607,U_606))],[f_272_2]) ).

fof(f_272_4,plain,
    ( ! [U_606,U_607,U_608] :
        ( U_606 = image_1551609309ol_nat(U_608,sK14(U_608,U_607,U_606))
        | ~ sP34(U_606,U_607,U_608) )
    & ! [U_606,U_607,U_608] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK14(U_608,U_607,U_606)))
        | ~ sP34(U_606,U_607,U_608) )
    & ! [U_606,U_607,U_608] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK14(U_608,U_607,U_606)),U_607))
        | ~ sP34(U_606,U_607,U_608) )
    & ! [U_606,U_607,U_608] :
        ( is_fun1661590463l_bool(sK14(U_608,U_607,U_606))
        | ~ sP34(U_606,U_607,U_608) )
    & ! [U_606,U_607,U_608] :
        ( sP34(U_606,U_607,U_608)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_606),image_1551609309ol_nat(U_608,U_607)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_606)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP34])],[f_272_3]) ).

cnf(f_272_5,plain,
    ( sP34(U_606,U_607,U_608)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_606),image_1551609309ol_nat(U_608,U_607)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_606)) ),
    inference(clausify,[status(thm)],[f_272_4]) ).

cnf(f_272_6,plain,
    ( is_fun1661590463l_bool(sK14(U_608,U_607,U_606))
    | ~ sP34(U_606,U_607,U_608) ),
    inference(clausify,[status(thm)],[f_272_4]) ).

cnf(f_272_7,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK14(U_608,U_607,U_606)),U_607))
    | ~ sP34(U_606,U_607,U_608) ),
    inference(clausify,[status(thm)],[f_272_4]) ).

cnf(f_272_8,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK14(U_608,U_607,U_606)))
    | ~ sP34(U_606,U_607,U_608) ),
    inference(clausify,[status(thm)],[f_272_4]) ).

cnf(f_272_9,plain,
    ( U_606 = image_1551609309ol_nat(U_608,sK14(U_608,U_607,U_606))
    | ~ sP34(U_606,U_607,U_608) ),
    inference(clausify,[status(thm)],[f_272_4]) ).

fof(f_273_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_fun_a_bool_nat(F,C_7)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_7))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_7),A_1))
          & is_fun949378684l_bool(C_7) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_fun_a_bool_nat(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_169_finite__subset__image]) ).

fof(f_273_2,plain,
    ! [U_612,U_611,U_610] :
      ( ? [U_609] :
          ( U_610 = image_fun_a_bool_nat(U_612,U_609)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_609))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_609),U_611))
          & is_fun949378684l_bool(U_609) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_610),image_fun_a_bool_nat(U_612,U_611)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_610)) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

fof(f_273_3,plain,
    ! [U_612,U_611,U_610] :
      ( ( U_610 = image_fun_a_bool_nat(U_612,sK15(U_612,U_611,U_610))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK15(U_612,U_611,U_610)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK15(U_612,U_611,U_610)),U_611))
        & is_fun949378684l_bool(sK15(U_612,U_611,U_610)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_610),image_fun_a_bool_nat(U_612,U_611)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_610)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_609,sK15(U_612,U_611,U_610))],[f_273_2]) ).

fof(f_273_4,plain,
    ( ! [U_611,U_610,U_612] :
        ( U_610 = image_fun_a_bool_nat(U_612,sK15(U_612,U_611,U_610))
        | ~ sP35(U_611,U_610,U_612) )
    & ! [U_611,U_610,U_612] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK15(U_612,U_611,U_610)))
        | ~ sP35(U_611,U_610,U_612) )
    & ! [U_611,U_610,U_612] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK15(U_612,U_611,U_610)),U_611))
        | ~ sP35(U_611,U_610,U_612) )
    & ! [U_611,U_610,U_612] :
        ( is_fun949378684l_bool(sK15(U_612,U_611,U_610))
        | ~ sP35(U_611,U_610,U_612) )
    & ! [U_611,U_610,U_612] :
        ( sP35(U_611,U_610,U_612)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_610),image_fun_a_bool_nat(U_612,U_611)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_610)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35])],[f_273_3]) ).

cnf(f_273_5,plain,
    ( sP35(U_611,U_610,U_612)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_610),image_fun_a_bool_nat(U_612,U_611)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_610)) ),
    inference(clausify,[status(thm)],[f_273_4]) ).

cnf(f_273_6,plain,
    ( is_fun949378684l_bool(sK15(U_612,U_611,U_610))
    | ~ sP35(U_611,U_610,U_612) ),
    inference(clausify,[status(thm)],[f_273_4]) ).

cnf(f_273_7,plain,
    ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK15(U_612,U_611,U_610)),U_611))
    | ~ sP35(U_611,U_610,U_612) ),
    inference(clausify,[status(thm)],[f_273_4]) ).

cnf(f_273_8,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK15(U_612,U_611,U_610)))
    | ~ sP35(U_611,U_610,U_612) ),
    inference(clausify,[status(thm)],[f_273_4]) ).

cnf(f_273_9,plain,
    ( U_610 = image_fun_a_bool_nat(U_612,sK15(U_612,U_611,U_610))
    | ~ sP35(U_611,U_610,U_612) ),
    inference(clausify,[status(thm)],[f_273_4]) ).

fof(f_274_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_2129980159t_bool(F,C_7)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1))
          & is_fun_pname_bool(C_7) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_2129980159t_bool(F,A_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_170_finite__subset__image]) ).

fof(f_274_2,plain,
    ! [U_616,U_615,U_614] :
      ( ? [U_613] :
          ( U_614 = image_2129980159t_bool(U_616,U_613)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_613))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_613),U_615))
          & is_fun_pname_bool(U_613) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_614),image_2129980159t_bool(U_616,U_615)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_614)) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ! [U_616,U_615,U_614] :
      ( ( U_614 = image_2129980159t_bool(U_616,sK16(U_616,U_615,U_614))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK16(U_616,U_615,U_614)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK16(U_616,U_615,U_614)),U_615))
        & is_fun_pname_bool(sK16(U_616,U_615,U_614)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_614),image_2129980159t_bool(U_616,U_615)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_614)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_613,sK16(U_616,U_615,U_614))],[f_274_2]) ).

fof(f_274_4,plain,
    ( ! [U_615,U_614,U_616] :
        ( U_614 = image_2129980159t_bool(U_616,sK16(U_616,U_615,U_614))
        | ~ sP36(U_615,U_614,U_616) )
    & ! [U_615,U_614,U_616] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK16(U_616,U_615,U_614)))
        | ~ sP36(U_615,U_614,U_616) )
    & ! [U_615,U_614,U_616] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK16(U_616,U_615,U_614)),U_615))
        | ~ sP36(U_615,U_614,U_616) )
    & ! [U_615,U_614,U_616] :
        ( is_fun_pname_bool(sK16(U_616,U_615,U_614))
        | ~ sP36(U_615,U_614,U_616) )
    & ! [U_615,U_614,U_616] :
        ( sP36(U_615,U_614,U_616)
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_614),image_2129980159t_bool(U_616,U_615)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_614)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36])],[f_274_3]) ).

cnf(f_274_5,plain,
    ( sP36(U_615,U_614,U_616)
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_614),image_2129980159t_bool(U_616,U_615)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_614)) ),
    inference(clausify,[status(thm)],[f_274_4]) ).

cnf(f_274_6,plain,
    ( is_fun_pname_bool(sK16(U_616,U_615,U_614))
    | ~ sP36(U_615,U_614,U_616) ),
    inference(clausify,[status(thm)],[f_274_4]) ).

cnf(f_274_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK16(U_616,U_615,U_614)),U_615))
    | ~ sP36(U_615,U_614,U_616) ),
    inference(clausify,[status(thm)],[f_274_4]) ).

cnf(f_274_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK16(U_616,U_615,U_614)))
    | ~ sP36(U_615,U_614,U_616) ),
    inference(clausify,[status(thm)],[f_274_4]) ).

cnf(f_274_9,plain,
    ( U_614 = image_2129980159t_bool(U_616,sK16(U_616,U_615,U_614))
    | ~ sP36(U_615,U_614,U_616) ),
    inference(clausify,[status(thm)],[f_274_4]) ).

fof(f_275_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_47868345e_bool(F,C_7)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1))
          & is_fun_pname_bool(C_7) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_47868345e_bool(F,A_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
      | ~ is_fun1661590463l_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_171_finite__subset__image]) ).

fof(f_275_2,plain,
    ! [U_620,U_619,U_618] :
      ( ? [U_617] :
          ( U_618 = image_47868345e_bool(U_620,U_617)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_617))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_617),U_619))
          & is_fun_pname_bool(U_617) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_618),image_47868345e_bool(U_620,U_619)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_618))
      | ~ is_fun1661590463l_bool(U_618) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

fof(f_275_3,plain,
    ! [U_620,U_619,U_618] :
      ( ( U_618 = image_47868345e_bool(U_620,sK17(U_620,U_619,U_618))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK17(U_620,U_619,U_618)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK17(U_620,U_619,U_618)),U_619))
        & is_fun_pname_bool(sK17(U_620,U_619,U_618)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_618),image_47868345e_bool(U_620,U_619)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_618))
      | ~ is_fun1661590463l_bool(U_618) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_617,sK17(U_620,U_619,U_618))],[f_275_2]) ).

fof(f_275_4,plain,
    ( ! [U_619,U_618,U_620] :
        ( U_618 = image_47868345e_bool(U_620,sK17(U_620,U_619,U_618))
        | ~ sP37(U_619,U_618,U_620) )
    & ! [U_619,U_618,U_620] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK17(U_620,U_619,U_618)))
        | ~ sP37(U_619,U_618,U_620) )
    & ! [U_619,U_618,U_620] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK17(U_620,U_619,U_618)),U_619))
        | ~ sP37(U_619,U_618,U_620) )
    & ! [U_619,U_618,U_620] :
        ( is_fun_pname_bool(sK17(U_620,U_619,U_618))
        | ~ sP37(U_619,U_618,U_620) )
    & ! [U_619,U_618,U_620] :
        ( sP37(U_619,U_618,U_620)
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_618),image_47868345e_bool(U_620,U_619)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_618))
        | ~ is_fun1661590463l_bool(U_618) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP37])],[f_275_3]) ).

cnf(f_275_5,plain,
    ( sP37(U_619,U_618,U_620)
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_618),image_47868345e_bool(U_620,U_619)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_618))
    | ~ is_fun1661590463l_bool(U_618) ),
    inference(clausify,[status(thm)],[f_275_4]) ).

cnf(f_275_6,plain,
    ( is_fun_pname_bool(sK17(U_620,U_619,U_618))
    | ~ sP37(U_619,U_618,U_620) ),
    inference(clausify,[status(thm)],[f_275_4]) ).

cnf(f_275_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK17(U_620,U_619,U_618)),U_619))
    | ~ sP37(U_619,U_618,U_620) ),
    inference(clausify,[status(thm)],[f_275_4]) ).

cnf(f_275_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK17(U_620,U_619,U_618)))
    | ~ sP37(U_619,U_618,U_620) ),
    inference(clausify,[status(thm)],[f_275_4]) ).

cnf(f_275_9,plain,
    ( U_618 = image_47868345e_bool(U_620,sK17(U_620,U_619,U_618))
    | ~ sP37(U_619,U_618,U_620) ),
    inference(clausify,[status(thm)],[f_275_4]) ).

fof(f_276_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_112932426a_bool(F,C_7)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1))
          & is_fun_pname_bool(C_7) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_112932426a_bool(F,A_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
      | ~ is_fun949378684l_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_172_finite__subset__image]) ).

fof(f_276_2,plain,
    ! [U_624,U_623,U_622] :
      ( ? [U_621] :
          ( U_622 = image_112932426a_bool(U_624,U_621)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_621))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_621),U_623))
          & is_fun_pname_bool(U_621) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_622),image_112932426a_bool(U_624,U_623)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_622))
      | ~ is_fun949378684l_bool(U_622) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

fof(f_276_3,plain,
    ! [U_624,U_623,U_622] :
      ( ( U_622 = image_112932426a_bool(U_624,sK18(U_624,U_623,U_622))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK18(U_624,U_623,U_622)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK18(U_624,U_623,U_622)),U_623))
        & is_fun_pname_bool(sK18(U_624,U_623,U_622)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_622),image_112932426a_bool(U_624,U_623)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_622))
      | ~ is_fun949378684l_bool(U_622) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_621,sK18(U_624,U_623,U_622))],[f_276_2]) ).

fof(f_276_4,plain,
    ( ! [U_622,U_623,U_624] :
        ( U_622 = image_112932426a_bool(U_624,sK18(U_624,U_623,U_622))
        | ~ sP38(U_622,U_623,U_624) )
    & ! [U_622,U_623,U_624] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK18(U_624,U_623,U_622)))
        | ~ sP38(U_622,U_623,U_624) )
    & ! [U_622,U_623,U_624] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK18(U_624,U_623,U_622)),U_623))
        | ~ sP38(U_622,U_623,U_624) )
    & ! [U_622,U_623,U_624] :
        ( is_fun_pname_bool(sK18(U_624,U_623,U_622))
        | ~ sP38(U_622,U_623,U_624) )
    & ! [U_622,U_623,U_624] :
        ( sP38(U_622,U_623,U_624)
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_622),image_112932426a_bool(U_624,U_623)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_622))
        | ~ is_fun949378684l_bool(U_622) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38])],[f_276_3]) ).

cnf(f_276_5,plain,
    ( sP38(U_622,U_623,U_624)
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_622),image_112932426a_bool(U_624,U_623)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_622))
    | ~ is_fun949378684l_bool(U_622) ),
    inference(clausify,[status(thm)],[f_276_4]) ).

cnf(f_276_6,plain,
    ( is_fun_pname_bool(sK18(U_624,U_623,U_622))
    | ~ sP38(U_622,U_623,U_624) ),
    inference(clausify,[status(thm)],[f_276_4]) ).

cnf(f_276_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK18(U_624,U_623,U_622)),U_623))
    | ~ sP38(U_622,U_623,U_624) ),
    inference(clausify,[status(thm)],[f_276_4]) ).

cnf(f_276_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK18(U_624,U_623,U_622)))
    | ~ sP38(U_622,U_623,U_624) ),
    inference(clausify,[status(thm)],[f_276_4]) ).

cnf(f_276_9,plain,
    ( U_622 = image_112932426a_bool(U_624,sK18(U_624,U_623,U_622))
    | ~ sP38(U_622,U_623,U_624) ),
    inference(clausify,[status(thm)],[f_276_4]) ).

fof(f_277_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_pname_pname(F,C_7)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1))
          & is_fun_pname_bool(C_7) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_pname_pname(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ is_fun_pname_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_173_finite__subset__image]) ).

fof(f_277_2,plain,
    ! [U_628,U_627,U_626] :
      ( ? [U_625] :
          ( U_626 = image_pname_pname(U_628,U_625)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_625))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_625),U_627))
          & is_fun_pname_bool(U_625) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_626),image_pname_pname(U_628,U_627)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_626))
      | ~ is_fun_pname_bool(U_626) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

fof(f_277_3,plain,
    ! [U_628,U_627,U_626] :
      ( ( U_626 = image_pname_pname(U_628,sK19(U_628,U_627,U_626))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK19(U_628,U_627,U_626)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK19(U_628,U_627,U_626)),U_627))
        & is_fun_pname_bool(sK19(U_628,U_627,U_626)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_626),image_pname_pname(U_628,U_627)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_626))
      | ~ is_fun_pname_bool(U_626) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_625,sK19(U_628,U_627,U_626))],[f_277_2]) ).

fof(f_277_4,plain,
    ( ! [U_626,U_627,U_628] :
        ( U_626 = image_pname_pname(U_628,sK19(U_628,U_627,U_626))
        | ~ sP39(U_626,U_627,U_628) )
    & ! [U_626,U_627,U_628] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK19(U_628,U_627,U_626)))
        | ~ sP39(U_626,U_627,U_628) )
    & ! [U_626,U_627,U_628] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK19(U_628,U_627,U_626)),U_627))
        | ~ sP39(U_626,U_627,U_628) )
    & ! [U_626,U_627,U_628] :
        ( is_fun_pname_bool(sK19(U_628,U_627,U_626))
        | ~ sP39(U_626,U_627,U_628) )
    & ! [U_626,U_627,U_628] :
        ( sP39(U_626,U_627,U_628)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_626),image_pname_pname(U_628,U_627)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_626))
        | ~ is_fun_pname_bool(U_626) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39])],[f_277_3]) ).

cnf(f_277_5,plain,
    ( sP39(U_626,U_627,U_628)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_626),image_pname_pname(U_628,U_627)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_626))
    | ~ is_fun_pname_bool(U_626) ),
    inference(clausify,[status(thm)],[f_277_4]) ).

cnf(f_277_6,plain,
    ( is_fun_pname_bool(sK19(U_628,U_627,U_626))
    | ~ sP39(U_626,U_627,U_628) ),
    inference(clausify,[status(thm)],[f_277_4]) ).

cnf(f_277_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK19(U_628,U_627,U_626)),U_627))
    | ~ sP39(U_626,U_627,U_628) ),
    inference(clausify,[status(thm)],[f_277_4]) ).

cnf(f_277_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK19(U_628,U_627,U_626)))
    | ~ sP39(U_626,U_627,U_628) ),
    inference(clausify,[status(thm)],[f_277_4]) ).

cnf(f_277_9,plain,
    ( U_626 = image_pname_pname(U_628,sK19(U_628,U_627,U_626))
    | ~ sP39(U_626,U_627,U_628) ),
    inference(clausify,[status(thm)],[f_277_4]) ).

fof(f_278_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_pname_nat(F,C_7)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1))
          & is_fun_pname_bool(C_7) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_pname_nat(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_174_finite__subset__image]) ).

fof(f_278_2,plain,
    ! [U_632,U_631,U_630] :
      ( ? [U_629] :
          ( U_630 = image_pname_nat(U_632,U_629)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_629))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_629),U_631))
          & is_fun_pname_bool(U_629) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_630),image_pname_nat(U_632,U_631)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_630)) ),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

fof(f_278_3,plain,
    ! [U_632,U_631,U_630] :
      ( ( U_630 = image_pname_nat(U_632,sK20(U_632,U_631,U_630))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK20(U_632,U_631,U_630)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK20(U_632,U_631,U_630)),U_631))
        & is_fun_pname_bool(sK20(U_632,U_631,U_630)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_630),image_pname_nat(U_632,U_631)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_630)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_629,sK20(U_632,U_631,U_630))],[f_278_2]) ).

fof(f_278_4,plain,
    ( ! [U_630,U_631,U_632] :
        ( U_630 = image_pname_nat(U_632,sK20(U_632,U_631,U_630))
        | ~ sP40(U_630,U_631,U_632) )
    & ! [U_630,U_631,U_632] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK20(U_632,U_631,U_630)))
        | ~ sP40(U_630,U_631,U_632) )
    & ! [U_630,U_631,U_632] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK20(U_632,U_631,U_630)),U_631))
        | ~ sP40(U_630,U_631,U_632) )
    & ! [U_630,U_631,U_632] :
        ( is_fun_pname_bool(sK20(U_632,U_631,U_630))
        | ~ sP40(U_630,U_631,U_632) )
    & ! [U_630,U_631,U_632] :
        ( sP40(U_630,U_631,U_632)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_630),image_pname_nat(U_632,U_631)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_630)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_278_3]) ).

cnf(f_278_5,plain,
    ( sP40(U_630,U_631,U_632)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_630),image_pname_nat(U_632,U_631)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_630)) ),
    inference(clausify,[status(thm)],[f_278_4]) ).

cnf(f_278_6,plain,
    ( is_fun_pname_bool(sK20(U_632,U_631,U_630))
    | ~ sP40(U_630,U_631,U_632) ),
    inference(clausify,[status(thm)],[f_278_4]) ).

cnf(f_278_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK20(U_632,U_631,U_630)),U_631))
    | ~ sP40(U_630,U_631,U_632) ),
    inference(clausify,[status(thm)],[f_278_4]) ).

cnf(f_278_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK20(U_632,U_631,U_630)))
    | ~ sP40(U_630,U_631,U_632) ),
    inference(clausify,[status(thm)],[f_278_4]) ).

cnf(f_278_9,plain,
    ( U_630 = image_pname_nat(U_632,sK20(U_632,U_631,U_630))
    | ~ sP40(U_630,U_631,U_632) ),
    inference(clausify,[status(thm)],[f_278_4]) ).

fof(f_279_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_nat_a(F,C_7)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ is_fun_a_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_175_finite__subset__image]) ).

fof(f_279_2,plain,
    ! [U_636,U_635,U_634] :
      ( ? [U_633] :
          ( U_634 = image_nat_a(U_636,U_633)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_633))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_633),U_635)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_634),image_nat_a(U_636,U_635)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_634))
      | ~ is_fun_a_bool(U_634) ),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

fof(f_279_3,plain,
    ! [U_636,U_635,U_634] :
      ( ( U_634 = image_nat_a(U_636,sK21(U_636,U_635,U_634))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK21(U_636,U_635,U_634)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK21(U_636,U_635,U_634)),U_635)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_634),image_nat_a(U_636,U_635)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_634))
      | ~ is_fun_a_bool(U_634) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_633,sK21(U_636,U_635,U_634))],[f_279_2]) ).

fof(f_279_4,plain,
    ( ! [U_635,U_634,U_636] :
        ( U_634 = image_nat_a(U_636,sK21(U_636,U_635,U_634))
        | ~ sP41(U_635,U_634,U_636) )
    & ! [U_635,U_634,U_636] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK21(U_636,U_635,U_634)))
        | ~ sP41(U_635,U_634,U_636) )
    & ! [U_635,U_634,U_636] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK21(U_636,U_635,U_634)),U_635))
        | ~ sP41(U_635,U_634,U_636) )
    & ! [U_635,U_634,U_636] :
        ( sP41(U_635,U_634,U_636)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_634),image_nat_a(U_636,U_635)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_634))
        | ~ is_fun_a_bool(U_634) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41])],[f_279_3]) ).

cnf(f_279_5,plain,
    ( sP41(U_635,U_634,U_636)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_634),image_nat_a(U_636,U_635)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_634))
    | ~ is_fun_a_bool(U_634) ),
    inference(clausify,[status(thm)],[f_279_4]) ).

cnf(f_279_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK21(U_636,U_635,U_634)),U_635))
    | ~ sP41(U_635,U_634,U_636) ),
    inference(clausify,[status(thm)],[f_279_4]) ).

cnf(f_279_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK21(U_636,U_635,U_634)))
    | ~ sP41(U_635,U_634,U_636) ),
    inference(clausify,[status(thm)],[f_279_4]) ).

cnf(f_279_8,plain,
    ( U_634 = image_nat_a(U_636,sK21(U_636,U_635,U_634))
    | ~ sP41(U_635,U_634,U_636) ),
    inference(clausify,[status(thm)],[f_279_4]) ).

fof(f_280_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_26036933t_bool(F,C_7)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B_6),image_26036933t_bool(F,A_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_176_finite__subset__image]) ).

fof(f_280_2,plain,
    ! [U_640,U_639,U_638] :
      ( ? [U_637] :
          ( U_638 = image_26036933t_bool(U_640,U_637)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_637))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_637),U_639)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_638),image_26036933t_bool(U_640,U_639)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_638)) ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

fof(f_280_3,plain,
    ! [U_640,U_639,U_638] :
      ( ( U_638 = image_26036933t_bool(U_640,sK22(U_640,U_639,U_638))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK22(U_640,U_639,U_638)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK22(U_640,U_639,U_638)),U_639)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_638),image_26036933t_bool(U_640,U_639)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_638)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_637,sK22(U_640,U_639,U_638))],[f_280_2]) ).

fof(f_280_4,plain,
    ( ! [U_638,U_639,U_640] :
        ( U_638 = image_26036933t_bool(U_640,sK22(U_640,U_639,U_638))
        | ~ sP42(U_638,U_639,U_640) )
    & ! [U_638,U_639,U_640] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK22(U_640,U_639,U_638)))
        | ~ sP42(U_638,U_639,U_640) )
    & ! [U_638,U_639,U_640] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK22(U_640,U_639,U_638)),U_639))
        | ~ sP42(U_638,U_639,U_640) )
    & ! [U_638,U_639,U_640] :
        ( sP42(U_638,U_639,U_640)
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_638),image_26036933t_bool(U_640,U_639)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_638)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42])],[f_280_3]) ).

cnf(f_280_5,plain,
    ( sP42(U_638,U_639,U_640)
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_638),image_26036933t_bool(U_640,U_639)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_638)) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

cnf(f_280_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK22(U_640,U_639,U_638)),U_639))
    | ~ sP42(U_638,U_639,U_640) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

cnf(f_280_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK22(U_640,U_639,U_638)))
    | ~ sP42(U_638,U_639,U_640) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

cnf(f_280_8,plain,
    ( U_638 = image_26036933t_bool(U_640,sK22(U_640,U_639,U_638))
    | ~ sP42(U_638,U_639,U_640) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

fof(f_281_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_1655916159e_bool(F,C_7)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B_6),image_1655916159e_bool(F,A_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B_6))
      | ~ is_fun1661590463l_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_177_finite__subset__image]) ).

fof(f_281_2,plain,
    ! [U_644,U_643,U_642] :
      ( ? [U_641] :
          ( U_642 = image_1655916159e_bool(U_644,U_641)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_641))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_641),U_643)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_642),image_1655916159e_bool(U_644,U_643)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_642))
      | ~ is_fun1661590463l_bool(U_642) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

fof(f_281_3,plain,
    ! [U_644,U_643,U_642] :
      ( ( U_642 = image_1655916159e_bool(U_644,sK23(U_644,U_643,U_642))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK23(U_644,U_643,U_642)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK23(U_644,U_643,U_642)),U_643)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_642),image_1655916159e_bool(U_644,U_643)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_642))
      | ~ is_fun1661590463l_bool(U_642) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_641,sK23(U_644,U_643,U_642))],[f_281_2]) ).

fof(f_281_4,plain,
    ( ! [U_643,U_642,U_644] :
        ( U_642 = image_1655916159e_bool(U_644,sK23(U_644,U_643,U_642))
        | ~ sP43(U_643,U_642,U_644) )
    & ! [U_643,U_642,U_644] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK23(U_644,U_643,U_642)))
        | ~ sP43(U_643,U_642,U_644) )
    & ! [U_643,U_642,U_644] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK23(U_644,U_643,U_642)),U_643))
        | ~ sP43(U_643,U_642,U_644) )
    & ! [U_643,U_642,U_644] :
        ( sP43(U_643,U_642,U_644)
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_642),image_1655916159e_bool(U_644,U_643)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_642))
        | ~ is_fun1661590463l_bool(U_642) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43])],[f_281_3]) ).

cnf(f_281_5,plain,
    ( sP43(U_643,U_642,U_644)
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_642),image_1655916159e_bool(U_644,U_643)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_642))
    | ~ is_fun1661590463l_bool(U_642) ),
    inference(clausify,[status(thm)],[f_281_4]) ).

cnf(f_281_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK23(U_644,U_643,U_642)),U_643))
    | ~ sP43(U_643,U_642,U_644) ),
    inference(clausify,[status(thm)],[f_281_4]) ).

cnf(f_281_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK23(U_644,U_643,U_642)))
    | ~ sP43(U_643,U_642,U_644) ),
    inference(clausify,[status(thm)],[f_281_4]) ).

cnf(f_281_8,plain,
    ( U_642 = image_1655916159e_bool(U_644,sK23(U_644,U_643,U_642))
    | ~ sP43(U_643,U_642,U_644) ),
    inference(clausify,[status(thm)],[f_281_4]) ).

fof(f_282_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_nat_fun_a_bool(F,C_7)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B_6),image_nat_fun_a_bool(F,A_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B_6))
      | ~ is_fun949378684l_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_178_finite__subset__image]) ).

fof(f_282_2,plain,
    ! [U_648,U_647,U_646] :
      ( ? [U_645] :
          ( U_646 = image_nat_fun_a_bool(U_648,U_645)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_645))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_645),U_647)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_646),image_nat_fun_a_bool(U_648,U_647)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_646))
      | ~ is_fun949378684l_bool(U_646) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

fof(f_282_3,plain,
    ! [U_648,U_647,U_646] :
      ( ( U_646 = image_nat_fun_a_bool(U_648,sK24(U_648,U_647,U_646))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK24(U_648,U_647,U_646)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK24(U_648,U_647,U_646)),U_647)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_646),image_nat_fun_a_bool(U_648,U_647)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_646))
      | ~ is_fun949378684l_bool(U_646) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_645,sK24(U_648,U_647,U_646))],[f_282_2]) ).

fof(f_282_4,plain,
    ( ! [U_646,U_648,U_647] :
        ( U_646 = image_nat_fun_a_bool(U_648,sK24(U_648,U_647,U_646))
        | ~ sP44(U_646,U_648,U_647) )
    & ! [U_646,U_648,U_647] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK24(U_648,U_647,U_646)))
        | ~ sP44(U_646,U_648,U_647) )
    & ! [U_646,U_648,U_647] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK24(U_648,U_647,U_646)),U_647))
        | ~ sP44(U_646,U_648,U_647) )
    & ! [U_646,U_648,U_647] :
        ( sP44(U_646,U_648,U_647)
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_646),image_nat_fun_a_bool(U_648,U_647)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_646))
        | ~ is_fun949378684l_bool(U_646) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44])],[f_282_3]) ).

cnf(f_282_5,plain,
    ( sP44(U_646,U_648,U_647)
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_646),image_nat_fun_a_bool(U_648,U_647)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_646))
    | ~ is_fun949378684l_bool(U_646) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

cnf(f_282_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK24(U_648,U_647,U_646)),U_647))
    | ~ sP44(U_646,U_648,U_647) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

cnf(f_282_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK24(U_648,U_647,U_646)))
    | ~ sP44(U_646,U_648,U_647) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

cnf(f_282_8,plain,
    ( U_646 = image_nat_fun_a_bool(U_648,sK24(U_648,U_647,U_646))
    | ~ sP44(U_646,U_648,U_647) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

fof(f_283_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_nat_pname(F,C_7)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_nat_pname(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B_6))
      | ~ is_fun_pname_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_179_finite__subset__image]) ).

fof(f_283_2,plain,
    ! [U_652,U_651,U_650] :
      ( ? [U_649] :
          ( U_650 = image_nat_pname(U_652,U_649)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_649))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_649),U_651)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_650),image_nat_pname(U_652,U_651)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_650))
      | ~ is_fun_pname_bool(U_650) ),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

fof(f_283_3,plain,
    ! [U_652,U_651,U_650] :
      ( ( U_650 = image_nat_pname(U_652,sK25(U_652,U_651,U_650))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK25(U_652,U_651,U_650)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK25(U_652,U_651,U_650)),U_651)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_650),image_nat_pname(U_652,U_651)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_650))
      | ~ is_fun_pname_bool(U_650) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_649,sK25(U_652,U_651,U_650))],[f_283_2]) ).

fof(f_283_4,plain,
    ( ! [U_652,U_651,U_650] :
        ( U_650 = image_nat_pname(U_652,sK25(U_652,U_651,U_650))
        | ~ sP45(U_652,U_651,U_650) )
    & ! [U_652,U_651,U_650] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK25(U_652,U_651,U_650)))
        | ~ sP45(U_652,U_651,U_650) )
    & ! [U_652,U_651,U_650] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK25(U_652,U_651,U_650)),U_651))
        | ~ sP45(U_652,U_651,U_650) )
    & ! [U_652,U_651,U_650] :
        ( sP45(U_652,U_651,U_650)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_650),image_nat_pname(U_652,U_651)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_650))
        | ~ is_fun_pname_bool(U_650) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45])],[f_283_3]) ).

cnf(f_283_5,plain,
    ( sP45(U_652,U_651,U_650)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_650),image_nat_pname(U_652,U_651)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_650))
    | ~ is_fun_pname_bool(U_650) ),
    inference(clausify,[status(thm)],[f_283_4]) ).

cnf(f_283_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK25(U_652,U_651,U_650)),U_651))
    | ~ sP45(U_652,U_651,U_650) ),
    inference(clausify,[status(thm)],[f_283_4]) ).

cnf(f_283_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK25(U_652,U_651,U_650)))
    | ~ sP45(U_652,U_651,U_650) ),
    inference(clausify,[status(thm)],[f_283_4]) ).

cnf(f_283_8,plain,
    ( U_650 = image_nat_pname(U_652,sK25(U_652,U_651,U_650))
    | ~ sP45(U_652,U_651,U_650) ),
    inference(clausify,[status(thm)],[f_283_4]) ).

fof(f_284_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_nat_nat(F,C_7)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_7))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_7),A_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_nat_nat(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_180_finite__subset__image]) ).

fof(f_284_2,plain,
    ! [U_656,U_655,U_654] :
      ( ? [U_653] :
          ( U_654 = image_nat_nat(U_656,U_653)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_653))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_653),U_655)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_654),image_nat_nat(U_656,U_655)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_654)) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

fof(f_284_3,plain,
    ! [U_656,U_655,U_654] :
      ( ( U_654 = image_nat_nat(U_656,sK26(U_656,U_655,U_654))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK26(U_656,U_655,U_654)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK26(U_656,U_655,U_654)),U_655)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_654),image_nat_nat(U_656,U_655)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_654)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_653,sK26(U_656,U_655,U_654))],[f_284_2]) ).

fof(f_284_4,plain,
    ( ! [U_656,U_654,U_655] :
        ( U_654 = image_nat_nat(U_656,sK26(U_656,U_655,U_654))
        | ~ sP46(U_656,U_654,U_655) )
    & ! [U_656,U_654,U_655] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK26(U_656,U_655,U_654)))
        | ~ sP46(U_656,U_654,U_655) )
    & ! [U_656,U_654,U_655] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK26(U_656,U_655,U_654)),U_655))
        | ~ sP46(U_656,U_654,U_655) )
    & ! [U_656,U_654,U_655] :
        ( sP46(U_656,U_654,U_655)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_654),image_nat_nat(U_656,U_655)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_654)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_284_3]) ).

cnf(f_284_5,plain,
    ( sP46(U_656,U_654,U_655)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_654),image_nat_nat(U_656,U_655)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_654)) ),
    inference(clausify,[status(thm)],[f_284_4]) ).

cnf(f_284_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK26(U_656,U_655,U_654)),U_655))
    | ~ sP46(U_656,U_654,U_655) ),
    inference(clausify,[status(thm)],[f_284_4]) ).

cnf(f_284_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK26(U_656,U_655,U_654)))
    | ~ sP46(U_656,U_654,U_655) ),
    inference(clausify,[status(thm)],[f_284_4]) ).

cnf(f_284_8,plain,
    ( U_654 = image_nat_nat(U_656,sK26(U_656,U_655,U_654))
    | ~ sP46(U_656,U_654,U_655) ),
    inference(clausify,[status(thm)],[f_284_4]) ).

fof(f_285_1,plain,
    ! [F,A_1,B_6] :
      ( ? [C_7] :
          ( B_6 = image_pname_a(F,C_7)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_7))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_7),A_1))
          & is_fun_pname_bool(C_7) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B_6))
      | ~ is_fun_a_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_181_finite__subset__image]) ).

fof(f_285_2,plain,
    ! [U_660,U_659,U_658] :
      ( ? [U_657] :
          ( U_658 = image_pname_a(U_660,U_657)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_657))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_657),U_659))
          & is_fun_pname_bool(U_657) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_658),image_pname_a(U_660,U_659)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_658))
      | ~ is_fun_a_bool(U_658) ),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

fof(f_285_3,plain,
    ! [U_660,U_659,U_658] :
      ( ( U_658 = image_pname_a(U_660,sK27(U_660,U_659,U_658))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK27(U_660,U_659,U_658)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK27(U_660,U_659,U_658)),U_659))
        & is_fun_pname_bool(sK27(U_660,U_659,U_658)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_658),image_pname_a(U_660,U_659)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_658))
      | ~ is_fun_a_bool(U_658) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_657,sK27(U_660,U_659,U_658))],[f_285_2]) ).

fof(f_285_4,plain,
    ( ! [U_658,U_659,U_660] :
        ( U_658 = image_pname_a(U_660,sK27(U_660,U_659,U_658))
        | ~ sP47(U_658,U_659,U_660) )
    & ! [U_658,U_659,U_660] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK27(U_660,U_659,U_658)))
        | ~ sP47(U_658,U_659,U_660) )
    & ! [U_658,U_659,U_660] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK27(U_660,U_659,U_658)),U_659))
        | ~ sP47(U_658,U_659,U_660) )
    & ! [U_658,U_659,U_660] :
        ( is_fun_pname_bool(sK27(U_660,U_659,U_658))
        | ~ sP47(U_658,U_659,U_660) )
    & ! [U_658,U_659,U_660] :
        ( sP47(U_658,U_659,U_660)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_658),image_pname_a(U_660,U_659)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_658))
        | ~ is_fun_a_bool(U_658) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_285_3]) ).

cnf(f_285_5,plain,
    ( sP47(U_658,U_659,U_660)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_658),image_pname_a(U_660,U_659)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_658))
    | ~ is_fun_a_bool(U_658) ),
    inference(clausify,[status(thm)],[f_285_4]) ).

cnf(f_285_6,plain,
    ( is_fun_pname_bool(sK27(U_660,U_659,U_658))
    | ~ sP47(U_658,U_659,U_660) ),
    inference(clausify,[status(thm)],[f_285_4]) ).

cnf(f_285_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK27(U_660,U_659,U_658)),U_659))
    | ~ sP47(U_658,U_659,U_660) ),
    inference(clausify,[status(thm)],[f_285_4]) ).

cnf(f_285_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK27(U_660,U_659,U_658)))
    | ~ sP47(U_658,U_659,U_660) ),
    inference(clausify,[status(thm)],[f_285_4]) ).

cnf(f_285_9,plain,
    ( U_658 = image_pname_a(U_660,sK27(U_660,U_659,U_658))
    | ~ sP47(U_658,U_659,U_660) ),
    inference(clausify,[status(thm)],[f_285_4]) ).

fof(f_286_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_2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,N_2)),hAPP_nat_bool(F,hAPP_nat_nat(suc,N_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_182_lift__Suc__mono__le]) ).

fof(f_286_2,plain,
    ! [U_664,U_663,U_662] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_662,U_664)),hAPP_nat_bool(U_662,U_663)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_664),U_663))
      | ? [U_661] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_662,U_661)),hAPP_nat_bool(U_662,hAPP_nat_nat(suc,U_661)))) ),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

fof(f_286_3,plain,
    ! [U_664,U_663,U_662] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_662,U_664)),hAPP_nat_bool(U_662,U_663)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_664),U_663))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_662,sK28(U_664,U_663,U_662))),hAPP_nat_bool(U_662,hAPP_nat_nat(suc,sK28(U_664,U_663,U_662))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_661,sK28(U_664,U_663,U_662))],[f_286_2]) ).

fof(f_286_4,plain,
    ! [U_662,U_663,U_664] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_662,U_664)),hAPP_nat_bool(U_662,U_663)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_664),U_663))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_662,sK28(U_664,U_663,U_662))),hAPP_nat_bool(U_662,hAPP_nat_nat(suc,sK28(U_664,U_663,U_662))))) ),
    inference(definitional_conversion,[status(esa)],[f_286_3]) ).

cnf(f_286_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_662,U_664)),hAPP_nat_bool(U_662,U_663)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_664),U_663))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_662,sK28(U_664,U_663,U_662))),hAPP_nat_bool(U_662,hAPP_nat_nat(suc,sK28(U_664,U_663,U_662))))) ),
    inference(clausify,[status(thm)],[f_286_4]) ).

fof(f_287_1,plain,
    ! [Na,N_3,F] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,Na)),hAPP_n1025906991e_bool(F,N_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
      | ? [N_2] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,N_2)),hAPP_n1025906991e_bool(F,hAPP_nat_nat(suc,N_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_183_lift__Suc__mono__le]) ).

fof(f_287_2,plain,
    ! [U_668,U_667,U_666] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_666,U_668)),hAPP_n1025906991e_bool(U_666,U_667)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_668),U_667))
      | ? [U_665] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_666,U_665)),hAPP_n1025906991e_bool(U_666,hAPP_nat_nat(suc,U_665)))) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

fof(f_287_3,plain,
    ! [U_668,U_667,U_666] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_666,U_668)),hAPP_n1025906991e_bool(U_666,U_667)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_668),U_667))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_666,sK29(U_668,U_667,U_666))),hAPP_n1025906991e_bool(U_666,hAPP_nat_nat(suc,sK29(U_668,U_667,U_666))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_665,sK29(U_668,U_667,U_666))],[f_287_2]) ).

fof(f_287_4,plain,
    ! [U_666,U_667,U_668] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_666,U_668)),hAPP_n1025906991e_bool(U_666,U_667)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_668),U_667))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_666,sK29(U_668,U_667,U_666))),hAPP_n1025906991e_bool(U_666,hAPP_nat_nat(suc,sK29(U_668,U_667,U_666))))) ),
    inference(definitional_conversion,[status(esa)],[f_287_3]) ).

cnf(f_287_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_666,U_668)),hAPP_n1025906991e_bool(U_666,U_667)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_668),U_667))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_666,sK29(U_668,U_667,U_666))),hAPP_n1025906991e_bool(U_666,hAPP_nat_nat(suc,sK29(U_668,U_667,U_666))))) ),
    inference(clausify,[status(thm)],[f_287_4]) ).

fof(f_288_1,plain,
    ! [Na,N_3,F] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Na)),hAPP_n1699378549t_bool(F,N_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
      | ? [N_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,N_2)),hAPP_n1699378549t_bool(F,hAPP_nat_nat(suc,N_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_184_lift__Suc__mono__le]) ).

fof(f_288_2,plain,
    ! [U_672,U_671,U_670] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_670,U_672)),hAPP_n1699378549t_bool(U_670,U_671)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_672),U_671))
      | ? [U_669] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_670,U_669)),hAPP_n1699378549t_bool(U_670,hAPP_nat_nat(suc,U_669)))) ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

fof(f_288_3,plain,
    ! [U_672,U_671,U_670] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_670,U_672)),hAPP_n1699378549t_bool(U_670,U_671)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_672),U_671))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_670,sK30(U_672,U_671,U_670))),hAPP_n1699378549t_bool(U_670,hAPP_nat_nat(suc,sK30(U_672,U_671,U_670))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_669,sK30(U_672,U_671,U_670))],[f_288_2]) ).

fof(f_288_4,plain,
    ! [U_670,U_671,U_672] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_670,U_672)),hAPP_n1699378549t_bool(U_670,U_671)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_672),U_671))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_670,sK30(U_672,U_671,U_670))),hAPP_n1699378549t_bool(U_670,hAPP_nat_nat(suc,sK30(U_672,U_671,U_670))))) ),
    inference(definitional_conversion,[status(esa)],[f_288_3]) ).

cnf(f_288_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_670,U_672)),hAPP_n1699378549t_bool(U_670,U_671)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_672),U_671))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_670,sK30(U_672,U_671,U_670))),hAPP_n1699378549t_bool(U_670,hAPP_nat_nat(suc,sK30(U_672,U_671,U_670))))) ),
    inference(clausify,[status(thm)],[f_288_4]) ).

fof(f_289_1,plain,
    ! [Na,N_3,F] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,Na)),hAPP_nat_fun_a_bool(F,N_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
      | ? [N_2] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,N_2)),hAPP_nat_fun_a_bool(F,hAPP_nat_nat(suc,N_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_185_lift__Suc__mono__le]) ).

fof(f_289_2,plain,
    ! [U_676,U_675,U_674] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_674,U_676)),hAPP_nat_fun_a_bool(U_674,U_675)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_676),U_675))
      | ? [U_673] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_674,U_673)),hAPP_nat_fun_a_bool(U_674,hAPP_nat_nat(suc,U_673)))) ),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

fof(f_289_3,plain,
    ! [U_676,U_675,U_674] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_674,U_676)),hAPP_nat_fun_a_bool(U_674,U_675)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_676),U_675))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_674,sK31(U_676,U_675,U_674))),hAPP_nat_fun_a_bool(U_674,hAPP_nat_nat(suc,sK31(U_676,U_675,U_674))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_673,sK31(U_676,U_675,U_674))],[f_289_2]) ).

fof(f_289_4,plain,
    ! [U_674,U_675,U_676] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_674,U_676)),hAPP_nat_fun_a_bool(U_674,U_675)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_676),U_675))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_674,sK31(U_676,U_675,U_674))),hAPP_nat_fun_a_bool(U_674,hAPP_nat_nat(suc,sK31(U_676,U_675,U_674))))) ),
    inference(definitional_conversion,[status(esa)],[f_289_3]) ).

cnf(f_289_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_674,U_676)),hAPP_nat_fun_a_bool(U_674,U_675)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_676),U_675))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_674,sK31(U_676,U_675,U_674))),hAPP_nat_fun_a_bool(U_674,hAPP_nat_nat(suc,sK31(U_676,U_675,U_674))))) ),
    inference(clausify,[status(thm)],[f_289_4]) ).

fof(f_290_1,plain,
    ! [Na,N_3,F] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Na)),hAPP_nat_nat(F,N_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
      | ? [N_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,N_2)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_186_lift__Suc__mono__le]) ).

fof(f_290_2,plain,
    ! [U_680,U_679,U_678] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_678,U_680)),hAPP_nat_nat(U_678,U_679)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_680),U_679))
      | ? [U_677] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_678,U_677)),hAPP_nat_nat(U_678,hAPP_nat_nat(suc,U_677)))) ),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

fof(f_290_3,plain,
    ! [U_680,U_679,U_678] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_678,U_680)),hAPP_nat_nat(U_678,U_679)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_680),U_679))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_678,sK32(U_680,U_679,U_678))),hAPP_nat_nat(U_678,hAPP_nat_nat(suc,sK32(U_680,U_679,U_678))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_677,sK32(U_680,U_679,U_678))],[f_290_2]) ).

fof(f_290_4,plain,
    ! [U_678,U_679,U_680] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_678,U_680)),hAPP_nat_nat(U_678,U_679)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_680),U_679))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_678,sK32(U_680,U_679,U_678))),hAPP_nat_nat(U_678,hAPP_nat_nat(suc,sK32(U_680,U_679,U_678))))) ),
    inference(definitional_conversion,[status(esa)],[f_290_3]) ).

cnf(f_290_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_678,U_680)),hAPP_nat_nat(U_678,U_679)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_680),U_679))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_678,sK32(U_680,U_679,U_678))),hAPP_nat_nat(U_678,hAPP_nat_nat(suc,sK32(U_680,U_679,U_678))))) ),
    inference(clausify,[status(thm)],[f_290_4]) ).

fof(f_291_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ 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_1)),hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,F)),hAPP_nat_pname(F,X_1))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(F,A_1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_187_pigeonhole__infinite]) ).

fof(f_291_2,plain,
    ! [U_683,U_682] :
      ( ? [U_681] :
          ( ~ 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_682)),hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,U_683)),hAPP_nat_pname(U_683,U_681))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_681),U_682)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(U_683,U_682)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_682)) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

fof(f_291_3,plain,
    ! [U_683,U_682] :
      ( ( ~ 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_682)),hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,U_683)),hAPP_nat_pname(U_683,sK33(U_683,U_682)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK33(U_683,U_682)),U_682)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(U_683,U_682)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_682)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_681,sK33(U_683,U_682))],[f_291_2]) ).

fof(f_291_4,plain,
    ( ! [U_682,U_683] :
        ( ~ 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_682)),hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,U_683)),hAPP_nat_pname(U_683,sK33(U_683,U_682)))))))
        | ~ sP48(U_682,U_683) )
    & ! [U_682,U_683] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK33(U_683,U_682)),U_682))
        | ~ sP48(U_682,U_683) )
    & ! [U_682,U_683] :
        ( sP48(U_682,U_683)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(U_683,U_682)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_682)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_291_3]) ).

cnf(f_291_5,plain,
    ( sP48(U_682,U_683)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(U_683,U_682)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_682)) ),
    inference(clausify,[status(thm)],[f_291_4]) ).

cnf(f_291_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK33(U_683,U_682)),U_682))
    | ~ sP48(U_682,U_683) ),
    inference(clausify,[status(thm)],[f_291_4]) ).

cnf(f_291_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_682)),hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,U_683)),hAPP_nat_pname(U_683,sK33(U_683,U_682)))))))
    | ~ sP48(U_682,U_683) ),
    inference(clausify,[status(thm)],[f_291_4]) ).

fof(f_292_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_p1534023578a_bool(cOMBC_a_pname_bool(cOMBB_610033911bool_a(fequal_pname,F)),hAPP_a_pname(F,X_1))))))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
          & is_a(X_1) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(F,A_1)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_188_pigeonhole__infinite]) ).

fof(f_292_2,plain,
    ! [U_686,U_685] :
      ( ? [U_684] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_685)),hAPP_p1534023578a_bool(cOMBC_a_pname_bool(cOMBB_610033911bool_a(fequal_pname,U_686)),hAPP_a_pname(U_686,U_684))))))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_684),U_685))
          & is_a(U_684) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(U_686,U_685)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_685)) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

fof(f_292_3,plain,
    ! [U_686,U_685] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_685)),hAPP_p1534023578a_bool(cOMBC_a_pname_bool(cOMBB_610033911bool_a(fequal_pname,U_686)),hAPP_a_pname(U_686,sK34(U_686,U_685)))))))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK34(U_686,U_685)),U_685))
        & is_a(sK34(U_686,U_685)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(U_686,U_685)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_685)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_684,sK34(U_686,U_685))],[f_292_2]) ).

fof(f_292_4,plain,
    ( ! [U_685,U_686] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_685)),hAPP_p1534023578a_bool(cOMBC_a_pname_bool(cOMBB_610033911bool_a(fequal_pname,U_686)),hAPP_a_pname(U_686,sK34(U_686,U_685)))))))
        | ~ sP49(U_685,U_686) )
    & ! [U_685,U_686] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK34(U_686,U_685)),U_685))
        | ~ sP49(U_685,U_686) )
    & ! [U_685,U_686] :
        ( is_a(sK34(U_686,U_685))
        | ~ sP49(U_685,U_686) )
    & ! [U_685,U_686] :
        ( sP49(U_685,U_686)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(U_686,U_685)))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_685)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_292_3]) ).

cnf(f_292_5,plain,
    ( sP49(U_685,U_686)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(U_686,U_685)))
    | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_685)) ),
    inference(clausify,[status(thm)],[f_292_4]) ).

cnf(f_292_6,plain,
    ( is_a(sK34(U_686,U_685))
    | ~ sP49(U_685,U_686) ),
    inference(clausify,[status(thm)],[f_292_4]) ).

cnf(f_292_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK34(U_686,U_685)),U_685))
    | ~ sP49(U_685,U_686) ),
    inference(clausify,[status(thm)],[f_292_4]) ).

cnf(f_292_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_685)),hAPP_p1534023578a_bool(cOMBC_a_pname_bool(cOMBB_610033911bool_a(fequal_pname,U_686)),hAPP_a_pname(U_686,sK34(U_686,U_685)))))))
    | ~ sP49(U_685,U_686) ),
    inference(clausify,[status(thm)],[f_292_4]) ).

fof(f_293_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_p61793385e_bool(cOMBC_1149511130e_bool(cOMBB_542850580_pname(fequal_pname,F)),hAPP_pname_pname(F,X_1))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
          & is_pname(X_1) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(F,A_1)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_189_pigeonhole__infinite]) ).

fof(f_293_2,plain,
    ! [U_689,U_688] :
      ( ? [U_687] :
          ( ~ 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_688)),hAPP_p61793385e_bool(cOMBC_1149511130e_bool(cOMBB_542850580_pname(fequal_pname,U_689)),hAPP_pname_pname(U_689,U_687))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_687),U_688))
          & is_pname(U_687) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(U_689,U_688)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_688)) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ! [U_689,U_688] :
      ( ( ~ 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_688)),hAPP_p61793385e_bool(cOMBC_1149511130e_bool(cOMBB_542850580_pname(fequal_pname,U_689)),hAPP_pname_pname(U_689,sK35(U_689,U_688)))))))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK35(U_689,U_688)),U_688))
        & is_pname(sK35(U_689,U_688)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(U_689,U_688)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_688)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_687,sK35(U_689,U_688))],[f_293_2]) ).

fof(f_293_4,plain,
    ( ! [U_689,U_688] :
        ( ~ 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_688)),hAPP_p61793385e_bool(cOMBC_1149511130e_bool(cOMBB_542850580_pname(fequal_pname,U_689)),hAPP_pname_pname(U_689,sK35(U_689,U_688)))))))
        | ~ sP50(U_689,U_688) )
    & ! [U_689,U_688] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK35(U_689,U_688)),U_688))
        | ~ sP50(U_689,U_688) )
    & ! [U_689,U_688] :
        ( is_pname(sK35(U_689,U_688))
        | ~ sP50(U_689,U_688) )
    & ! [U_689,U_688] :
        ( sP50(U_689,U_688)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(U_689,U_688)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_688)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50])],[f_293_3]) ).

cnf(f_293_5,plain,
    ( sP50(U_689,U_688)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(U_689,U_688)))
    | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_688)) ),
    inference(clausify,[status(thm)],[f_293_4]) ).

cnf(f_293_6,plain,
    ( is_pname(sK35(U_689,U_688))
    | ~ sP50(U_689,U_688) ),
    inference(clausify,[status(thm)],[f_293_4]) ).

cnf(f_293_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK35(U_689,U_688)),U_688))
    | ~ sP50(U_689,U_688) ),
    inference(clausify,[status(thm)],[f_293_4]) ).

cnf(f_293_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_688)),hAPP_p61793385e_bool(cOMBC_1149511130e_bool(cOMBB_542850580_pname(fequal_pname,U_689)),hAPP_pname_pname(U_689,sK35(U_689,U_688)))))))
    | ~ sP50(U_689,U_688) ),
    inference(clausify,[status(thm)],[f_293_4]) ).

fof(f_294_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),A_1)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,F)),hAPP_f1291551745_pname(F,X_1))))))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A_1)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(F,A_1)))
      | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_190_pigeonhole__infinite]) ).

fof(f_294_2,plain,
    ! [U_692,U_691] :
      ( ? [U_690] :
          ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_691)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,U_692)),hAPP_f1291551745_pname(U_692,U_690))))))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_690),U_691)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(U_692,U_691)))
      | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_691)) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

fof(f_294_3,plain,
    ! [U_692,U_691] :
      ( ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_691)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,U_692)),hAPP_f1291551745_pname(U_692,sK36(U_692,U_691)))))))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK36(U_692,U_691)),U_691)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(U_692,U_691)))
      | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_691)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_690,sK36(U_692,U_691))],[f_294_2]) ).

fof(f_294_4,plain,
    ( ! [U_692,U_691] :
        ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_691)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,U_692)),hAPP_f1291551745_pname(U_692,sK36(U_692,U_691)))))))
        | ~ sP51(U_692,U_691) )
    & ! [U_692,U_691] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK36(U_692,U_691)),U_691))
        | ~ sP51(U_692,U_691) )
    & ! [U_692,U_691] :
        ( sP51(U_692,U_691)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(U_692,U_691)))
        | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_691)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_294_3]) ).

cnf(f_294_5,plain,
    ( sP51(U_692,U_691)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(U_692,U_691)))
    | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_691)) ),
    inference(clausify,[status(thm)],[f_294_4]) ).

cnf(f_294_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK36(U_692,U_691)),U_691))
    | ~ sP51(U_692,U_691) ),
    inference(clausify,[status(thm)],[f_294_4]) ).

cnf(f_294_7,plain,
    ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_691)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,U_692)),hAPP_f1291551745_pname(U_692,sK36(U_692,U_691)))))))
    | ~ sP51(U_692,U_691) ),
    inference(clausify,[status(thm)],[f_294_4]) ).

fof(f_295_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),A_1)),hAPP_p338031245l_bool(cOMBC_1004116266e_bool(cOMBB_598082538e_bool(fequal_pname,F)),hAPP_f1297739591_pname(F,X_1))))))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1))
          & is_fun_pname_bool(X_1) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(F,A_1)))
      | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_191_pigeonhole__infinite]) ).

fof(f_295_2,plain,
    ! [U_695,U_694] :
      ( ? [U_693] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_694)),hAPP_p338031245l_bool(cOMBC_1004116266e_bool(cOMBB_598082538e_bool(fequal_pname,U_695)),hAPP_f1297739591_pname(U_695,U_693))))))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_693),U_694))
          & is_fun_pname_bool(U_693) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_695,U_694)))
      | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_694)) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

fof(f_295_3,plain,
    ! [U_695,U_694] :
      ( ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_694)),hAPP_p338031245l_bool(cOMBC_1004116266e_bool(cOMBB_598082538e_bool(fequal_pname,U_695)),hAPP_f1297739591_pname(U_695,sK37(U_695,U_694)))))))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK37(U_695,U_694)),U_694))
        & is_fun_pname_bool(sK37(U_695,U_694)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_695,U_694)))
      | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_694)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_693,sK37(U_695,U_694))],[f_295_2]) ).

fof(f_295_4,plain,
    ( ! [U_694,U_695] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_694)),hAPP_p338031245l_bool(cOMBC_1004116266e_bool(cOMBB_598082538e_bool(fequal_pname,U_695)),hAPP_f1297739591_pname(U_695,sK37(U_695,U_694)))))))
        | ~ sP52(U_694,U_695) )
    & ! [U_694,U_695] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK37(U_695,U_694)),U_694))
        | ~ sP52(U_694,U_695) )
    & ! [U_694,U_695] :
        ( is_fun_pname_bool(sK37(U_695,U_694))
        | ~ sP52(U_694,U_695) )
    & ! [U_694,U_695] :
        ( sP52(U_694,U_695)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_695,U_694)))
        | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_694)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52])],[f_295_3]) ).

cnf(f_295_5,plain,
    ( sP52(U_694,U_695)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_695,U_694)))
    | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_694)) ),
    inference(clausify,[status(thm)],[f_295_4]) ).

cnf(f_295_6,plain,
    ( is_fun_pname_bool(sK37(U_695,U_694))
    | ~ sP52(U_694,U_695) ),
    inference(clausify,[status(thm)],[f_295_4]) ).

cnf(f_295_7,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK37(U_695,U_694)),U_694))
    | ~ sP52(U_694,U_695) ),
    inference(clausify,[status(thm)],[f_295_4]) ).

cnf(f_295_8,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_694)),hAPP_p338031245l_bool(cOMBC_1004116266e_bool(cOMBB_598082538e_bool(fequal_pname,U_695)),hAPP_f1297739591_pname(U_695,sK37(U_695,U_694)))))))
    | ~ sP52(U_694,U_695) ),
    inference(clausify,[status(thm)],[f_295_4]) ).

fof(f_296_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),A_1)),hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(cOMBB_1693087065a_bool(fequal_pname,F)),hAPP_f1128469712_pname(F,X_1))))))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A_1))
          & is_fun_a_bool(X_1) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(F,A_1)))
      | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_192_pigeonhole__infinite]) ).

fof(f_296_2,plain,
    ! [U_698,U_697] :
      ( ? [U_696] :
          ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_697)),hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(cOMBB_1693087065a_bool(fequal_pname,U_698)),hAPP_f1128469712_pname(U_698,U_696))))))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_696),U_697))
          & is_fun_a_bool(U_696) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(U_698,U_697)))
      | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_697)) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ! [U_698,U_697] :
      ( ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_697)),hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(cOMBB_1693087065a_bool(fequal_pname,U_698)),hAPP_f1128469712_pname(U_698,sK38(U_698,U_697)))))))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK38(U_698,U_697)),U_697))
        & is_fun_a_bool(sK38(U_698,U_697)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(U_698,U_697)))
      | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_697)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_696,sK38(U_698,U_697))],[f_296_2]) ).

fof(f_296_4,plain,
    ( ! [U_697,U_698] :
        ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_697)),hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(cOMBB_1693087065a_bool(fequal_pname,U_698)),hAPP_f1128469712_pname(U_698,sK38(U_698,U_697)))))))
        | ~ sP53(U_697,U_698) )
    & ! [U_697,U_698] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK38(U_698,U_697)),U_697))
        | ~ sP53(U_697,U_698) )
    & ! [U_697,U_698] :
        ( is_fun_a_bool(sK38(U_698,U_697))
        | ~ sP53(U_697,U_698) )
    & ! [U_697,U_698] :
        ( sP53(U_697,U_698)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(U_698,U_697)))
        | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_697)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53])],[f_296_3]) ).

cnf(f_296_5,plain,
    ( sP53(U_697,U_698)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(U_698,U_697)))
    | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_697)) ),
    inference(clausify,[status(thm)],[f_296_4]) ).

cnf(f_296_6,plain,
    ( is_fun_a_bool(sK38(U_698,U_697))
    | ~ sP53(U_697,U_698) ),
    inference(clausify,[status(thm)],[f_296_4]) ).

cnf(f_296_7,plain,
    ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK38(U_698,U_697)),U_697))
    | ~ sP53(U_697,U_698) ),
    inference(clausify,[status(thm)],[f_296_4]) ).

cnf(f_296_8,plain,
    ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_697)),hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(cOMBB_1693087065a_bool(fequal_pname,U_698)),hAPP_f1128469712_pname(U_698,sK38(U_698,U_697)))))))
    | ~ sP53(U_697,U_698) ),
    inference(clausify,[status(thm)],[f_296_4]) ).

fof(f_297_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ 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_1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,F)),hAPP_nat_nat(F,X_1))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(F,A_1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_193_pigeonhole__infinite]) ).

fof(f_297_2,plain,
    ! [U_701,U_700] :
      ( ? [U_699] :
          ( ~ 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_700)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,U_701)),hAPP_nat_nat(U_701,U_699))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_699),U_700)) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(U_701,U_700)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_700)) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

fof(f_297_3,plain,
    ! [U_701,U_700] :
      ( ( ~ 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_700)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,U_701)),hAPP_nat_nat(U_701,sK39(U_701,U_700)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK39(U_701,U_700)),U_700)) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(U_701,U_700)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_700)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_699,sK39(U_701,U_700))],[f_297_2]) ).

fof(f_297_4,plain,
    ( ! [U_700,U_701] :
        ( ~ 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_700)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,U_701)),hAPP_nat_nat(U_701,sK39(U_701,U_700)))))))
        | ~ sP54(U_700,U_701) )
    & ! [U_700,U_701] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK39(U_701,U_700)),U_700))
        | ~ sP54(U_700,U_701) )
    & ! [U_700,U_701] :
        ( sP54(U_700,U_701)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(U_701,U_700)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_700)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54])],[f_297_3]) ).

cnf(f_297_5,plain,
    ( sP54(U_700,U_701)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(U_701,U_700)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_700)) ),
    inference(clausify,[status(thm)],[f_297_4]) ).

cnf(f_297_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK39(U_701,U_700)),U_700))
    | ~ sP54(U_700,U_701) ),
    inference(clausify,[status(thm)],[f_297_4]) ).

cnf(f_297_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_700)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,U_701)),hAPP_nat_nat(U_701,sK39(U_701,U_700)))))))
    | ~ sP54(U_700,U_701) ),
    inference(clausify,[status(thm)],[f_297_4]) ).

fof(f_298_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(cOMBB_1321347587bool_a(fequal_nat,F)),hAPP_a_nat(F,X_1))))))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
          & is_a(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(F,A_1)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_194_pigeonhole__infinite]) ).

fof(f_298_2,plain,
    ! [U_704,U_703] :
      ( ? [U_702] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_703)),hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(cOMBB_1321347587bool_a(fequal_nat,U_704)),hAPP_a_nat(U_704,U_702))))))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_702),U_703))
          & is_a(U_702) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(U_704,U_703)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_703)) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

fof(f_298_3,plain,
    ! [U_704,U_703] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_703)),hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(cOMBB_1321347587bool_a(fequal_nat,U_704)),hAPP_a_nat(U_704,sK40(U_704,U_703)))))))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK40(U_704,U_703)),U_703))
        & is_a(sK40(U_704,U_703)) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(U_704,U_703)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_703)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_702,sK40(U_704,U_703))],[f_298_2]) ).

fof(f_298_4,plain,
    ( ! [U_703,U_704] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_703)),hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(cOMBB_1321347587bool_a(fequal_nat,U_704)),hAPP_a_nat(U_704,sK40(U_704,U_703)))))))
        | ~ sP55(U_703,U_704) )
    & ! [U_703,U_704] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK40(U_704,U_703)),U_703))
        | ~ sP55(U_703,U_704) )
    & ! [U_703,U_704] :
        ( is_a(sK40(U_704,U_703))
        | ~ sP55(U_703,U_704) )
    & ! [U_703,U_704] :
        ( sP55(U_703,U_704)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(U_704,U_703)))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_703)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_298_3]) ).

cnf(f_298_5,plain,
    ( sP55(U_703,U_704)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(U_704,U_703)))
    | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_703)) ),
    inference(clausify,[status(thm)],[f_298_4]) ).

cnf(f_298_6,plain,
    ( is_a(sK40(U_704,U_703))
    | ~ sP55(U_703,U_704) ),
    inference(clausify,[status(thm)],[f_298_4]) ).

cnf(f_298_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK40(U_704,U_703)),U_703))
    | ~ sP55(U_703,U_704) ),
    inference(clausify,[status(thm)],[f_298_4]) ).

cnf(f_298_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_703)),hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(cOMBB_1321347587bool_a(fequal_nat,U_704)),hAPP_a_nat(U_704,sK40(U_704,U_703)))))))
    | ~ sP55(U_703,U_704) ),
    inference(clausify,[status(thm)],[f_298_4]) ).

fof(f_299_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(cOMBB_523834888_pname(fequal_nat,F)),hAPP_pname_nat(F,X_1))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
          & is_pname(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(F,A_1)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_195_pigeonhole__infinite]) ).

fof(f_299_2,plain,
    ! [U_707,U_706] :
      ( ? [U_705] :
          ( ~ 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_706)),hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(cOMBB_523834888_pname(fequal_nat,U_707)),hAPP_pname_nat(U_707,U_705))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_705),U_706))
          & is_pname(U_705) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(U_707,U_706)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_706)) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

fof(f_299_3,plain,
    ! [U_707,U_706] :
      ( ( ~ 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_706)),hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(cOMBB_523834888_pname(fequal_nat,U_707)),hAPP_pname_nat(U_707,sK41(U_707,U_706)))))))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK41(U_707,U_706)),U_706))
        & is_pname(sK41(U_707,U_706)) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(U_707,U_706)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_706)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_705,sK41(U_707,U_706))],[f_299_2]) ).

fof(f_299_4,plain,
    ( ! [U_706,U_707] :
        ( ~ 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_706)),hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(cOMBB_523834888_pname(fequal_nat,U_707)),hAPP_pname_nat(U_707,sK41(U_707,U_706)))))))
        | ~ sP56(U_706,U_707) )
    & ! [U_706,U_707] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK41(U_707,U_706)),U_706))
        | ~ sP56(U_706,U_707) )
    & ! [U_706,U_707] :
        ( is_pname(sK41(U_707,U_706))
        | ~ sP56(U_706,U_707) )
    & ! [U_706,U_707] :
        ( sP56(U_706,U_707)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(U_707,U_706)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_706)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56])],[f_299_3]) ).

cnf(f_299_5,plain,
    ( sP56(U_706,U_707)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(U_707,U_706)))
    | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_706)) ),
    inference(clausify,[status(thm)],[f_299_4]) ).

cnf(f_299_6,plain,
    ( is_pname(sK41(U_707,U_706))
    | ~ sP56(U_706,U_707) ),
    inference(clausify,[status(thm)],[f_299_4]) ).

cnf(f_299_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK41(U_707,U_706)),U_706))
    | ~ sP56(U_706,U_707) ),
    inference(clausify,[status(thm)],[f_299_4]) ).

cnf(f_299_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_706)),hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(cOMBB_523834888_pname(fequal_nat,U_707)),hAPP_pname_nat(U_707,sK41(U_707,U_706)))))))
    | ~ sP56(U_706,U_707) ),
    inference(clausify,[status(thm)],[f_299_4]) ).

fof(f_300_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),A_1)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,F)),hAPP_f22106695ol_nat(F,X_1))))))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A_1)) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(F,A_1)))
      | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_196_pigeonhole__infinite]) ).

fof(f_300_2,plain,
    ! [U_710,U_709] :
      ( ? [U_708] :
          ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_709)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,U_710)),hAPP_f22106695ol_nat(U_710,U_708))))))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_708),U_709)) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(U_710,U_709)))
      | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_709)) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

fof(f_300_3,plain,
    ! [U_710,U_709] :
      ( ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_709)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,U_710)),hAPP_f22106695ol_nat(U_710,sK42(U_710,U_709)))))))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK42(U_710,U_709)),U_709)) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(U_710,U_709)))
      | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_709)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_708,sK42(U_710,U_709))],[f_300_2]) ).

fof(f_300_4,plain,
    ( ! [U_710,U_709] :
        ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_709)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,U_710)),hAPP_f22106695ol_nat(U_710,sK42(U_710,U_709)))))))
        | ~ sP57(U_710,U_709) )
    & ! [U_710,U_709] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK42(U_710,U_709)),U_709))
        | ~ sP57(U_710,U_709) )
    & ! [U_710,U_709] :
        ( sP57(U_710,U_709)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(U_710,U_709)))
        | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_709)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57])],[f_300_3]) ).

cnf(f_300_5,plain,
    ( sP57(U_710,U_709)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(U_710,U_709)))
    | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_709)) ),
    inference(clausify,[status(thm)],[f_300_4]) ).

cnf(f_300_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK42(U_710,U_709)),U_709))
    | ~ sP57(U_710,U_709) ),
    inference(clausify,[status(thm)],[f_300_4]) ).

cnf(f_300_7,plain,
    ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_709)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,U_710)),hAPP_f22106695ol_nat(U_710,sK42(U_710,U_709)))))))
    | ~ sP57(U_710,U_709) ),
    inference(clausify,[status(thm)],[f_300_4]) ).

fof(f_301_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),A_1)),hAPP_n850744903l_bool(cOMBC_1666426608t_bool(cOMBB_1896684278e_bool(fequal_nat,F)),hAPP_f921600141ol_nat(F,X_1))))))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A_1))
          & is_fun_pname_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(F,A_1)))
      | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_197_pigeonhole__infinite]) ).

fof(f_301_2,plain,
    ! [U_713,U_712] :
      ( ? [U_711] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_712)),hAPP_n850744903l_bool(cOMBC_1666426608t_bool(cOMBB_1896684278e_bool(fequal_nat,U_713)),hAPP_f921600141ol_nat(U_713,U_711))))))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_711),U_712))
          & is_fun_pname_bool(U_711) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(U_713,U_712)))
      | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_712)) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

fof(f_301_3,plain,
    ! [U_713,U_712] :
      ( ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_712)),hAPP_n850744903l_bool(cOMBC_1666426608t_bool(cOMBB_1896684278e_bool(fequal_nat,U_713)),hAPP_f921600141ol_nat(U_713,sK43(U_713,U_712)))))))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK43(U_713,U_712)),U_712))
        & is_fun_pname_bool(sK43(U_713,U_712)) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(U_713,U_712)))
      | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_712)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_711,sK43(U_713,U_712))],[f_301_2]) ).

fof(f_301_4,plain,
    ( ! [U_712,U_713] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_712)),hAPP_n850744903l_bool(cOMBC_1666426608t_bool(cOMBB_1896684278e_bool(fequal_nat,U_713)),hAPP_f921600141ol_nat(U_713,sK43(U_713,U_712)))))))
        | ~ sP58(U_712,U_713) )
    & ! [U_712,U_713] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK43(U_713,U_712)),U_712))
        | ~ sP58(U_712,U_713) )
    & ! [U_712,U_713] :
        ( is_fun_pname_bool(sK43(U_713,U_712))
        | ~ sP58(U_712,U_713) )
    & ! [U_712,U_713] :
        ( sP58(U_712,U_713)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(U_713,U_712)))
        | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_712)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58])],[f_301_3]) ).

cnf(f_301_5,plain,
    ( sP58(U_712,U_713)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(U_713,U_712)))
    | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_712)) ),
    inference(clausify,[status(thm)],[f_301_4]) ).

cnf(f_301_6,plain,
    ( is_fun_pname_bool(sK43(U_713,U_712))
    | ~ sP58(U_712,U_713) ),
    inference(clausify,[status(thm)],[f_301_4]) ).

cnf(f_301_7,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK43(U_713,U_712)),U_712))
    | ~ sP58(U_712,U_713) ),
    inference(clausify,[status(thm)],[f_301_4]) ).

cnf(f_301_8,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_712)),hAPP_n850744903l_bool(cOMBC_1666426608t_bool(cOMBB_1896684278e_bool(fequal_nat,U_713)),hAPP_f921600141ol_nat(U_713,sK43(U_713,U_712)))))))
    | ~ sP58(U_712,U_713) ),
    inference(clausify,[status(thm)],[f_301_4]) ).

fof(f_302_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),A_1)),hAPP_n1414589940l_bool(cOMBC_619334683t_bool(cOMBB_164527437a_bool(fequal_nat,F)),hAPP_fun_a_bool_nat(F,X_1))))))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A_1))
          & is_fun_a_bool(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(F,A_1)))
      | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_198_pigeonhole__infinite]) ).

fof(f_302_2,plain,
    ! [U_716,U_715] :
      ( ? [U_714] :
          ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_715)),hAPP_n1414589940l_bool(cOMBC_619334683t_bool(cOMBB_164527437a_bool(fequal_nat,U_716)),hAPP_fun_a_bool_nat(U_716,U_714))))))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_714),U_715))
          & is_fun_a_bool(U_714) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(U_716,U_715)))
      | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_715)) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ! [U_716,U_715] :
      ( ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_715)),hAPP_n1414589940l_bool(cOMBC_619334683t_bool(cOMBB_164527437a_bool(fequal_nat,U_716)),hAPP_fun_a_bool_nat(U_716,sK44(U_716,U_715)))))))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK44(U_716,U_715)),U_715))
        & is_fun_a_bool(sK44(U_716,U_715)) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(U_716,U_715)))
      | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_715)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_714,sK44(U_716,U_715))],[f_302_2]) ).

fof(f_302_4,plain,
    ( ! [U_715,U_716] :
        ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_715)),hAPP_n1414589940l_bool(cOMBC_619334683t_bool(cOMBB_164527437a_bool(fequal_nat,U_716)),hAPP_fun_a_bool_nat(U_716,sK44(U_716,U_715)))))))
        | ~ sP59(U_715,U_716) )
    & ! [U_715,U_716] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK44(U_716,U_715)),U_715))
        | ~ sP59(U_715,U_716) )
    & ! [U_715,U_716] :
        ( is_fun_a_bool(sK44(U_716,U_715))
        | ~ sP59(U_715,U_716) )
    & ! [U_715,U_716] :
        ( sP59(U_715,U_716)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(U_716,U_715)))
        | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_715)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_302_3]) ).

cnf(f_302_5,plain,
    ( sP59(U_715,U_716)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(U_716,U_715)))
    | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_715)) ),
    inference(clausify,[status(thm)],[f_302_4]) ).

cnf(f_302_6,plain,
    ( is_fun_a_bool(sK44(U_716,U_715))
    | ~ sP59(U_715,U_716) ),
    inference(clausify,[status(thm)],[f_302_4]) ).

cnf(f_302_7,plain,
    ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK44(U_716,U_715)),U_715))
    | ~ sP59(U_715,U_716) ),
    inference(clausify,[status(thm)],[f_302_4]) ).

cnf(f_302_8,plain,
    ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_715)),hAPP_n1414589940l_bool(cOMBC_619334683t_bool(cOMBB_164527437a_bool(fequal_nat,U_716)),hAPP_fun_a_bool_nat(U_716,sK44(U_716,U_715)))))))
    | ~ sP59(U_715,U_716) ),
    inference(clausify,[status(thm)],[f_302_4]) ).

fof(f_303_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ 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_1)),hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,F)),hAPP_nat_a(F,X_1))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(F,A_1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_199_pigeonhole__infinite]) ).

fof(f_303_2,plain,
    ! [U_719,U_718] :
      ( ? [U_717] :
          ( ~ 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_718)),hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,U_719)),hAPP_nat_a(U_719,U_717))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_717),U_718)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(U_719,U_718)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_718)) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

fof(f_303_3,plain,
    ! [U_719,U_718] :
      ( ( ~ 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_718)),hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,U_719)),hAPP_nat_a(U_719,sK45(U_719,U_718)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK45(U_719,U_718)),U_718)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(U_719,U_718)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_718)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_717,sK45(U_719,U_718))],[f_303_2]) ).

fof(f_303_4,plain,
    ( ! [U_718,U_719] :
        ( ~ 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_718)),hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,U_719)),hAPP_nat_a(U_719,sK45(U_719,U_718)))))))
        | ~ sP60(U_718,U_719) )
    & ! [U_718,U_719] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK45(U_719,U_718)),U_718))
        | ~ sP60(U_718,U_719) )
    & ! [U_718,U_719] :
        ( sP60(U_718,U_719)
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(U_719,U_718)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_718)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60])],[f_303_3]) ).

cnf(f_303_5,plain,
    ( sP60(U_718,U_719)
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(U_719,U_718)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_718)) ),
    inference(clausify,[status(thm)],[f_303_4]) ).

cnf(f_303_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK45(U_719,U_718)),U_718))
    | ~ sP60(U_718,U_719) ),
    inference(clausify,[status(thm)],[f_303_4]) ).

cnf(f_303_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_718)),hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,U_719)),hAPP_nat_a(U_719,sK45(U_719,U_718)))))))
    | ~ sP60(U_718,U_719) ),
    inference(clausify,[status(thm)],[f_303_4]) ).

fof(f_304_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ 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_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,F)),hAPP_n1699378549t_bool(F,X_1))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(F,A_1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_200_pigeonhole__infinite]) ).

fof(f_304_2,plain,
    ! [U_722,U_721] :
      ( ? [U_720] :
          ( ~ 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_721)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,U_722)),hAPP_n1699378549t_bool(U_722,U_720))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_720),U_721)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_722,U_721)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_721)) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

fof(f_304_3,plain,
    ! [U_722,U_721] :
      ( ( ~ 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_721)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,U_722)),hAPP_n1699378549t_bool(U_722,sK46(U_722,U_721)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK46(U_722,U_721)),U_721)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_722,U_721)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_721)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_720,sK46(U_722,U_721))],[f_304_2]) ).

fof(f_304_4,plain,
    ( ! [U_721,U_722] :
        ( ~ 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_721)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,U_722)),hAPP_n1699378549t_bool(U_722,sK46(U_722,U_721)))))))
        | ~ sP61(U_721,U_722) )
    & ! [U_721,U_722] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK46(U_722,U_721)),U_721))
        | ~ sP61(U_721,U_722) )
    & ! [U_721,U_722] :
        ( sP61(U_721,U_722)
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_722,U_721)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_721)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_304_3]) ).

cnf(f_304_5,plain,
    ( sP61(U_721,U_722)
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_722,U_721)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_721)) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

cnf(f_304_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK46(U_722,U_721)),U_721))
    | ~ sP61(U_721,U_722) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

cnf(f_304_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_721)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,U_722)),hAPP_n1699378549t_bool(U_722,sK46(U_722,U_721)))))))
    | ~ sP61(U_721,U_722) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

fof(f_305_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ 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_1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,F)),hAPP_n1025906991e_bool(F,X_1))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(F,A_1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_201_pigeonhole__infinite]) ).

fof(f_305_2,plain,
    ! [U_725,U_724] :
      ( ? [U_723] :
          ( ~ 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_724)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,U_725)),hAPP_n1025906991e_bool(U_725,U_723))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_723),U_724)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_725,U_724)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_724)) ),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

fof(f_305_3,plain,
    ! [U_725,U_724] :
      ( ( ~ 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_724)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,U_725)),hAPP_n1025906991e_bool(U_725,sK47(U_725,U_724)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK47(U_725,U_724)),U_724)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_725,U_724)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_724)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_723,sK47(U_725,U_724))],[f_305_2]) ).

fof(f_305_4,plain,
    ( ! [U_724,U_725] :
        ( ~ 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_724)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,U_725)),hAPP_n1025906991e_bool(U_725,sK47(U_725,U_724)))))))
        | ~ sP62(U_724,U_725) )
    & ! [U_724,U_725] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK47(U_725,U_724)),U_724))
        | ~ sP62(U_724,U_725) )
    & ! [U_724,U_725] :
        ( sP62(U_724,U_725)
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_725,U_724)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_724)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_305_3]) ).

cnf(f_305_5,plain,
    ( sP62(U_724,U_725)
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_725,U_724)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_724)) ),
    inference(clausify,[status(thm)],[f_305_4]) ).

cnf(f_305_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK47(U_725,U_724)),U_724))
    | ~ sP62(U_724,U_725) ),
    inference(clausify,[status(thm)],[f_305_4]) ).

cnf(f_305_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_724)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,U_725)),hAPP_n1025906991e_bool(U_725,sK47(U_725,U_724)))))))
    | ~ sP62(U_724,U_725) ),
    inference(clausify,[status(thm)],[f_305_4]) ).

fof(f_306_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ 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_1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,F)),hAPP_nat_fun_a_bool(F,X_1))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(F,A_1)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_202_pigeonhole__infinite]) ).

fof(f_306_2,plain,
    ! [U_728,U_727] :
      ( ? [U_726] :
          ( ~ 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_727)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,U_728)),hAPP_nat_fun_a_bool(U_728,U_726))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_726),U_727)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_728,U_727)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_727)) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ! [U_728,U_727] :
      ( ( ~ 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_727)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,U_728)),hAPP_nat_fun_a_bool(U_728,sK48(U_728,U_727)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK48(U_728,U_727)),U_727)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_728,U_727)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_727)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_726,sK48(U_728,U_727))],[f_306_2]) ).

fof(f_306_4,plain,
    ( ! [U_728,U_727] :
        ( ~ 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_727)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,U_728)),hAPP_nat_fun_a_bool(U_728,sK48(U_728,U_727)))))))
        | ~ sP63(U_728,U_727) )
    & ! [U_728,U_727] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK48(U_728,U_727)),U_727))
        | ~ sP63(U_728,U_727) )
    & ! [U_728,U_727] :
        ( sP63(U_728,U_727)
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_728,U_727)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_727)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_306_3]) ).

cnf(f_306_5,plain,
    ( sP63(U_728,U_727)
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_728,U_727)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_727)) ),
    inference(clausify,[status(thm)],[f_306_4]) ).

cnf(f_306_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK48(U_728,U_727)),U_727))
    | ~ sP63(U_728,U_727) ),
    inference(clausify,[status(thm)],[f_306_4]) ).

cnf(f_306_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_727)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,U_728)),hAPP_nat_fun_a_bool(U_728,sK48(U_728,U_727)))))))
    | ~ sP63(U_728,U_727) ),
    inference(clausify,[status(thm)],[f_306_4]) ).

fof(f_307_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_f654413245e_bool(cOMBC_267053842l_bool(cOMBB_928955006_pname(fequal_fun_nat_bool,F)),hAPP_p1499970991t_bool(F,X_1))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
          & is_pname(X_1) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(F,A_1)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_203_pigeonhole__infinite]) ).

fof(f_307_2,plain,
    ! [U_731,U_730] :
      ( ? [U_729] :
          ( ~ 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_730)),hAPP_f654413245e_bool(cOMBC_267053842l_bool(cOMBB_928955006_pname(fequal_fun_nat_bool,U_731)),hAPP_p1499970991t_bool(U_731,U_729))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_729),U_730))
          & is_pname(U_729) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(U_731,U_730)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_730)) ),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

fof(f_307_3,plain,
    ! [U_731,U_730] :
      ( ( ~ 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_730)),hAPP_f654413245e_bool(cOMBC_267053842l_bool(cOMBB_928955006_pname(fequal_fun_nat_bool,U_731)),hAPP_p1499970991t_bool(U_731,sK49(U_731,U_730)))))))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK49(U_731,U_730)),U_730))
        & is_pname(sK49(U_731,U_730)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(U_731,U_730)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_730)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_729,sK49(U_731,U_730))],[f_307_2]) ).

fof(f_307_4,plain,
    ( ! [U_730,U_731] :
        ( ~ 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_730)),hAPP_f654413245e_bool(cOMBC_267053842l_bool(cOMBB_928955006_pname(fequal_fun_nat_bool,U_731)),hAPP_p1499970991t_bool(U_731,sK49(U_731,U_730)))))))
        | ~ sP64(U_730,U_731) )
    & ! [U_730,U_731] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK49(U_731,U_730)),U_730))
        | ~ sP64(U_730,U_731) )
    & ! [U_730,U_731] :
        ( is_pname(sK49(U_731,U_730))
        | ~ sP64(U_730,U_731) )
    & ! [U_730,U_731] :
        ( sP64(U_730,U_731)
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(U_731,U_730)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_730)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64])],[f_307_3]) ).

cnf(f_307_5,plain,
    ( sP64(U_730,U_731)
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(U_731,U_730)))
    | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_730)) ),
    inference(clausify,[status(thm)],[f_307_4]) ).

cnf(f_307_6,plain,
    ( is_pname(sK49(U_731,U_730))
    | ~ sP64(U_730,U_731) ),
    inference(clausify,[status(thm)],[f_307_4]) ).

cnf(f_307_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK49(U_731,U_730)),U_730))
    | ~ sP64(U_730,U_731) ),
    inference(clausify,[status(thm)],[f_307_4]) ).

cnf(f_307_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_730)),hAPP_f654413245e_bool(cOMBC_267053842l_bool(cOMBB_928955006_pname(fequal_fun_nat_bool,U_731)),hAPP_p1499970991t_bool(U_731,sK49(U_731,U_730)))))))
    | ~ sP64(U_730,U_731) ),
    inference(clausify,[status(thm)],[f_307_4]) ).

fof(f_308_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(cOMBB_408569982_pname(fequal533582459e_bool,F)),hAPP_p61793385e_bool(F,X_1))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
          & is_pname(X_1) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(F,A_1)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_204_pigeonhole__infinite]) ).

fof(f_308_2,plain,
    ! [U_734,U_733] :
      ( ? [U_732] :
          ( ~ 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_733)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(cOMBB_408569982_pname(fequal533582459e_bool,U_734)),hAPP_p61793385e_bool(U_734,U_732))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_732),U_733))
          & is_pname(U_732) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_734,U_733)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_733)) ),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

fof(f_308_3,plain,
    ! [U_734,U_733] :
      ( ( ~ 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_733)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(cOMBB_408569982_pname(fequal533582459e_bool,U_734)),hAPP_p61793385e_bool(U_734,sK50(U_734,U_733)))))))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK50(U_734,U_733)),U_733))
        & is_pname(sK50(U_734,U_733)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_734,U_733)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_733)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_732,sK50(U_734,U_733))],[f_308_2]) ).

fof(f_308_4,plain,
    ( ! [U_733,U_734] :
        ( ~ 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_733)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(cOMBB_408569982_pname(fequal533582459e_bool,U_734)),hAPP_p61793385e_bool(U_734,sK50(U_734,U_733)))))))
        | ~ sP65(U_733,U_734) )
    & ! [U_733,U_734] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK50(U_734,U_733)),U_733))
        | ~ sP65(U_733,U_734) )
    & ! [U_733,U_734] :
        ( is_pname(sK50(U_734,U_733))
        | ~ sP65(U_733,U_734) )
    & ! [U_733,U_734] :
        ( sP65(U_733,U_734)
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_734,U_733)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_733)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_308_3]) ).

cnf(f_308_5,plain,
    ( sP65(U_733,U_734)
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_734,U_733)))
    | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_733)) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

cnf(f_308_6,plain,
    ( is_pname(sK50(U_734,U_733))
    | ~ sP65(U_733,U_734) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

cnf(f_308_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK50(U_734,U_733)),U_733))
    | ~ sP65(U_733,U_734) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

cnf(f_308_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_733)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(cOMBB_408569982_pname(fequal533582459e_bool,U_734)),hAPP_p61793385e_bool(U_734,sK50(U_734,U_733)))))))
    | ~ sP65(U_733,U_734) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

fof(f_309_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_f1794073134e_bool(cOMBC_445755039l_bool(cOMBB_392435466_pname(fequal_fun_a_bool,F)),hAPP_p1534023578a_bool(F,X_1))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
          & is_pname(X_1) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(F,A_1)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_205_pigeonhole__infinite]) ).

fof(f_309_2,plain,
    ! [U_737,U_736] :
      ( ? [U_735] :
          ( ~ 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_736)),hAPP_f1794073134e_bool(cOMBC_445755039l_bool(cOMBB_392435466_pname(fequal_fun_a_bool,U_737)),hAPP_p1534023578a_bool(U_737,U_735))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_735),U_736))
          & is_pname(U_735) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(U_737,U_736)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_736)) ),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

fof(f_309_3,plain,
    ! [U_737,U_736] :
      ( ( ~ 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_736)),hAPP_f1794073134e_bool(cOMBC_445755039l_bool(cOMBB_392435466_pname(fequal_fun_a_bool,U_737)),hAPP_p1534023578a_bool(U_737,sK51(U_737,U_736)))))))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK51(U_737,U_736)),U_736))
        & is_pname(sK51(U_737,U_736)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(U_737,U_736)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_736)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_735,sK51(U_737,U_736))],[f_309_2]) ).

fof(f_309_4,plain,
    ( ! [U_736,U_737] :
        ( ~ 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_736)),hAPP_f1794073134e_bool(cOMBC_445755039l_bool(cOMBB_392435466_pname(fequal_fun_a_bool,U_737)),hAPP_p1534023578a_bool(U_737,sK51(U_737,U_736)))))))
        | ~ sP66(U_736,U_737) )
    & ! [U_736,U_737] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK51(U_737,U_736)),U_736))
        | ~ sP66(U_736,U_737) )
    & ! [U_736,U_737] :
        ( is_pname(sK51(U_737,U_736))
        | ~ sP66(U_736,U_737) )
    & ! [U_736,U_737] :
        ( sP66(U_736,U_737)
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(U_737,U_736)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_736)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66])],[f_309_3]) ).

cnf(f_309_5,plain,
    ( sP66(U_736,U_737)
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(U_737,U_736)))
    | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_736)) ),
    inference(clausify,[status(thm)],[f_309_4]) ).

cnf(f_309_6,plain,
    ( is_pname(sK51(U_737,U_736))
    | ~ sP66(U_736,U_737) ),
    inference(clausify,[status(thm)],[f_309_4]) ).

cnf(f_309_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK51(U_737,U_736)),U_736))
    | ~ sP66(U_736,U_737) ),
    inference(clausify,[status(thm)],[f_309_4]) ).

cnf(f_309_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_736)),hAPP_f1794073134e_bool(cOMBC_445755039l_bool(cOMBB_392435466_pname(fequal_fun_a_bool,U_737)),hAPP_p1534023578a_bool(U_737,sK51(U_737,U_736)))))))
    | ~ sP66(U_736,U_737) ),
    inference(clausify,[status(thm)],[f_309_4]) ).

fof(f_310_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_a_fun_a_bool(cOMBC_a_a_bool(cOMBB_a_fun_a_bool_a(fequal_a,F)),hAPP_a_a(F,X_1))))))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
          & is_a(X_1) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(F,A_1)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_206_pigeonhole__infinite]) ).

fof(f_310_2,plain,
    ! [U_740,U_739] :
      ( ? [U_738] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_739)),hAPP_a_fun_a_bool(cOMBC_a_a_bool(cOMBB_a_fun_a_bool_a(fequal_a,U_740)),hAPP_a_a(U_740,U_738))))))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_738),U_739))
          & is_a(U_738) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(U_740,U_739)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_739)) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

fof(f_310_3,plain,
    ! [U_740,U_739] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_739)),hAPP_a_fun_a_bool(cOMBC_a_a_bool(cOMBB_a_fun_a_bool_a(fequal_a,U_740)),hAPP_a_a(U_740,sK52(U_740,U_739)))))))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK52(U_740,U_739)),U_739))
        & is_a(sK52(U_740,U_739)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(U_740,U_739)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_739)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_738,sK52(U_740,U_739))],[f_310_2]) ).

fof(f_310_4,plain,
    ( ! [U_739,U_740] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_739)),hAPP_a_fun_a_bool(cOMBC_a_a_bool(cOMBB_a_fun_a_bool_a(fequal_a,U_740)),hAPP_a_a(U_740,sK52(U_740,U_739)))))))
        | ~ sP67(U_739,U_740) )
    & ! [U_739,U_740] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK52(U_740,U_739)),U_739))
        | ~ sP67(U_739,U_740) )
    & ! [U_739,U_740] :
        ( is_a(sK52(U_740,U_739))
        | ~ sP67(U_739,U_740) )
    & ! [U_739,U_740] :
        ( sP67(U_739,U_740)
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(U_740,U_739)))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_739)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67])],[f_310_3]) ).

cnf(f_310_5,plain,
    ( sP67(U_739,U_740)
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(U_740,U_739)))
    | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_739)) ),
    inference(clausify,[status(thm)],[f_310_4]) ).

cnf(f_310_6,plain,
    ( is_a(sK52(U_740,U_739))
    | ~ sP67(U_739,U_740) ),
    inference(clausify,[status(thm)],[f_310_4]) ).

cnf(f_310_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK52(U_740,U_739)),U_739))
    | ~ sP67(U_739,U_740) ),
    inference(clausify,[status(thm)],[f_310_4]) ).

cnf(f_310_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_739)),hAPP_a_fun_a_bool(cOMBC_a_a_bool(cOMBB_a_fun_a_bool_a(fequal_a,U_740)),hAPP_a_a(U_740,sK52(U_740,U_739)))))))
    | ~ sP67(U_739,U_740) ),
    inference(clausify,[status(thm)],[f_310_4]) ).

fof(f_311_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_f1549043526a_bool(cOMBC_777206479l_bool(cOMBB_743407885bool_a(fequal_fun_nat_bool,F)),hAPP_a_fun_nat_bool(F,X_1))))))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
          & is_a(X_1) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(F,A_1)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_207_pigeonhole__infinite]) ).

fof(f_311_2,plain,
    ! [U_743,U_742] :
      ( ? [U_741] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_742)),hAPP_f1549043526a_bool(cOMBC_777206479l_bool(cOMBB_743407885bool_a(fequal_fun_nat_bool,U_743)),hAPP_a_fun_nat_bool(U_743,U_741))))))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_741),U_742))
          & is_a(U_741) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(U_743,U_742)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_742)) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

fof(f_311_3,plain,
    ! [U_743,U_742] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_742)),hAPP_f1549043526a_bool(cOMBC_777206479l_bool(cOMBB_743407885bool_a(fequal_fun_nat_bool,U_743)),hAPP_a_fun_nat_bool(U_743,sK53(U_743,U_742)))))))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK53(U_743,U_742)),U_742))
        & is_a(sK53(U_743,U_742)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(U_743,U_742)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_742)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_741,sK53(U_743,U_742))],[f_311_2]) ).

fof(f_311_4,plain,
    ( ! [U_742,U_743] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_742)),hAPP_f1549043526a_bool(cOMBC_777206479l_bool(cOMBB_743407885bool_a(fequal_fun_nat_bool,U_743)),hAPP_a_fun_nat_bool(U_743,sK53(U_743,U_742)))))))
        | ~ sP68(U_742,U_743) )
    & ! [U_742,U_743] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK53(U_743,U_742)),U_742))
        | ~ sP68(U_742,U_743) )
    & ! [U_742,U_743] :
        ( is_a(sK53(U_743,U_742))
        | ~ sP68(U_742,U_743) )
    & ! [U_742,U_743] :
        ( sP68(U_742,U_743)
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(U_743,U_742)))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_742)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68])],[f_311_3]) ).

cnf(f_311_5,plain,
    ( sP68(U_742,U_743)
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(U_743,U_742)))
    | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_742)) ),
    inference(clausify,[status(thm)],[f_311_4]) ).

cnf(f_311_6,plain,
    ( is_a(sK53(U_743,U_742))
    | ~ sP68(U_742,U_743) ),
    inference(clausify,[status(thm)],[f_311_4]) ).

cnf(f_311_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK53(U_743,U_742)),U_742))
    | ~ sP68(U_742,U_743) ),
    inference(clausify,[status(thm)],[f_311_4]) ).

cnf(f_311_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_742)),hAPP_f1549043526a_bool(cOMBC_777206479l_bool(cOMBB_743407885bool_a(fequal_fun_nat_bool,U_743)),hAPP_a_fun_nat_bool(U_743,sK53(U_743,U_742)))))))
    | ~ sP68(U_742,U_743) ),
    inference(clausify,[status(thm)],[f_311_4]) ).

fof(f_312_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(cOMBB_1137537805bool_a(fequal533582459e_bool,F)),hAPP_a93125764e_bool(F,X_1))))))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
          & is_a(X_1) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(F,A_1)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_208_pigeonhole__infinite]) ).

fof(f_312_2,plain,
    ! [U_746,U_745] :
      ( ? [U_744] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_745)),hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(cOMBB_1137537805bool_a(fequal533582459e_bool,U_746)),hAPP_a93125764e_bool(U_746,U_744))))))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_744),U_745))
          & is_a(U_744) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(U_746,U_745)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_745)) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

fof(f_312_3,plain,
    ! [U_746,U_745] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_745)),hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(cOMBB_1137537805bool_a(fequal533582459e_bool,U_746)),hAPP_a93125764e_bool(U_746,sK54(U_746,U_745)))))))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK54(U_746,U_745)),U_745))
        & is_a(sK54(U_746,U_745)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(U_746,U_745)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_745)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_744,sK54(U_746,U_745))],[f_312_2]) ).

fof(f_312_4,plain,
    ( ! [U_746,U_745] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_745)),hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(cOMBB_1137537805bool_a(fequal533582459e_bool,U_746)),hAPP_a93125764e_bool(U_746,sK54(U_746,U_745)))))))
        | ~ sP69(U_746,U_745) )
    & ! [U_746,U_745] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK54(U_746,U_745)),U_745))
        | ~ sP69(U_746,U_745) )
    & ! [U_746,U_745] :
        ( is_a(sK54(U_746,U_745))
        | ~ sP69(U_746,U_745) )
    & ! [U_746,U_745] :
        ( sP69(U_746,U_745)
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(U_746,U_745)))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_745)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69])],[f_312_3]) ).

cnf(f_312_5,plain,
    ( sP69(U_746,U_745)
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(U_746,U_745)))
    | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_745)) ),
    inference(clausify,[status(thm)],[f_312_4]) ).

cnf(f_312_6,plain,
    ( is_a(sK54(U_746,U_745))
    | ~ sP69(U_746,U_745) ),
    inference(clausify,[status(thm)],[f_312_4]) ).

cnf(f_312_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK54(U_746,U_745)),U_745))
    | ~ sP69(U_746,U_745) ),
    inference(clausify,[status(thm)],[f_312_4]) ).

cnf(f_312_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_745)),hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(cOMBB_1137537805bool_a(fequal533582459e_bool,U_746)),hAPP_a93125764e_bool(U_746,sK54(U_746,U_745)))))))
    | ~ sP69(U_746,U_745) ),
    inference(clausify,[status(thm)],[f_312_4]) ).

fof(f_313_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(cOMBB_472261505bool_a(fequal_fun_a_bool,F)),hAPP_a_fun_a_bool(F,X_1))))))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
          & is_a(X_1) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(F,A_1)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_209_pigeonhole__infinite]) ).

fof(f_313_2,plain,
    ! [U_749,U_748] :
      ( ? [U_747] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_748)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(cOMBB_472261505bool_a(fequal_fun_a_bool,U_749)),hAPP_a_fun_a_bool(U_749,U_747))))))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_747),U_748))
          & is_a(U_747) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(U_749,U_748)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_748)) ),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

fof(f_313_3,plain,
    ! [U_749,U_748] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_748)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(cOMBB_472261505bool_a(fequal_fun_a_bool,U_749)),hAPP_a_fun_a_bool(U_749,sK55(U_749,U_748)))))))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK55(U_749,U_748)),U_748))
        & is_a(sK55(U_749,U_748)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(U_749,U_748)))
      | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_748)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_747,sK55(U_749,U_748))],[f_313_2]) ).

fof(f_313_4,plain,
    ( ! [U_748,U_749] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_748)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(cOMBB_472261505bool_a(fequal_fun_a_bool,U_749)),hAPP_a_fun_a_bool(U_749,sK55(U_749,U_748)))))))
        | ~ sP70(U_748,U_749) )
    & ! [U_748,U_749] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK55(U_749,U_748)),U_748))
        | ~ sP70(U_748,U_749) )
    & ! [U_748,U_749] :
        ( is_a(sK55(U_749,U_748))
        | ~ sP70(U_748,U_749) )
    & ! [U_748,U_749] :
        ( sP70(U_748,U_749)
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(U_749,U_748)))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_748)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP70])],[f_313_3]) ).

cnf(f_313_5,plain,
    ( sP70(U_748,U_749)
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(U_749,U_748)))
    | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_748)) ),
    inference(clausify,[status(thm)],[f_313_4]) ).

cnf(f_313_6,plain,
    ( is_a(sK55(U_749,U_748))
    | ~ sP70(U_748,U_749) ),
    inference(clausify,[status(thm)],[f_313_4]) ).

cnf(f_313_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK55(U_749,U_748)),U_748))
    | ~ sP70(U_748,U_749) ),
    inference(clausify,[status(thm)],[f_313_4]) ).

cnf(f_313_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_748)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(cOMBB_472261505bool_a(fequal_fun_a_bool,U_749)),hAPP_a_fun_a_bool(U_749,sK55(U_749,U_748)))))))
    | ~ sP70(U_748,U_749) ),
    inference(clausify,[status(thm)],[f_313_4]) ).

fof(f_314_1,plain,
    ! [F,A_1] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A_1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,F)),hAPP_pname_a(F,X_1))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
          & is_pname(X_1) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(F,A_1)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_210_pigeonhole__infinite]) ).

fof(f_314_2,plain,
    ! [U_752,U_751] :
      ( ? [U_750] :
          ( ~ 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_751)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,U_752)),hAPP_pname_a(U_752,U_750))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_750),U_751))
          & is_pname(U_750) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_752,U_751)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_751)) ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

fof(f_314_3,plain,
    ! [U_752,U_751] :
      ( ( ~ 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_751)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,U_752)),hAPP_pname_a(U_752,sK56(U_752,U_751)))))))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK56(U_752,U_751)),U_751))
        & is_pname(sK56(U_752,U_751)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_752,U_751)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_751)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_750,sK56(U_752,U_751))],[f_314_2]) ).

fof(f_314_4,plain,
    ( ! [U_751,U_752] :
        ( ~ 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_751)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,U_752)),hAPP_pname_a(U_752,sK56(U_752,U_751)))))))
        | ~ sP71(U_751,U_752) )
    & ! [U_751,U_752] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK56(U_752,U_751)),U_751))
        | ~ sP71(U_751,U_752) )
    & ! [U_751,U_752] :
        ( is_pname(sK56(U_752,U_751))
        | ~ sP71(U_751,U_752) )
    & ! [U_751,U_752] :
        ( sP71(U_751,U_752)
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_752,U_751)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_751)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71])],[f_314_3]) ).

cnf(f_314_5,plain,
    ( sP71(U_751,U_752)
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_752,U_751)))
    | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_751)) ),
    inference(clausify,[status(thm)],[f_314_4]) ).

cnf(f_314_6,plain,
    ( is_pname(sK56(U_752,U_751))
    | ~ sP71(U_751,U_752) ),
    inference(clausify,[status(thm)],[f_314_4]) ).

cnf(f_314_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK56(U_752,U_751)),U_751))
    | ~ sP71(U_751,U_752) ),
    inference(clausify,[status(thm)],[f_314_4]) ).

cnf(f_314_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_751)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,U_752)),hAPP_pname_a(U_752,sK56(U_752,U_751)))))))
    | ~ sP71(U_751,U_752) ),
    inference(clausify,[status(thm)],[f_314_4]) ).

fof(f_315_1,plain,
    ! [A_1,B_1,F,X_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_pname_nat(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
      | B_1 != hAPP_pname_nat(F,X_3) ),
    inference(fof_nnf,[status(thm)],[fact_211_image__eqI]) ).

fof(f_315_2,plain,
    ! [U_756,U_755,U_754,U_753] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_755),image_pname_nat(U_754,U_756)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_753),U_756))
      | U_755 != hAPP_pname_nat(U_754,U_753) ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

fof(f_315_3,plain,
    ! [U_755,U_754,U_756,U_753] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_755),image_pname_nat(U_754,U_756)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_753),U_756))
      | U_755 != hAPP_pname_nat(U_754,U_753) ),
    inference(definitional_conversion,[status(esa)],[f_315_2]) ).

cnf(f_315_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_755),image_pname_nat(U_754,U_756)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_753),U_756))
    | U_755 != hAPP_pname_nat(U_754,U_753) ),
    inference(clausify,[status(thm)],[f_315_3]) ).

fof(f_316_1,plain,
    ! [A_1,B_1,F,X_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_a_nat(F,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
      | B_1 != hAPP_a_nat(F,X_3) ),
    inference(fof_nnf,[status(thm)],[fact_212_image__eqI]) ).

fof(f_316_2,plain,
    ! [U_760,U_759,U_758,U_757] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_759),image_a_nat(U_758,U_760)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_757),U_760))
      | U_759 != hAPP_a_nat(U_758,U_757) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

fof(f_316_3,plain,
    ! [U_757,U_758,U_759,U_760] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_759),image_a_nat(U_758,U_760)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_757),U_760))
      | U_759 != hAPP_a_nat(U_758,U_757) ),
    inference(definitional_conversion,[status(esa)],[f_316_2]) ).

cnf(f_316_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_759),image_a_nat(U_758,U_760)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_757),U_760))
    | U_759 != hAPP_a_nat(U_758,U_757) ),
    inference(clausify,[status(thm)],[f_316_3]) ).

fof(f_317_1,plain,
    ! [A_1,B_1,F,X_3] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_nat_pname(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
      | B_1 != hAPP_nat_pname(F,X_3) ),
    inference(fof_nnf,[status(thm)],[fact_213_image__eqI]) ).

fof(f_317_2,plain,
    ! [U_764,U_763,U_762,U_761] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_763),image_nat_pname(U_762,U_764)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_761),U_764))
      | U_763 != hAPP_nat_pname(U_762,U_761) ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

fof(f_317_3,plain,
    ! [U_762,U_761,U_763,U_764] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_763),image_nat_pname(U_762,U_764)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_761),U_764))
      | U_763 != hAPP_nat_pname(U_762,U_761) ),
    inference(definitional_conversion,[status(esa)],[f_317_2]) ).

cnf(f_317_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_763),image_nat_pname(U_762,U_764)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_761),U_764))
    | U_763 != hAPP_nat_pname(U_762,U_761) ),
    inference(clausify,[status(thm)],[f_317_3]) ).

fof(f_318_1,plain,
    ! [A_1,B_1,F,X_3] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_nat_a(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
      | B_1 != hAPP_nat_a(F,X_3) ),
    inference(fof_nnf,[status(thm)],[fact_214_image__eqI]) ).

fof(f_318_2,plain,
    ! [U_768,U_767,U_766,U_765] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_767),image_nat_a(U_766,U_768)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_765),U_768))
      | U_767 != hAPP_nat_a(U_766,U_765) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ! [U_765,U_766,U_767,U_768] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_767),image_nat_a(U_766,U_768)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_765),U_768))
      | U_767 != hAPP_nat_a(U_766,U_765) ),
    inference(definitional_conversion,[status(esa)],[f_318_2]) ).

cnf(f_318_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_767),image_nat_a(U_766,U_768)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_765),U_768))
    | U_767 != hAPP_nat_a(U_766,U_765) ),
    inference(clausify,[status(thm)],[f_318_3]) ).

fof(f_319_1,plain,
    ! [A_1,B_1,F,X_3] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
      | B_1 != hAPP_pname_a(F,X_3) ),
    inference(fof_nnf,[status(thm)],[fact_215_image__eqI]) ).

fof(f_319_2,plain,
    ! [U_772,U_771,U_770,U_769] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_771),image_pname_a(U_770,U_772)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_769),U_772))
      | U_771 != hAPP_pname_a(U_770,U_769) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

fof(f_319_3,plain,
    ! [U_770,U_769,U_771,U_772] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_771),image_pname_a(U_770,U_772)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_769),U_772))
      | U_771 != hAPP_pname_a(U_770,U_769) ),
    inference(definitional_conversion,[status(esa)],[f_319_2]) ).

cnf(f_319_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_771),image_pname_a(U_770,U_772)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_769),U_772))
    | U_771 != hAPP_pname_a(U_770,U_769) ),
    inference(clausify,[status(thm)],[f_319_3]) ).

fof(f_320_1,plain,
    ! [A_1,B_6] :
      ( A_1 = B_6
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
      | ~ is_fun_pname_bool(B_6)
      | ~ is_fun_pname_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_216_equalityI]) ).

fof(f_320_2,plain,
    ! [U_774,U_773] :
      ( U_774 = U_773
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_773),U_774))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_774),U_773))
      | ~ is_fun_pname_bool(U_773)
      | ~ is_fun_pname_bool(U_774) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

fof(f_320_3,plain,
    ! [U_774,U_773] :
      ( U_774 = U_773
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_773),U_774))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_774),U_773))
      | ~ is_fun_pname_bool(U_773)
      | ~ is_fun_pname_bool(U_774) ),
    inference(definitional_conversion,[status(esa)],[f_320_2]) ).

cnf(f_320_4,plain,
    ( U_774 = U_773
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_773),U_774))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_774),U_773))
    | ~ is_fun_pname_bool(U_773)
    | ~ is_fun_pname_bool(U_774) ),
    inference(clausify,[status(thm)],[f_320_3]) ).

fof(f_321_1,plain,
    ! [A_1,B_6] :
      ( A_1 = B_6
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_217_equalityI]) ).

fof(f_321_2,plain,
    ! [U_776,U_775] :
      ( U_776 = U_775
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_775),U_776))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_776),U_775)) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

fof(f_321_3,plain,
    ! [U_776,U_775] :
      ( U_776 = U_775
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_775),U_776))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_776),U_775)) ),
    inference(definitional_conversion,[status(esa)],[f_321_2]) ).

cnf(f_321_4,plain,
    ( U_776 = U_775
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_775),U_776))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_776),U_775)) ),
    inference(clausify,[status(thm)],[f_321_3]) ).

fof(f_322_1,plain,
    ! [A_1,B_6] :
      ( A_1 = B_6
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
      | ~ is_fun_a_bool(B_6)
      | ~ is_fun_a_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_218_equalityI]) ).

fof(f_322_2,plain,
    ! [U_778,U_777] :
      ( U_778 = U_777
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_777),U_778))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_778),U_777))
      | ~ is_fun_a_bool(U_777)
      | ~ is_fun_a_bool(U_778) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

fof(f_322_3,plain,
    ! [U_777,U_778] :
      ( U_778 = U_777
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_777),U_778))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_778),U_777))
      | ~ is_fun_a_bool(U_777)
      | ~ is_fun_a_bool(U_778) ),
    inference(definitional_conversion,[status(esa)],[f_322_2]) ).

cnf(f_322_4,plain,
    ( U_778 = U_777
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_777),U_778))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_778),U_777))
    | ~ is_fun_a_bool(U_777)
    | ~ is_fun_a_bool(U_778) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

fof(f_323_1,plain,
    ! [C_1,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_219_subsetD]) ).

fof(f_323_2,plain,
    ! [U_781,U_780,U_779] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_781),U_779))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_781),U_780))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_780),U_779)) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

fof(f_323_3,plain,
    ! [U_781,U_779,U_780] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_781),U_779))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_781),U_780))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_780),U_779)) ),
    inference(definitional_conversion,[status(esa)],[f_323_2]) ).

cnf(f_323_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_781),U_779))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_781),U_780))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_780),U_779)) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

fof(f_324_1,plain,
    ! [C_1,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),A_1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_220_subsetD]) ).

fof(f_324_2,plain,
    ! [U_784,U_783,U_782] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_784),U_782))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_784),U_783))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_783),U_782)) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

fof(f_324_3,plain,
    ! [U_783,U_782,U_784] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_784),U_782))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_784),U_783))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_783),U_782)) ),
    inference(definitional_conversion,[status(esa)],[f_324_2]) ).

cnf(f_324_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_784),U_782))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_784),U_783))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_783),U_782)) ),
    inference(clausify,[status(thm)],[f_324_3]) ).

fof(f_325_1,plain,
    ! [C_1,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),A_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_221_subsetD]) ).

fof(f_325_2,plain,
    ! [U_787,U_786,U_785] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_787),U_785))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_787),U_786))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_786),U_785)) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

fof(f_325_3,plain,
    ! [U_785,U_786,U_787] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_787),U_785))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_787),U_786))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_786),U_785)) ),
    inference(definitional_conversion,[status(esa)],[f_325_2]) ).

cnf(f_325_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_787),U_785))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_787),U_786))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_786),U_785)) ),
    inference(clausify,[status(thm)],[f_325_3]) ).

fof(f_326_1,plain,
    ! [B_1,A_3,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,B_6)))
      | ( A_3 != B_1
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),B_6)) ) ),
    inference(fof_nnf,[status(thm)],[fact_222_insertCI]) ).

fof(f_326_2,plain,
    ! [U_790,U_789,U_788] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_789),insert_nat(U_790,U_788)))
      | ( U_789 != U_790
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_789),U_788)) ) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

fof(f_326_3,plain,
    ( ! [U_788,U_789,U_790] :
        ( U_789 != U_790
        | ~ sP72(U_788,U_789,U_790) )
    & ! [U_788,U_789,U_790] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_789),U_788))
        | ~ sP72(U_788,U_789,U_790) )
    & ! [U_788,U_789,U_790] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_789),insert_nat(U_790,U_788)))
        | sP72(U_788,U_789,U_790) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_326_2]) ).

cnf(f_326_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_789),insert_nat(U_790,U_788)))
    | sP72(U_788,U_789,U_790) ),
    inference(clausify,[status(thm)],[f_326_3]) ).

cnf(f_326_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_789),U_788))
    | ~ sP72(U_788,U_789,U_790) ),
    inference(clausify,[status(thm)],[f_326_3]) ).

cnf(f_326_6,plain,
    ( U_789 != U_790
    | ~ sP72(U_788,U_789,U_790) ),
    inference(clausify,[status(thm)],[f_326_3]) ).

fof(f_327_1,plain,
    ! [B_1,A_3,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,B_6)))
      | ( A_3 != B_1
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),B_6)) ) ),
    inference(fof_nnf,[status(thm)],[fact_223_insertCI]) ).

fof(f_327_2,plain,
    ! [U_793,U_792,U_791] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_792),insert_pname(U_793,U_791)))
      | ( U_792 != U_793
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_792),U_791)) ) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

fof(f_327_3,plain,
    ( ! [U_791,U_792,U_793] :
        ( U_792 != U_793
        | ~ sP73(U_791,U_792,U_793) )
    & ! [U_791,U_792,U_793] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_792),U_791))
        | ~ sP73(U_791,U_792,U_793) )
    & ! [U_791,U_792,U_793] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_792),insert_pname(U_793,U_791)))
        | sP73(U_791,U_792,U_793) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_327_2]) ).

cnf(f_327_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_792),insert_pname(U_793,U_791)))
    | sP73(U_791,U_792,U_793) ),
    inference(clausify,[status(thm)],[f_327_3]) ).

cnf(f_327_5,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_792),U_791))
    | ~ sP73(U_791,U_792,U_793) ),
    inference(clausify,[status(thm)],[f_327_3]) ).

cnf(f_327_6,plain,
    ( U_792 != U_793
    | ~ sP73(U_791,U_792,U_793) ),
    inference(clausify,[status(thm)],[f_327_3]) ).

fof(f_328_1,plain,
    ! [B_1,A_3,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,B_6)))
      | ( A_3 != B_1
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),B_6)) ) ),
    inference(fof_nnf,[status(thm)],[fact_224_insertCI]) ).

fof(f_328_2,plain,
    ! [U_796,U_795,U_794] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_795),insert_a(U_796,U_794)))
      | ( U_795 != U_796
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_795),U_794)) ) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

fof(f_328_3,plain,
    ( ! [U_794,U_795,U_796] :
        ( U_795 != U_796
        | ~ sP74(U_794,U_795,U_796) )
    & ! [U_794,U_795,U_796] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_795),U_794))
        | ~ sP74(U_794,U_795,U_796) )
    & ! [U_794,U_795,U_796] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_795),insert_a(U_796,U_794)))
        | sP74(U_794,U_795,U_796) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74])],[f_328_2]) ).

cnf(f_328_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_795),insert_a(U_796,U_794)))
    | sP74(U_794,U_795,U_796) ),
    inference(clausify,[status(thm)],[f_328_3]) ).

cnf(f_328_5,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_795),U_794))
    | ~ sP74(U_794,U_795,U_796) ),
    inference(clausify,[status(thm)],[f_328_3]) ).

cnf(f_328_6,plain,
    ( U_795 != U_796
    | ~ sP74(U_794,U_795,U_796) ),
    inference(clausify,[status(thm)],[f_328_3]) ).

fof(f_329_1,plain,
    ! [A_3,B_1,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1))
      | A_3 = B_1
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_225_insertE]) ).

fof(f_329_2,plain,
    ! [U_799,U_798,U_797] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_799),U_797))
      | U_799 = U_798
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_799),insert_nat(U_798,U_797))) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

fof(f_329_3,plain,
    ! [U_797,U_798,U_799] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_799),U_797))
      | U_799 = U_798
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_799),insert_nat(U_798,U_797))) ),
    inference(definitional_conversion,[status(esa)],[f_329_2]) ).

cnf(f_329_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_799),U_797))
    | U_799 = U_798
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_799),insert_nat(U_798,U_797))) ),
    inference(clausify,[status(thm)],[f_329_3]) ).

fof(f_330_1,plain,
    ! [A_3,B_1,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1))
      | A_3 = B_1
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,A_1)))
      | ~ is_pname(B_1)
      | ~ is_pname(A_3) ),
    inference(fof_nnf,[status(thm)],[fact_226_insertE]) ).

fof(f_330_2,plain,
    ! [U_802,U_801,U_800] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_802),U_800))
      | U_802 = U_801
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_802),insert_pname(U_801,U_800)))
      | ~ is_pname(U_801)
      | ~ is_pname(U_802) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

fof(f_330_3,plain,
    ! [U_802,U_801] :
      ( ! [U_800] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_802),U_800))
          | U_802 = U_801
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_802),insert_pname(U_801,U_800))) )
      | ~ is_pname(U_801)
      | ~ is_pname(U_802) ),
    inference(miniscope,[status(thm)],[f_330_2]) ).

fof(f_330_4,plain,
    ! [U_800,U_801,U_802] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_802),U_800))
      | U_802 = U_801
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_802),insert_pname(U_801,U_800)))
      | ~ is_pname(U_801)
      | ~ is_pname(U_802) ),
    inference(definitional_conversion,[status(esa)],[f_330_3]) ).

cnf(f_330_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_802),U_800))
    | U_802 = U_801
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_802),insert_pname(U_801,U_800)))
    | ~ is_pname(U_801)
    | ~ is_pname(U_802) ),
    inference(clausify,[status(thm)],[f_330_4]) ).

fof(f_331_1,plain,
    ! [A_3,B_1,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
      | A_3 = B_1
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
      | ~ is_a(B_1)
      | ~ is_a(A_3) ),
    inference(fof_nnf,[status(thm)],[fact_227_insertE]) ).

fof(f_331_2,plain,
    ! [U_805,U_804,U_803] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_805),U_803))
      | U_805 = U_804
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_805),insert_a(U_804,U_803)))
      | ~ is_a(U_804)
      | ~ is_a(U_805) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

fof(f_331_3,plain,
    ! [U_805,U_804] :
      ( ! [U_803] :
          ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_805),U_803))
          | U_805 = U_804
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_805),insert_a(U_804,U_803))) )
      | ~ is_a(U_804)
      | ~ is_a(U_805) ),
    inference(miniscope,[status(thm)],[f_331_2]) ).

fof(f_331_4,plain,
    ! [U_804,U_805,U_803] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_805),U_803))
      | U_805 = U_804
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_805),insert_a(U_804,U_803)))
      | ~ is_a(U_804)
      | ~ is_a(U_805) ),
    inference(definitional_conversion,[status(esa)],[f_331_3]) ).

cnf(f_331_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_805),U_803))
    | U_805 = U_804
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_805),insert_a(U_804,U_803)))
    | ~ is_a(U_804)
    | ~ is_a(U_805) ),
    inference(clausify,[status(thm)],[f_331_4]) ).

fof(f_332_1,plain,
    ! [I_1,Pa,K_2] :
      ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(K_2),I_1)))
      | ? [N_2] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,N_2))
          & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2))) )
      | ~ hBOOL(hAPP_nat_bool(Pa,K_2)) ),
    inference(fof_nnf,[status(thm)],[fact_228_zero__induct__lemma]) ).

fof(f_332_2,plain,
    ! [U_809,U_808,U_807] :
      ( hBOOL(hAPP_nat_bool(U_808,hAPP_nat_nat(minus_minus_nat(U_807),U_809)))
      | ? [U_806] :
          ( ~ hBOOL(hAPP_nat_bool(U_808,U_806))
          & hBOOL(hAPP_nat_bool(U_808,hAPP_nat_nat(suc,U_806))) )
      | ~ hBOOL(hAPP_nat_bool(U_808,U_807)) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

fof(f_332_3,plain,
    ! [U_809,U_808,U_807] :
      ( hBOOL(hAPP_nat_bool(U_808,hAPP_nat_nat(minus_minus_nat(U_807),U_809)))
      | ( ~ hBOOL(hAPP_nat_bool(U_808,sK57(U_809,U_808,U_807)))
        & hBOOL(hAPP_nat_bool(U_808,hAPP_nat_nat(suc,sK57(U_809,U_808,U_807)))) )
      | ~ hBOOL(hAPP_nat_bool(U_808,U_807)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_806,sK57(U_809,U_808,U_807))],[f_332_2]) ).

fof(f_332_4,plain,
    ( ! [U_807,U_808,U_809] :
        ( ~ hBOOL(hAPP_nat_bool(U_808,sK57(U_809,U_808,U_807)))
        | ~ sP75(U_807,U_808,U_809) )
    & ! [U_807,U_808,U_809] :
        ( hBOOL(hAPP_nat_bool(U_808,hAPP_nat_nat(suc,sK57(U_809,U_808,U_807))))
        | ~ sP75(U_807,U_808,U_809) )
    & ! [U_807,U_808,U_809] :
        ( hBOOL(hAPP_nat_bool(U_808,hAPP_nat_nat(minus_minus_nat(U_807),U_809)))
        | sP75(U_807,U_808,U_809)
        | ~ hBOOL(hAPP_nat_bool(U_808,U_807)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75])],[f_332_3]) ).

cnf(f_332_5,plain,
    ( hBOOL(hAPP_nat_bool(U_808,hAPP_nat_nat(minus_minus_nat(U_807),U_809)))
    | sP75(U_807,U_808,U_809)
    | ~ hBOOL(hAPP_nat_bool(U_808,U_807)) ),
    inference(clausify,[status(thm)],[f_332_4]) ).

cnf(f_332_6,plain,
    ( hBOOL(hAPP_nat_bool(U_808,hAPP_nat_nat(suc,sK57(U_809,U_808,U_807))))
    | ~ sP75(U_807,U_808,U_809) ),
    inference(clausify,[status(thm)],[f_332_4]) ).

cnf(f_332_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_808,sK57(U_809,U_808,U_807)))
    | ~ sP75(U_807,U_808,U_809) ),
    inference(clausify,[status(thm)],[f_332_4]) ).

fof(f_333_1,plain,
    ! [N,M_3] :
      ( ? [M_2] : M_3 = hAPP_nat_nat(suc,M_2)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_229_Suc__le__D]) ).

fof(f_333_2,plain,
    ! [U_812,U_811] :
      ( ? [U_810] : U_811 = hAPP_nat_nat(suc,U_810)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_812)),U_811)) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

fof(f_333_3,plain,
    ! [U_812,U_811] :
      ( U_811 = hAPP_nat_nat(suc,sK58(U_812,U_811))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_812)),U_811)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_810,sK58(U_812,U_811))],[f_333_2]) ).

fof(f_333_4,plain,
    ! [U_811,U_812] :
      ( U_811 = hAPP_nat_nat(suc,sK58(U_812,U_811))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_812)),U_811)) ),
    inference(definitional_conversion,[status(esa)],[f_333_3]) ).

cnf(f_333_5,plain,
    ( U_811 = hAPP_nat_nat(suc,sK58(U_812,U_811))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_812)),U_811)) ),
    inference(clausify,[status(thm)],[f_333_4]) ).

fof(f_334_1,plain,
    ! [A_3,B_6] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(A_3,B_6))),
    inference(fof_nnf,[status(thm)],[fact_230_insertI1]) ).

fof(f_334_2,plain,
    ! [U_814,U_813] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_814),insert_nat(U_814,U_813))),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

fof(f_334_3,plain,
    ! [U_813,U_814] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_814),insert_nat(U_814,U_813))),
    inference(definitional_conversion,[status(esa)],[f_334_2]) ).

cnf(f_334_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_814),insert_nat(U_814,U_813))),
    inference(clausify,[status(thm)],[f_334_3]) ).

fof(f_335_1,plain,
    ! [A_3,B_6] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(A_3,B_6))),
    inference(fof_nnf,[status(thm)],[fact_231_insertI1]) ).

fof(f_335_2,plain,
    ! [U_816,U_815] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_816),insert_pname(U_816,U_815))),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

fof(f_335_3,plain,
    ! [U_815,U_816] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_816),insert_pname(U_816,U_815))),
    inference(definitional_conversion,[status(esa)],[f_335_2]) ).

cnf(f_335_4,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_816),insert_pname(U_816,U_815))),
    inference(clausify,[status(thm)],[f_335_3]) ).

fof(f_336_1,plain,
    ! [A_3,B_6] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(A_3,B_6))),
    inference(fof_nnf,[status(thm)],[fact_232_insertI1]) ).

fof(f_336_2,plain,
    ! [U_818,U_817] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_818),insert_a(U_818,U_817))),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

fof(f_336_3,plain,
    ! [U_817,U_818] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_818),insert_a(U_818,U_817))),
    inference(definitional_conversion,[status(esa)],[f_336_2]) ).

cnf(f_336_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_818),insert_a(U_818,U_817))),
    inference(clausify,[status(thm)],[f_336_3]) ).

fof(f_337_1,plain,
    ! [A_3,B_6] : insert_fun_nat_bool(A_3,B_6) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),B_6))),
    inference(fof_nnf,[status(thm)],[fact_233_insert__compr]) ).

fof(f_337_2,plain,
    ! [U_820,U_819] : insert_fun_nat_bool(U_820,U_819) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_820)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_819))),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

fof(f_337_3,plain,
    ! [U_819,U_820] : insert_fun_nat_bool(U_820,U_819) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_820)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_819))),
    inference(definitional_conversion,[status(esa)],[f_337_2]) ).

cnf(f_337_4,plain,
    insert_fun_nat_bool(U_820,U_819) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_820)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_819))),
    inference(clausify,[status(thm)],[f_337_3]) ).

fof(f_338_1,plain,
    ! [A_3,B_6] : insert1325755072e_bool(A_3,B_6) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),B_6))),
    inference(fof_nnf,[status(thm)],[fact_234_insert__compr]) ).

fof(f_338_2,plain,
    ! [U_822,U_821] : insert1325755072e_bool(U_822,U_821) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_822)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_821))),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

fof(f_338_3,plain,
    ! [U_821,U_822] : insert1325755072e_bool(U_822,U_821) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_822)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_821))),
    inference(definitional_conversion,[status(esa)],[f_338_2]) ).

cnf(f_338_4,plain,
    insert1325755072e_bool(U_822,U_821) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_822)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_821))),
    inference(clausify,[status(thm)],[f_338_3]) ).

fof(f_339_1,plain,
    ! [A_3,B_6] : insert_fun_a_bool(A_3,B_6) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),B_6))),
    inference(fof_nnf,[status(thm)],[fact_235_insert__compr]) ).

fof(f_339_2,plain,
    ! [U_824,U_823] : insert_fun_a_bool(U_824,U_823) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_824)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_823))),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

fof(f_339_3,plain,
    ! [U_823,U_824] : insert_fun_a_bool(U_824,U_823) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_824)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_823))),
    inference(definitional_conversion,[status(esa)],[f_339_2]) ).

cnf(f_339_4,plain,
    insert_fun_a_bool(U_824,U_823) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_824)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_823))),
    inference(clausify,[status(thm)],[f_339_3]) ).

fof(f_340_1,plain,
    ! [A_3,B_6] : insert_nat(A_3,B_6) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B_6))),
    inference(fof_nnf,[status(thm)],[fact_236_insert__compr]) ).

fof(f_340_2,plain,
    ! [U_826,U_825] : insert_nat(U_826,U_825) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_826)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_825))),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

fof(f_340_3,plain,
    ! [U_825,U_826] : insert_nat(U_826,U_825) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_826)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_825))),
    inference(definitional_conversion,[status(esa)],[f_340_2]) ).

cnf(f_340_4,plain,
    insert_nat(U_826,U_825) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_826)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_825))),
    inference(clausify,[status(thm)],[f_340_3]) ).

fof(f_341_1,plain,
    ! [A_3,B_6] : insert_pname(A_3,B_6) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B_6))),
    inference(fof_nnf,[status(thm)],[fact_237_insert__compr]) ).

fof(f_341_2,plain,
    ! [U_828,U_827] : insert_pname(U_828,U_827) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_828)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_827))),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

fof(f_341_3,plain,
    ! [U_827,U_828] : insert_pname(U_828,U_827) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_828)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_827))),
    inference(definitional_conversion,[status(esa)],[f_341_2]) ).

cnf(f_341_4,plain,
    insert_pname(U_828,U_827) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_828)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_827))),
    inference(clausify,[status(thm)],[f_341_3]) ).

fof(f_342_1,plain,
    ! [A_3,B_6] : insert_a(A_3,B_6) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B_6))),
    inference(fof_nnf,[status(thm)],[fact_238_insert__compr]) ).

fof(f_342_2,plain,
    ! [U_830,U_829] : insert_a(U_830,U_829) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_830)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_829))),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

fof(f_342_3,plain,
    ! [U_829,U_830] : insert_a(U_830,U_829) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_830)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_829))),
    inference(definitional_conversion,[status(esa)],[f_342_2]) ).

cnf(f_342_4,plain,
    insert_a(U_830,U_829) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_830)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_829))),
    inference(clausify,[status(thm)],[f_342_3]) ).

fof(f_343_1,plain,
    ! [A_3,Pa] : insert_pname(A_3,collect_pname(Pa)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_239_insert__Collect]) ).

fof(f_343_2,plain,
    ! [U_832,U_831] : insert_pname(U_832,collect_pname(U_831)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_832))),U_831)),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

fof(f_343_3,plain,
    ! [U_831,U_832] : insert_pname(U_832,collect_pname(U_831)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_832))),U_831)),
    inference(definitional_conversion,[status(esa)],[f_343_2]) ).

cnf(f_343_4,plain,
    insert_pname(U_832,collect_pname(U_831)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_832))),U_831)),
    inference(clausify,[status(thm)],[f_343_3]) ).

fof(f_344_1,plain,
    ! [A_3,Pa] : insert_fun_nat_bool(A_3,collect_fun_nat_bool(Pa)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_240_insert__Collect]) ).

fof(f_344_2,plain,
    ! [U_834,U_833] : insert_fun_nat_bool(U_834,collect_fun_nat_bool(U_833)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_834))),U_833)),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

fof(f_344_3,plain,
    ! [U_833,U_834] : insert_fun_nat_bool(U_834,collect_fun_nat_bool(U_833)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_834))),U_833)),
    inference(definitional_conversion,[status(esa)],[f_344_2]) ).

cnf(f_344_4,plain,
    insert_fun_nat_bool(U_834,collect_fun_nat_bool(U_833)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_834))),U_833)),
    inference(clausify,[status(thm)],[f_344_3]) ).

fof(f_345_1,plain,
    ! [A_3,Pa] : insert1325755072e_bool(A_3,collec1974731493e_bool(Pa)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_241_insert__Collect]) ).

fof(f_345_2,plain,
    ! [U_836,U_835] : insert1325755072e_bool(U_836,collec1974731493e_bool(U_835)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_836))),U_835)),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

fof(f_345_3,plain,
    ! [U_835,U_836] : insert1325755072e_bool(U_836,collec1974731493e_bool(U_835)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_836))),U_835)),
    inference(definitional_conversion,[status(esa)],[f_345_2]) ).

cnf(f_345_4,plain,
    insert1325755072e_bool(U_836,collec1974731493e_bool(U_835)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_836))),U_835)),
    inference(clausify,[status(thm)],[f_345_3]) ).

fof(f_346_1,plain,
    ! [A_3,Pa] : insert_fun_a_bool(A_3,collect_fun_a_bool(Pa)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_242_insert__Collect]) ).

fof(f_346_2,plain,
    ! [U_838,U_837] : insert_fun_a_bool(U_838,collect_fun_a_bool(U_837)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_838))),U_837)),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

fof(f_346_3,plain,
    ! [U_837,U_838] : insert_fun_a_bool(U_838,collect_fun_a_bool(U_837)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_838))),U_837)),
    inference(definitional_conversion,[status(esa)],[f_346_2]) ).

cnf(f_346_4,plain,
    insert_fun_a_bool(U_838,collect_fun_a_bool(U_837)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_838))),U_837)),
    inference(clausify,[status(thm)],[f_346_3]) ).

fof(f_347_1,plain,
    ! [A_3,Pa] : insert_nat(A_3,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_3))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_243_insert__Collect]) ).

fof(f_347_2,plain,
    ! [U_840,U_839] : insert_nat(U_840,collect_nat(U_839)) = 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_840))),U_839)),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

fof(f_347_3,plain,
    ! [U_839,U_840] : insert_nat(U_840,collect_nat(U_839)) = 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_840))),U_839)),
    inference(definitional_conversion,[status(esa)],[f_347_2]) ).

cnf(f_347_4,plain,
    insert_nat(U_840,collect_nat(U_839)) = 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_840))),U_839)),
    inference(clausify,[status(thm)],[f_347_3]) ).

fof(f_348_1,plain,
    ! [A_3,Pa] : insert_a(A_3,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_3))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_244_insert__Collect]) ).

fof(f_348_2,plain,
    ! [U_842,U_841] : insert_a(U_842,collect_a(U_841)) = 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_842))),U_841)),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ! [U_841,U_842] : insert_a(U_842,collect_a(U_841)) = 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_842))),U_841)),
    inference(definitional_conversion,[status(esa)],[f_348_2]) ).

cnf(f_348_4,plain,
    insert_a(U_842,collect_a(U_841)) = 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_842))),U_841)),
    inference(clausify,[status(thm)],[f_348_3]) ).

fof(f_349_1,plain,
    ! [X_3,A_1] : insert_pname(X_3,insert_pname(X_3,A_1)) = insert_pname(X_3,A_1),
    inference(fof_nnf,[status(thm)],[fact_245_insert__absorb2]) ).

fof(f_349_2,plain,
    ! [U_844,U_843] : insert_pname(U_844,insert_pname(U_844,U_843)) = insert_pname(U_844,U_843),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

fof(f_349_3,plain,
    ! [U_843,U_844] : insert_pname(U_844,insert_pname(U_844,U_843)) = insert_pname(U_844,U_843),
    inference(definitional_conversion,[status(esa)],[f_349_2]) ).

cnf(f_349_4,plain,
    insert_pname(U_844,insert_pname(U_844,U_843)) = insert_pname(U_844,U_843),
    inference(clausify,[status(thm)],[f_349_3]) ).

fof(f_350_1,plain,
    ! [X_3,A_1] : insert_nat(X_3,insert_nat(X_3,A_1)) = insert_nat(X_3,A_1),
    inference(fof_nnf,[status(thm)],[fact_246_insert__absorb2]) ).

fof(f_350_2,plain,
    ! [U_846,U_845] : insert_nat(U_846,insert_nat(U_846,U_845)) = insert_nat(U_846,U_845),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

fof(f_350_3,plain,
    ! [U_845,U_846] : insert_nat(U_846,insert_nat(U_846,U_845)) = insert_nat(U_846,U_845),
    inference(definitional_conversion,[status(esa)],[f_350_2]) ).

cnf(f_350_4,plain,
    insert_nat(U_846,insert_nat(U_846,U_845)) = insert_nat(U_846,U_845),
    inference(clausify,[status(thm)],[f_350_3]) ).

fof(f_351_1,plain,
    ! [X_3,A_1] : insert_a(X_3,insert_a(X_3,A_1)) = insert_a(X_3,A_1),
    inference(fof_nnf,[status(thm)],[fact_247_insert__absorb2]) ).

fof(f_351_2,plain,
    ! [U_848,U_847] : insert_a(U_848,insert_a(U_848,U_847)) = insert_a(U_848,U_847),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

fof(f_351_3,plain,
    ! [U_847,U_848] : insert_a(U_848,insert_a(U_848,U_847)) = insert_a(U_848,U_847),
    inference(definitional_conversion,[status(esa)],[f_351_2]) ).

cnf(f_351_4,plain,
    insert_a(U_848,insert_a(U_848,U_847)) = insert_a(U_848,U_847),
    inference(clausify,[status(thm)],[f_351_3]) ).

fof(f_352_1,plain,
    ! [X_3,Y_2,A_1] : insert_pname(X_3,insert_pname(Y_2,A_1)) = insert_pname(Y_2,insert_pname(X_3,A_1)),
    inference(fof_nnf,[status(thm)],[fact_248_insert__commute]) ).

fof(f_352_2,plain,
    ! [U_851,U_850,U_849] : insert_pname(U_851,insert_pname(U_850,U_849)) = insert_pname(U_850,insert_pname(U_851,U_849)),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

fof(f_352_3,plain,
    ! [U_849,U_850,U_851] : insert_pname(U_851,insert_pname(U_850,U_849)) = insert_pname(U_850,insert_pname(U_851,U_849)),
    inference(definitional_conversion,[status(esa)],[f_352_2]) ).

cnf(f_352_4,plain,
    insert_pname(U_851,insert_pname(U_850,U_849)) = insert_pname(U_850,insert_pname(U_851,U_849)),
    inference(clausify,[status(thm)],[f_352_3]) ).

fof(f_353_1,plain,
    ! [X_3,Y_2,A_1] : insert_nat(X_3,insert_nat(Y_2,A_1)) = insert_nat(Y_2,insert_nat(X_3,A_1)),
    inference(fof_nnf,[status(thm)],[fact_249_insert__commute]) ).

fof(f_353_2,plain,
    ! [U_854,U_853,U_852] : insert_nat(U_854,insert_nat(U_853,U_852)) = insert_nat(U_853,insert_nat(U_854,U_852)),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

fof(f_353_3,plain,
    ! [U_852,U_853,U_854] : insert_nat(U_854,insert_nat(U_853,U_852)) = insert_nat(U_853,insert_nat(U_854,U_852)),
    inference(definitional_conversion,[status(esa)],[f_353_2]) ).

cnf(f_353_4,plain,
    insert_nat(U_854,insert_nat(U_853,U_852)) = insert_nat(U_853,insert_nat(U_854,U_852)),
    inference(clausify,[status(thm)],[f_353_3]) ).

fof(f_354_1,plain,
    ! [X_3,Y_2,A_1] : insert_a(X_3,insert_a(Y_2,A_1)) = insert_a(Y_2,insert_a(X_3,A_1)),
    inference(fof_nnf,[status(thm)],[fact_250_insert__commute]) ).

fof(f_354_2,plain,
    ! [U_857,U_856,U_855] : insert_a(U_857,insert_a(U_856,U_855)) = insert_a(U_856,insert_a(U_857,U_855)),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

fof(f_354_3,plain,
    ! [U_855,U_856,U_857] : insert_a(U_857,insert_a(U_856,U_855)) = insert_a(U_856,insert_a(U_857,U_855)),
    inference(definitional_conversion,[status(esa)],[f_354_2]) ).

cnf(f_354_4,plain,
    insert_a(U_857,insert_a(U_856,U_855)) = insert_a(U_856,insert_a(U_857,U_855)),
    inference(clausify,[status(thm)],[f_354_3]) ).

fof(f_355_1,plain,
    ! [A_3,B_1,A_1] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,A_1)))
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1))
          & A_3 != B_1 ) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1))
        | A_3 = B_1
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,A_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_251_insert__iff]) ).

fof(f_355_2,plain,
    ! [U_860,U_859,U_858] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_860),insert_nat(U_859,U_858)))
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_860),U_858))
          & U_860 != U_859 ) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_860),U_858))
        | U_860 = U_859
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_860),insert_nat(U_859,U_858))) ) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

fof(f_355_3,plain,
    ( ! [U_866,U_864,U_862] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_866),insert_nat(U_864,U_862)))
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_866),U_862))
          & U_866 != U_864 ) )
    & ! [U_865,U_863,U_861] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_865),U_861))
        | U_865 = U_863
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_865),insert_nat(U_863,U_861))) ) ),
    inference(miniscope,[status(thm)],[f_355_2]) ).

fof(f_355_4,plain,
    ( ! [U_866,U_862,U_864] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_866),U_862))
        | ~ sP76(U_866,U_862,U_864) )
    & ! [U_866,U_862,U_864] :
        ( U_866 != U_864
        | ~ sP76(U_866,U_862,U_864) )
    & ! [U_866,U_862,U_864] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_866),insert_nat(U_864,U_862)))
        | sP76(U_866,U_862,U_864) )
    & ! [U_863,U_861,U_865] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_865),U_861))
        | U_865 = U_863
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_865),insert_nat(U_863,U_861))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76])],[f_355_3]) ).

cnf(f_355_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_865),U_861))
    | U_865 = U_863
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_865),insert_nat(U_863,U_861))) ),
    inference(clausify,[status(thm)],[f_355_4]) ).

cnf(f_355_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_866),insert_nat(U_864,U_862)))
    | sP76(U_866,U_862,U_864) ),
    inference(clausify,[status(thm)],[f_355_4]) ).

cnf(f_355_7,plain,
    ( U_866 != U_864
    | ~ sP76(U_866,U_862,U_864) ),
    inference(clausify,[status(thm)],[f_355_4]) ).

cnf(f_355_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_866),U_862))
    | ~ sP76(U_866,U_862,U_864) ),
    inference(clausify,[status(thm)],[f_355_4]) ).

fof(f_356_1,plain,
    ! [A_3,B_1,A_1] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,A_1)))
          | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1))
            & A_3 != B_1 ) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1))
          | A_3 = B_1
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,A_1))) ) )
      | ~ is_pname(B_1)
      | ~ is_pname(A_3) ),
    inference(fof_nnf,[status(thm)],[fact_252_insert__iff]) ).

fof(f_356_2,plain,
    ! [U_869,U_868,U_867] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),insert_pname(U_868,U_867)))
          | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),U_867))
            & U_869 != U_868 ) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),U_867))
          | U_869 = U_868
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),insert_pname(U_868,U_867))) ) )
      | ~ is_pname(U_868)
      | ~ is_pname(U_869) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ! [U_869,U_868] :
      ( ( ! [U_871] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),insert_pname(U_868,U_871)))
            | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),U_871))
              & U_869 != U_868 ) )
        & ! [U_870] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),U_870))
            | U_869 = U_868
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),insert_pname(U_868,U_870))) ) )
      | ~ is_pname(U_868)
      | ~ is_pname(U_869) ),
    inference(miniscope,[status(thm)],[f_356_2]) ).

fof(f_356_4,plain,
    ( ! [U_868,U_869,U_871] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),U_871))
        | ~ sP77(U_868,U_869,U_871) )
    & ! [U_868,U_869,U_871] :
        ( U_869 != U_868
        | ~ sP77(U_868,U_869,U_871) )
    & ! [U_868,U_869,U_870,U_871] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),insert_pname(U_868,U_871)))
        | sP77(U_868,U_869,U_871)
        | ~ sP78(U_868,U_869,U_870,U_871) )
    & ! [U_868,U_869,U_870,U_871] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),U_870))
        | U_869 = U_868
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),insert_pname(U_868,U_870)))
        | ~ sP78(U_868,U_869,U_870,U_871) )
    & ! [U_868,U_869,U_870,U_871] :
        ( sP78(U_868,U_869,U_870,U_871)
        | ~ is_pname(U_868)
        | ~ is_pname(U_869) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77,sP78])],[f_356_3]) ).

cnf(f_356_5,plain,
    ( sP78(U_868,U_869,U_870,U_871)
    | ~ is_pname(U_868)
    | ~ is_pname(U_869) ),
    inference(clausify,[status(thm)],[f_356_4]) ).

cnf(f_356_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),U_870))
    | U_869 = U_868
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),insert_pname(U_868,U_870)))
    | ~ sP78(U_868,U_869,U_870,U_871) ),
    inference(clausify,[status(thm)],[f_356_4]) ).

cnf(f_356_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),insert_pname(U_868,U_871)))
    | sP77(U_868,U_869,U_871)
    | ~ sP78(U_868,U_869,U_870,U_871) ),
    inference(clausify,[status(thm)],[f_356_4]) ).

cnf(f_356_8,plain,
    ( U_869 != U_868
    | ~ sP77(U_868,U_869,U_871) ),
    inference(clausify,[status(thm)],[f_356_4]) ).

cnf(f_356_9,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_869),U_871))
    | ~ sP77(U_868,U_869,U_871) ),
    inference(clausify,[status(thm)],[f_356_4]) ).

fof(f_357_1,plain,
    ! [A_3,B_1,A_1] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1)))
          | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
            & A_3 != B_1 ) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
          | A_3 = B_1
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,A_1))) ) )
      | ~ is_a(B_1)
      | ~ is_a(A_3) ),
    inference(fof_nnf,[status(thm)],[fact_253_insert__iff]) ).

fof(f_357_2,plain,
    ! [U_874,U_873,U_872] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),insert_a(U_873,U_872)))
          | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),U_872))
            & U_874 != U_873 ) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),U_872))
          | U_874 = U_873
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),insert_a(U_873,U_872))) ) )
      | ~ is_a(U_873)
      | ~ is_a(U_874) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

fof(f_357_3,plain,
    ! [U_874,U_873] :
      ( ( ! [U_876] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),insert_a(U_873,U_876)))
            | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),U_876))
              & U_874 != U_873 ) )
        & ! [U_875] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),U_875))
            | U_874 = U_873
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),insert_a(U_873,U_875))) ) )
      | ~ is_a(U_873)
      | ~ is_a(U_874) ),
    inference(miniscope,[status(thm)],[f_357_2]) ).

fof(f_357_4,plain,
    ( ! [U_874,U_873,U_876] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),U_876))
        | ~ sP79(U_874,U_873,U_876) )
    & ! [U_874,U_873,U_876] :
        ( U_874 != U_873
        | ~ sP79(U_874,U_873,U_876) )
    & ! [U_874,U_875,U_873,U_876] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),insert_a(U_873,U_876)))
        | sP79(U_874,U_873,U_876)
        | ~ sP80(U_874,U_875,U_873,U_876) )
    & ! [U_874,U_875,U_873,U_876] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),U_875))
        | U_874 = U_873
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),insert_a(U_873,U_875)))
        | ~ sP80(U_874,U_875,U_873,U_876) )
    & ! [U_874,U_875,U_873,U_876] :
        ( sP80(U_874,U_875,U_873,U_876)
        | ~ is_a(U_873)
        | ~ is_a(U_874) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79,sP80])],[f_357_3]) ).

cnf(f_357_5,plain,
    ( sP80(U_874,U_875,U_873,U_876)
    | ~ is_a(U_873)
    | ~ is_a(U_874) ),
    inference(clausify,[status(thm)],[f_357_4]) ).

cnf(f_357_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),U_875))
    | U_874 = U_873
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),insert_a(U_873,U_875)))
    | ~ sP80(U_874,U_875,U_873,U_876) ),
    inference(clausify,[status(thm)],[f_357_4]) ).

cnf(f_357_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),insert_a(U_873,U_876)))
    | sP79(U_874,U_873,U_876)
    | ~ sP80(U_874,U_875,U_873,U_876) ),
    inference(clausify,[status(thm)],[f_357_4]) ).

cnf(f_357_8,plain,
    ( U_874 != U_873
    | ~ sP79(U_874,U_873,U_876) ),
    inference(clausify,[status(thm)],[f_357_4]) ).

cnf(f_357_9,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_874),U_876))
    | ~ sP79(U_874,U_873,U_876) ),
    inference(clausify,[status(thm)],[f_357_4]) ).

fof(f_358_1,plain,
    ! [Y_2,A_1,X_3] :
      ( ( ( hBOOL(hAPP_pname_bool(insert_pname(Y_2,A_1),X_3))
          | ( ~ hBOOL(hAPP_pname_bool(A_1,X_3))
            & Y_2 != X_3 ) )
        & ( hBOOL(hAPP_pname_bool(A_1,X_3))
          | Y_2 = X_3
          | ~ hBOOL(hAPP_pname_bool(insert_pname(Y_2,A_1),X_3)) ) )
      | ~ is_pname(X_3)
      | ~ is_pname(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_254_insert__code]) ).

fof(f_358_2,plain,
    ! [U_879,U_878,U_877] :
      ( ( ( hBOOL(hAPP_pname_bool(insert_pname(U_879,U_878),U_877))
          | ( ~ hBOOL(hAPP_pname_bool(U_878,U_877))
            & U_879 != U_877 ) )
        & ( hBOOL(hAPP_pname_bool(U_878,U_877))
          | U_879 = U_877
          | ~ hBOOL(hAPP_pname_bool(insert_pname(U_879,U_878),U_877)) ) )
      | ~ is_pname(U_877)
      | ~ is_pname(U_879) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

fof(f_358_3,plain,
    ( ! [U_878,U_879,U_877] :
        ( ~ hBOOL(hAPP_pname_bool(U_878,U_877))
        | ~ sP81(U_878,U_879,U_877) )
    & ! [U_878,U_879,U_877] :
        ( U_879 != U_877
        | ~ sP81(U_878,U_879,U_877) )
    & ! [U_878,U_879,U_877] :
        ( hBOOL(hAPP_pname_bool(insert_pname(U_879,U_878),U_877))
        | sP81(U_878,U_879,U_877)
        | ~ sP82(U_878,U_879,U_877) )
    & ! [U_878,U_879,U_877] :
        ( hBOOL(hAPP_pname_bool(U_878,U_877))
        | U_879 = U_877
        | ~ hBOOL(hAPP_pname_bool(insert_pname(U_879,U_878),U_877))
        | ~ sP82(U_878,U_879,U_877) )
    & ! [U_878,U_879,U_877] :
        ( sP82(U_878,U_879,U_877)
        | ~ is_pname(U_877)
        | ~ is_pname(U_879) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81,sP82])],[f_358_2]) ).

cnf(f_358_4,plain,
    ( sP82(U_878,U_879,U_877)
    | ~ is_pname(U_877)
    | ~ is_pname(U_879) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

cnf(f_358_5,plain,
    ( hBOOL(hAPP_pname_bool(U_878,U_877))
    | U_879 = U_877
    | ~ hBOOL(hAPP_pname_bool(insert_pname(U_879,U_878),U_877))
    | ~ sP82(U_878,U_879,U_877) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

cnf(f_358_6,plain,
    ( hBOOL(hAPP_pname_bool(insert_pname(U_879,U_878),U_877))
    | sP81(U_878,U_879,U_877)
    | ~ sP82(U_878,U_879,U_877) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

cnf(f_358_7,plain,
    ( U_879 != U_877
    | ~ sP81(U_878,U_879,U_877) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

cnf(f_358_8,plain,
    ( ~ hBOOL(hAPP_pname_bool(U_878,U_877))
    | ~ sP81(U_878,U_879,U_877) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

fof(f_359_1,plain,
    ! [Y_2,A_1,X_3] :
      ( ( hBOOL(hAPP_nat_bool(insert_nat(Y_2,A_1),X_3))
        | ( ~ hBOOL(hAPP_nat_bool(A_1,X_3))
          & Y_2 != X_3 ) )
      & ( hBOOL(hAPP_nat_bool(A_1,X_3))
        | Y_2 = X_3
        | ~ hBOOL(hAPP_nat_bool(insert_nat(Y_2,A_1),X_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_255_insert__code]) ).

fof(f_359_2,plain,
    ! [U_882,U_881,U_880] :
      ( ( hBOOL(hAPP_nat_bool(insert_nat(U_882,U_881),U_880))
        | ( ~ hBOOL(hAPP_nat_bool(U_881,U_880))
          & U_882 != U_880 ) )
      & ( hBOOL(hAPP_nat_bool(U_881,U_880))
        | U_882 = U_880
        | ~ hBOOL(hAPP_nat_bool(insert_nat(U_882,U_881),U_880)) ) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ( ! [U_888,U_886,U_884] :
        ( hBOOL(hAPP_nat_bool(insert_nat(U_888,U_886),U_884))
        | ( ~ hBOOL(hAPP_nat_bool(U_886,U_884))
          & U_888 != U_884 ) )
    & ! [U_887,U_885,U_883] :
        ( hBOOL(hAPP_nat_bool(U_885,U_883))
        | U_887 = U_883
        | ~ hBOOL(hAPP_nat_bool(insert_nat(U_887,U_885),U_883)) ) ),
    inference(miniscope,[status(thm)],[f_359_2]) ).

fof(f_359_4,plain,
    ( ! [U_884,U_886,U_888] :
        ( ~ hBOOL(hAPP_nat_bool(U_886,U_884))
        | ~ sP83(U_884,U_886,U_888) )
    & ! [U_884,U_886,U_888] :
        ( U_888 != U_884
        | ~ sP83(U_884,U_886,U_888) )
    & ! [U_884,U_886,U_888] :
        ( hBOOL(hAPP_nat_bool(insert_nat(U_888,U_886),U_884))
        | sP83(U_884,U_886,U_888) )
    & ! [U_883,U_885,U_887] :
        ( hBOOL(hAPP_nat_bool(U_885,U_883))
        | U_887 = U_883
        | ~ hBOOL(hAPP_nat_bool(insert_nat(U_887,U_885),U_883)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_359_3]) ).

cnf(f_359_5,plain,
    ( hBOOL(hAPP_nat_bool(U_885,U_883))
    | U_887 = U_883
    | ~ hBOOL(hAPP_nat_bool(insert_nat(U_887,U_885),U_883)) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_6,plain,
    ( hBOOL(hAPP_nat_bool(insert_nat(U_888,U_886),U_884))
    | sP83(U_884,U_886,U_888) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_7,plain,
    ( U_888 != U_884
    | ~ sP83(U_884,U_886,U_888) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_886,U_884))
    | ~ sP83(U_884,U_886,U_888) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

fof(f_360_1,plain,
    ! [Y_2,A_1,X_3] :
      ( ( ( hBOOL(hAPP_a_bool(insert_a(Y_2,A_1),X_3))
          | ( ~ hBOOL(hAPP_a_bool(A_1,X_3))
            & Y_2 != X_3 ) )
        & ( hBOOL(hAPP_a_bool(A_1,X_3))
          | Y_2 = X_3
          | ~ hBOOL(hAPP_a_bool(insert_a(Y_2,A_1),X_3)) ) )
      | ~ is_a(X_3)
      | ~ is_a(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_256_insert__code]) ).

fof(f_360_2,plain,
    ! [U_891,U_890,U_889] :
      ( ( ( hBOOL(hAPP_a_bool(insert_a(U_891,U_890),U_889))
          | ( ~ hBOOL(hAPP_a_bool(U_890,U_889))
            & U_891 != U_889 ) )
        & ( hBOOL(hAPP_a_bool(U_890,U_889))
          | U_891 = U_889
          | ~ hBOOL(hAPP_a_bool(insert_a(U_891,U_890),U_889)) ) )
      | ~ is_a(U_889)
      | ~ is_a(U_891) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

fof(f_360_3,plain,
    ( ! [U_889,U_890,U_891] :
        ( ~ hBOOL(hAPP_a_bool(U_890,U_889))
        | ~ sP84(U_889,U_890,U_891) )
    & ! [U_889,U_890,U_891] :
        ( U_891 != U_889
        | ~ sP84(U_889,U_890,U_891) )
    & ! [U_889,U_890,U_891] :
        ( hBOOL(hAPP_a_bool(insert_a(U_891,U_890),U_889))
        | sP84(U_889,U_890,U_891)
        | ~ sP85(U_889,U_890,U_891) )
    & ! [U_889,U_890,U_891] :
        ( hBOOL(hAPP_a_bool(U_890,U_889))
        | U_891 = U_889
        | ~ hBOOL(hAPP_a_bool(insert_a(U_891,U_890),U_889))
        | ~ sP85(U_889,U_890,U_891) )
    & ! [U_889,U_890,U_891] :
        ( sP85(U_889,U_890,U_891)
        | ~ is_a(U_889)
        | ~ is_a(U_891) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84,sP85])],[f_360_2]) ).

cnf(f_360_4,plain,
    ( sP85(U_889,U_890,U_891)
    | ~ is_a(U_889)
    | ~ is_a(U_891) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

cnf(f_360_5,plain,
    ( hBOOL(hAPP_a_bool(U_890,U_889))
    | U_891 = U_889
    | ~ hBOOL(hAPP_a_bool(insert_a(U_891,U_890),U_889))
    | ~ sP85(U_889,U_890,U_891) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

cnf(f_360_6,plain,
    ( hBOOL(hAPP_a_bool(insert_a(U_891,U_890),U_889))
    | sP84(U_889,U_890,U_891)
    | ~ sP85(U_889,U_890,U_891) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

cnf(f_360_7,plain,
    ( U_891 != U_889
    | ~ sP84(U_889,U_890,U_891) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

cnf(f_360_8,plain,
    ( ~ hBOOL(hAPP_a_bool(U_890,U_889))
    | ~ sP84(U_889,U_890,U_891) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

fof(f_361_1,plain,
    ! [B_6,X_3,A_1] :
      ( ( ( insert_nat(X_3,A_1) = insert_nat(X_3,B_6)
          | A_1 != B_6 )
        & ( A_1 = B_6
          | insert_nat(X_3,A_1) != insert_nat(X_3,B_6) ) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_257_insert__ident]) ).

fof(f_361_2,plain,
    ! [U_894,U_893,U_892] :
      ( ( ( insert_nat(U_893,U_892) = insert_nat(U_893,U_894)
          | U_892 != U_894 )
        & ( U_892 = U_894
          | insert_nat(U_893,U_892) != insert_nat(U_893,U_894) ) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_893),U_894))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_893),U_892)) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

fof(f_361_3,plain,
    ( ! [U_894,U_893,U_892] :
        ( insert_nat(U_893,U_892) = insert_nat(U_893,U_894)
        | U_892 != U_894
        | ~ sP86(U_894,U_893,U_892) )
    & ! [U_894,U_893,U_892] :
        ( U_892 = U_894
        | insert_nat(U_893,U_892) != insert_nat(U_893,U_894)
        | ~ sP86(U_894,U_893,U_892) )
    & ! [U_894,U_893,U_892] :
        ( sP86(U_894,U_893,U_892)
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_893),U_894))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_893),U_892)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_361_2]) ).

cnf(f_361_4,plain,
    ( sP86(U_894,U_893,U_892)
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_893),U_894))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_893),U_892)) ),
    inference(clausify,[status(thm)],[f_361_3]) ).

cnf(f_361_5,plain,
    ( U_892 = U_894
    | insert_nat(U_893,U_892) != insert_nat(U_893,U_894)
    | ~ sP86(U_894,U_893,U_892) ),
    inference(clausify,[status(thm)],[f_361_3]) ).

cnf(f_361_6,plain,
    ( insert_nat(U_893,U_892) = insert_nat(U_893,U_894)
    | U_892 != U_894
    | ~ sP86(U_894,U_893,U_892) ),
    inference(clausify,[status(thm)],[f_361_3]) ).

fof(f_362_1,plain,
    ! [B_6,X_3,A_1] :
      ( ( ( insert_pname(X_3,A_1) = insert_pname(X_3,B_6)
          | A_1 != B_6 )
        & ( A_1 = B_6
          | insert_pname(X_3,A_1) != insert_pname(X_3,B_6) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
      | ~ is_fun_pname_bool(A_1)
      | ~ is_fun_pname_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_258_insert__ident]) ).

fof(f_362_2,plain,
    ! [U_897,U_896,U_895] :
      ( ( ( insert_pname(U_896,U_895) = insert_pname(U_896,U_897)
          | U_895 != U_897 )
        & ( U_895 = U_897
          | insert_pname(U_896,U_895) != insert_pname(U_896,U_897) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_896),U_897))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_896),U_895))
      | ~ is_fun_pname_bool(U_895)
      | ~ is_fun_pname_bool(U_897) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

fof(f_362_3,plain,
    ( ! [U_896,U_897,U_895] :
        ( insert_pname(U_896,U_895) = insert_pname(U_896,U_897)
        | U_895 != U_897
        | ~ sP87(U_896,U_897,U_895) )
    & ! [U_896,U_897,U_895] :
        ( U_895 = U_897
        | insert_pname(U_896,U_895) != insert_pname(U_896,U_897)
        | ~ sP87(U_896,U_897,U_895) )
    & ! [U_896,U_897,U_895] :
        ( sP87(U_896,U_897,U_895)
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_896),U_897))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_896),U_895))
        | ~ is_fun_pname_bool(U_895)
        | ~ is_fun_pname_bool(U_897) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_362_2]) ).

cnf(f_362_4,plain,
    ( sP87(U_896,U_897,U_895)
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_896),U_897))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_896),U_895))
    | ~ is_fun_pname_bool(U_895)
    | ~ is_fun_pname_bool(U_897) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

cnf(f_362_5,plain,
    ( U_895 = U_897
    | insert_pname(U_896,U_895) != insert_pname(U_896,U_897)
    | ~ sP87(U_896,U_897,U_895) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

cnf(f_362_6,plain,
    ( insert_pname(U_896,U_895) = insert_pname(U_896,U_897)
    | U_895 != U_897
    | ~ sP87(U_896,U_897,U_895) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

fof(f_363_1,plain,
    ! [B_6,X_3,A_1] :
      ( ( ( insert_a(X_3,A_1) = insert_a(X_3,B_6)
          | A_1 != B_6 )
        & ( A_1 = B_6
          | insert_a(X_3,A_1) != insert_a(X_3,B_6) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
      | ~ is_fun_a_bool(A_1)
      | ~ is_fun_a_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_259_insert__ident]) ).

fof(f_363_2,plain,
    ! [U_900,U_899,U_898] :
      ( ( ( insert_a(U_899,U_898) = insert_a(U_899,U_900)
          | U_898 != U_900 )
        & ( U_898 = U_900
          | insert_a(U_899,U_898) != insert_a(U_899,U_900) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_899),U_900))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_899),U_898))
      | ~ is_fun_a_bool(U_898)
      | ~ is_fun_a_bool(U_900) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

fof(f_363_3,plain,
    ( ! [U_899,U_900,U_898] :
        ( insert_a(U_899,U_898) = insert_a(U_899,U_900)
        | U_898 != U_900
        | ~ sP88(U_899,U_900,U_898) )
    & ! [U_899,U_900,U_898] :
        ( U_898 = U_900
        | insert_a(U_899,U_898) != insert_a(U_899,U_900)
        | ~ sP88(U_899,U_900,U_898) )
    & ! [U_899,U_900,U_898] :
        ( sP88(U_899,U_900,U_898)
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_899),U_900))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_899),U_898))
        | ~ is_fun_a_bool(U_898)
        | ~ is_fun_a_bool(U_900) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_363_2]) ).

cnf(f_363_4,plain,
    ( sP88(U_899,U_900,U_898)
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_899),U_900))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_899),U_898))
    | ~ is_fun_a_bool(U_898)
    | ~ is_fun_a_bool(U_900) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

cnf(f_363_5,plain,
    ( U_898 = U_900
    | insert_a(U_899,U_898) != insert_a(U_899,U_900)
    | ~ sP88(U_899,U_900,U_898) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

cnf(f_363_6,plain,
    ( insert_a(U_899,U_898) = insert_a(U_899,U_900)
    | U_898 != U_900
    | ~ sP88(U_899,U_900,U_898) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

fof(f_364_1,plain,
    ! [B_1,A_3,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),insert_nat(B_1,B_6)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_260_insertI2]) ).

fof(f_364_2,plain,
    ! [U_903,U_902,U_901] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_902),insert_nat(U_903,U_901)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_902),U_901)) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

fof(f_364_3,plain,
    ! [U_903,U_902,U_901] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_902),insert_nat(U_903,U_901)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_902),U_901)) ),
    inference(definitional_conversion,[status(esa)],[f_364_2]) ).

cnf(f_364_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_902),insert_nat(U_903,U_901)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_902),U_901)) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

fof(f_365_1,plain,
    ! [B_1,A_3,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),insert_pname(B_1,B_6)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_261_insertI2]) ).

fof(f_365_2,plain,
    ! [U_906,U_905,U_904] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_905),insert_pname(U_906,U_904)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_905),U_904)) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

fof(f_365_3,plain,
    ! [U_905,U_904,U_906] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_905),insert_pname(U_906,U_904)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_905),U_904)) ),
    inference(definitional_conversion,[status(esa)],[f_365_2]) ).

cnf(f_365_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_905),insert_pname(U_906,U_904)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_905),U_904)) ),
    inference(clausify,[status(thm)],[f_365_3]) ).

fof(f_366_1,plain,
    ! [B_1,A_3,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),insert_a(B_1,B_6)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_262_insertI2]) ).

fof(f_366_2,plain,
    ! [U_909,U_908,U_907] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_908),insert_a(U_909,U_907)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_908),U_907)) ),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

fof(f_366_3,plain,
    ! [U_908,U_907,U_909] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_908),insert_a(U_909,U_907)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_908),U_907)) ),
    inference(definitional_conversion,[status(esa)],[f_366_2]) ).

cnf(f_366_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_908),insert_a(U_909,U_907)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_908),U_907)) ),
    inference(clausify,[status(thm)],[f_366_3]) ).

fof(f_367_1,plain,
    ! [A_3,A_1] :
      ( insert_nat(A_3,A_1) = A_1
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_263_insert__absorb]) ).

fof(f_367_2,plain,
    ! [U_911,U_910] :
      ( insert_nat(U_911,U_910) = U_910
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_911),U_910)) ),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

fof(f_367_3,plain,
    ! [U_910,U_911] :
      ( insert_nat(U_911,U_910) = U_910
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_911),U_910)) ),
    inference(definitional_conversion,[status(esa)],[f_367_2]) ).

cnf(f_367_4,plain,
    ( insert_nat(U_911,U_910) = U_910
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_911),U_910)) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

fof(f_368_1,plain,
    ! [A_3,A_1] :
      ( insert_pname(A_3,A_1) = A_1
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1))
      | ~ is_fun_pname_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_264_insert__absorb]) ).

fof(f_368_2,plain,
    ! [U_913,U_912] :
      ( insert_pname(U_913,U_912) = U_912
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_913),U_912))
      | ~ is_fun_pname_bool(U_912) ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

fof(f_368_3,plain,
    ! [U_912,U_913] :
      ( insert_pname(U_913,U_912) = U_912
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_913),U_912))
      | ~ is_fun_pname_bool(U_912) ),
    inference(definitional_conversion,[status(esa)],[f_368_2]) ).

cnf(f_368_4,plain,
    ( insert_pname(U_913,U_912) = U_912
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_913),U_912))
    | ~ is_fun_pname_bool(U_912) ),
    inference(clausify,[status(thm)],[f_368_3]) ).

fof(f_369_1,plain,
    ! [A_3,A_1] :
      ( insert_a(A_3,A_1) = A_1
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
      | ~ is_fun_a_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_265_insert__absorb]) ).

fof(f_369_2,plain,
    ! [U_915,U_914] :
      ( insert_a(U_915,U_914) = U_914
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_915),U_914))
      | ~ is_fun_a_bool(U_914) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

fof(f_369_3,plain,
    ! [U_914,U_915] :
      ( insert_a(U_915,U_914) = U_914
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_915),U_914))
      | ~ is_fun_a_bool(U_914) ),
    inference(definitional_conversion,[status(esa)],[f_369_2]) ).

cnf(f_369_4,plain,
    ( insert_a(U_915,U_914) = U_914
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_915),U_914))
    | ~ is_fun_a_bool(U_914) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

fof(f_370_1,plain,
    ! [A_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),A_1)),
    inference(fof_nnf,[status(thm)],[fact_266_subset__refl]) ).

fof(f_370_2,plain,
    ! [U_916] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_916),U_916)),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

fof(f_370_3,plain,
    ! [U_916] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_916),U_916)),
    inference(definitional_conversion,[status(esa)],[f_370_2]) ).

cnf(f_370_4,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_916),U_916)),
    inference(clausify,[status(thm)],[f_370_3]) ).

fof(f_371_1,plain,
    ! [A_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),A_1)),
    inference(fof_nnf,[status(thm)],[fact_267_subset__refl]) ).

fof(f_371_2,plain,
    ! [U_917] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_917),U_917)),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

fof(f_371_3,plain,
    ! [U_917] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_917),U_917)),
    inference(definitional_conversion,[status(esa)],[f_371_2]) ).

cnf(f_371_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_917),U_917)),
    inference(clausify,[status(thm)],[f_371_3]) ).

fof(f_372_1,plain,
    ! [A_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),A_1)),
    inference(fof_nnf,[status(thm)],[fact_268_subset__refl]) ).

fof(f_372_2,plain,
    ! [U_918] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_918),U_918)),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

fof(f_372_3,plain,
    ! [U_918] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_918),U_918)),
    inference(definitional_conversion,[status(esa)],[f_372_2]) ).

cnf(f_372_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_918),U_918)),
    inference(clausify,[status(thm)],[f_372_3]) ).

fof(f_373_1,plain,
    ! [A_1,B_6] :
      ( ( ( A_1 = B_6
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) )
        & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) )
          | A_1 != B_6 ) )
      | ~ is_fun_pname_bool(B_6)
      | ~ is_fun_pname_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_269_set__eq__subset]) ).

fof(f_373_2,plain,
    ! [U_920,U_919] :
      ( ( ( U_920 = U_919
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_919),U_920))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_920),U_919)) )
        & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_919),U_920))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_920),U_919)) )
          | U_920 != U_919 ) )
      | ~ is_fun_pname_bool(U_919)
      | ~ is_fun_pname_bool(U_920) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

fof(f_373_3,plain,
    ( ! [U_919,U_920] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_919),U_920))
        | ~ sP89(U_919,U_920) )
    & ! [U_919,U_920] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_920),U_919))
        | ~ sP89(U_919,U_920) )
    & ! [U_919,U_920] :
        ( U_920 = U_919
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_919),U_920))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_920),U_919))
        | ~ sP90(U_919,U_920) )
    & ! [U_919,U_920] :
        ( sP89(U_919,U_920)
        | U_920 != U_919
        | ~ sP90(U_919,U_920) )
    & ! [U_919,U_920] :
        ( sP90(U_919,U_920)
        | ~ is_fun_pname_bool(U_919)
        | ~ is_fun_pname_bool(U_920) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89,sP90])],[f_373_2]) ).

cnf(f_373_4,plain,
    ( sP90(U_919,U_920)
    | ~ is_fun_pname_bool(U_919)
    | ~ is_fun_pname_bool(U_920) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

cnf(f_373_5,plain,
    ( sP89(U_919,U_920)
    | U_920 != U_919
    | ~ sP90(U_919,U_920) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

cnf(f_373_6,plain,
    ( U_920 = U_919
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_919),U_920))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_920),U_919))
    | ~ sP90(U_919,U_920) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

cnf(f_373_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_920),U_919))
    | ~ sP89(U_919,U_920) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

cnf(f_373_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_919),U_920))
    | ~ sP89(U_919,U_920) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

fof(f_374_1,plain,
    ! [A_1,B_6] :
      ( ( A_1 = B_6
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) )
        | A_1 != B_6 ) ),
    inference(fof_nnf,[status(thm)],[fact_270_set__eq__subset]) ).

fof(f_374_2,plain,
    ! [U_922,U_921] :
      ( ( U_922 = U_921
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_921),U_922))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_922),U_921)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_921),U_922))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_922),U_921)) )
        | U_922 != U_921 ) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

fof(f_374_3,plain,
    ( ! [U_926,U_924] :
        ( U_926 = U_924
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_924),U_926))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_926),U_924)) )
    & ! [U_925,U_923] :
        ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_923),U_925))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_925),U_923)) )
        | U_925 != U_923 ) ),
    inference(miniscope,[status(thm)],[f_374_2]) ).

fof(f_374_4,plain,
    ( ! [U_923,U_925] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_923),U_925))
        | ~ sP91(U_923,U_925) )
    & ! [U_923,U_925] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_925),U_923))
        | ~ sP91(U_923,U_925) )
    & ! [U_926,U_924] :
        ( U_926 = U_924
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_924),U_926))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_926),U_924)) )
    & ! [U_923,U_925] :
        ( sP91(U_923,U_925)
        | U_925 != U_923 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_374_3]) ).

cnf(f_374_5,plain,
    ( sP91(U_923,U_925)
    | U_925 != U_923 ),
    inference(clausify,[status(thm)],[f_374_4]) ).

cnf(f_374_6,plain,
    ( U_926 = U_924
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_924),U_926))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_926),U_924)) ),
    inference(clausify,[status(thm)],[f_374_4]) ).

cnf(f_374_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_925),U_923))
    | ~ sP91(U_923,U_925) ),
    inference(clausify,[status(thm)],[f_374_4]) ).

cnf(f_374_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_923),U_925))
    | ~ sP91(U_923,U_925) ),
    inference(clausify,[status(thm)],[f_374_4]) ).

fof(f_375_1,plain,
    ! [A_1,B_6] :
      ( ( ( A_1 = B_6
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) )
        & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) )
          | A_1 != B_6 ) )
      | ~ is_fun_a_bool(B_6)
      | ~ is_fun_a_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_271_set__eq__subset]) ).

fof(f_375_2,plain,
    ! [U_928,U_927] :
      ( ( ( U_928 = U_927
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_927),U_928))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_928),U_927)) )
        & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_927),U_928))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_928),U_927)) )
          | U_928 != U_927 ) )
      | ~ is_fun_a_bool(U_927)
      | ~ is_fun_a_bool(U_928) ),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

fof(f_375_3,plain,
    ( ! [U_927,U_928] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_927),U_928))
        | ~ sP92(U_927,U_928) )
    & ! [U_927,U_928] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_928),U_927))
        | ~ sP92(U_927,U_928) )
    & ! [U_927,U_928] :
        ( U_928 = U_927
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_927),U_928))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_928),U_927))
        | ~ sP93(U_927,U_928) )
    & ! [U_927,U_928] :
        ( sP92(U_927,U_928)
        | U_928 != U_927
        | ~ sP93(U_927,U_928) )
    & ! [U_927,U_928] :
        ( sP93(U_927,U_928)
        | ~ is_fun_a_bool(U_927)
        | ~ is_fun_a_bool(U_928) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92,sP93])],[f_375_2]) ).

cnf(f_375_4,plain,
    ( sP93(U_927,U_928)
    | ~ is_fun_a_bool(U_927)
    | ~ is_fun_a_bool(U_928) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

cnf(f_375_5,plain,
    ( sP92(U_927,U_928)
    | U_928 != U_927
    | ~ sP93(U_927,U_928) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

cnf(f_375_6,plain,
    ( U_928 = U_927
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_927),U_928))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_928),U_927))
    | ~ sP93(U_927,U_928) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

cnf(f_375_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_928),U_927))
    | ~ sP92(U_927,U_928) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

cnf(f_375_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_927),U_928))
    | ~ sP92(U_927,U_928) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

fof(f_376_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
      | A_1 != B_6 ),
    inference(fof_nnf,[status(thm)],[fact_272_equalityD1]) ).

fof(f_376_2,plain,
    ! [U_930,U_929] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_930),U_929))
      | U_930 != U_929 ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

fof(f_376_3,plain,
    ! [U_929,U_930] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_930),U_929))
      | U_930 != U_929 ),
    inference(definitional_conversion,[status(esa)],[f_376_2]) ).

cnf(f_376_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_930),U_929))
    | U_930 != U_929 ),
    inference(clausify,[status(thm)],[f_376_3]) ).

fof(f_377_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
      | A_1 != B_6 ),
    inference(fof_nnf,[status(thm)],[fact_273_equalityD1]) ).

fof(f_377_2,plain,
    ! [U_932,U_931] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_932),U_931))
      | U_932 != U_931 ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

fof(f_377_3,plain,
    ! [U_931,U_932] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_932),U_931))
      | U_932 != U_931 ),
    inference(definitional_conversion,[status(esa)],[f_377_2]) ).

cnf(f_377_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_932),U_931))
    | U_932 != U_931 ),
    inference(clausify,[status(thm)],[f_377_3]) ).

fof(f_378_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
      | A_1 != B_6 ),
    inference(fof_nnf,[status(thm)],[fact_274_equalityD1]) ).

fof(f_378_2,plain,
    ! [U_934,U_933] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_934),U_933))
      | U_934 != U_933 ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

fof(f_378_3,plain,
    ! [U_934,U_933] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_934),U_933))
      | U_934 != U_933 ),
    inference(definitional_conversion,[status(esa)],[f_378_2]) ).

cnf(f_378_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_934),U_933))
    | U_934 != U_933 ),
    inference(clausify,[status(thm)],[f_378_3]) ).

fof(f_379_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1))
      | A_1 != B_6 ),
    inference(fof_nnf,[status(thm)],[fact_275_equalityD2]) ).

fof(f_379_2,plain,
    ! [U_936,U_935] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_935),U_936))
      | U_936 != U_935 ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

fof(f_379_3,plain,
    ! [U_935,U_936] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_935),U_936))
      | U_936 != U_935 ),
    inference(definitional_conversion,[status(esa)],[f_379_2]) ).

cnf(f_379_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_935),U_936))
    | U_936 != U_935 ),
    inference(clausify,[status(thm)],[f_379_3]) ).

fof(f_380_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1))
      | A_1 != B_6 ),
    inference(fof_nnf,[status(thm)],[fact_276_equalityD2]) ).

fof(f_380_2,plain,
    ! [U_938,U_937] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_937),U_938))
      | U_938 != U_937 ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

fof(f_380_3,plain,
    ! [U_937,U_938] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_937),U_938))
      | U_938 != U_937 ),
    inference(definitional_conversion,[status(esa)],[f_380_2]) ).

cnf(f_380_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_937),U_938))
    | U_938 != U_937 ),
    inference(clausify,[status(thm)],[f_380_3]) ).

fof(f_381_1,plain,
    ! [A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1))
      | A_1 != B_6 ),
    inference(fof_nnf,[status(thm)],[fact_277_equalityD2]) ).

fof(f_381_2,plain,
    ! [U_940,U_939] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_939),U_940))
      | U_940 != U_939 ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

fof(f_381_3,plain,
    ! [U_939,U_940] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_939),U_940))
      | U_940 != U_939 ),
    inference(definitional_conversion,[status(esa)],[f_381_2]) ).

cnf(f_381_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_939),U_940))
    | U_940 != U_939 ),
    inference(clausify,[status(thm)],[f_381_3]) ).

fof(f_382_1,plain,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_278_in__mono]) ).

fof(f_382_2,plain,
    ! [U_943,U_942,U_941] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_943),U_941))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_943),U_942))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_942),U_941)) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

fof(f_382_3,plain,
    ! [U_941,U_942,U_943] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_943),U_941))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_943),U_942))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_942),U_941)) ),
    inference(definitional_conversion,[status(esa)],[f_382_2]) ).

cnf(f_382_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_943),U_941))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_943),U_942))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_942),U_941)) ),
    inference(clausify,[status(thm)],[f_382_3]) ).

fof(f_383_1,plain,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_279_in__mono]) ).

fof(f_383_2,plain,
    ! [U_946,U_945,U_944] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_946),U_944))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_946),U_945))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_945),U_944)) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

fof(f_383_3,plain,
    ! [U_945,U_944,U_946] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_946),U_944))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_946),U_945))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_945),U_944)) ),
    inference(definitional_conversion,[status(esa)],[f_383_2]) ).

cnf(f_383_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_946),U_944))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_946),U_945))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_945),U_944)) ),
    inference(clausify,[status(thm)],[f_383_3]) ).

fof(f_384_1,plain,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_280_in__mono]) ).

fof(f_384_2,plain,
    ! [U_949,U_948,U_947] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_949),U_947))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_949),U_948))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_948),U_947)) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ! [U_947,U_948,U_949] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_949),U_947))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_949),U_948))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_948),U_947)) ),
    inference(definitional_conversion,[status(esa)],[f_384_2]) ).

cnf(f_384_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_949),U_947))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_949),U_948))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_948),U_947)) ),
    inference(clausify,[status(thm)],[f_384_3]) ).

fof(f_385_1,plain,
    ! [B_6,X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_281_set__rev__mp]) ).

fof(f_385_2,plain,
    ! [U_952,U_951,U_950] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_951),U_952))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_950),U_952))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_951),U_950)) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

fof(f_385_3,plain,
    ! [U_950,U_951,U_952] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_951),U_952))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_950),U_952))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_951),U_950)) ),
    inference(definitional_conversion,[status(esa)],[f_385_2]) ).

cnf(f_385_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_951),U_952))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_950),U_952))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_951),U_950)) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

fof(f_386_1,plain,
    ! [B_6,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_282_set__rev__mp]) ).

fof(f_386_2,plain,
    ! [U_955,U_954,U_953] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_954),U_955))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_953),U_955))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_954),U_953)) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

fof(f_386_3,plain,
    ! [U_953,U_954,U_955] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_954),U_955))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_953),U_955))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_954),U_953)) ),
    inference(definitional_conversion,[status(esa)],[f_386_2]) ).

cnf(f_386_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_954),U_955))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_953),U_955))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_954),U_953)) ),
    inference(clausify,[status(thm)],[f_386_3]) ).

fof(f_387_1,plain,
    ! [B_6,X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_283_set__rev__mp]) ).

fof(f_387_2,plain,
    ! [U_958,U_957,U_956] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_957),U_958))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_956),U_958))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_957),U_956)) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

fof(f_387_3,plain,
    ! [U_956,U_957,U_958] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_957),U_958))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_956),U_958))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_957),U_956)) ),
    inference(definitional_conversion,[status(esa)],[f_387_2]) ).

cnf(f_387_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_957),U_958))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_956),U_958))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_957),U_956)) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

fof(f_388_1,plain,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_284_set__mp]) ).

fof(f_388_2,plain,
    ! [U_961,U_960,U_959] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_961),U_959))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_961),U_960))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_960),U_959)) ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

fof(f_388_3,plain,
    ! [U_959,U_960,U_961] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_961),U_959))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_961),U_960))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_960),U_959)) ),
    inference(definitional_conversion,[status(esa)],[f_388_2]) ).

cnf(f_388_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_961),U_959))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_961),U_960))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_960),U_959)) ),
    inference(clausify,[status(thm)],[f_388_3]) ).

fof(f_389_1,plain,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_285_set__mp]) ).

fof(f_389_2,plain,
    ! [U_964,U_963,U_962] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_964),U_962))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_964),U_963))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_963),U_962)) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

fof(f_389_3,plain,
    ! [U_963,U_962,U_964] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_964),U_962))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_964),U_963))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_963),U_962)) ),
    inference(definitional_conversion,[status(esa)],[f_389_2]) ).

cnf(f_389_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_964),U_962))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_964),U_963))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_963),U_962)) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

fof(f_390_1,plain,
    ! [X_3,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_286_set__mp]) ).

fof(f_390_2,plain,
    ! [U_967,U_966,U_965] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_967),U_965))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_967),U_966))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_966),U_965)) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

fof(f_390_3,plain,
    ! [U_965,U_966,U_967] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_967),U_965))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_967),U_966))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_966),U_965)) ),
    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_967),U_965))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_967),U_966))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_966),U_965)) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

fof(f_391_1,plain,
    ! [X_3,A_1] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1))
        | ~ hBOOL(hAPP_nat_bool(A_1,X_3)) )
      & ( hBOOL(hAPP_nat_bool(A_1,X_3))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_287_mem__def]) ).

fof(f_391_2,plain,
    ! [U_969,U_968] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_969),U_968))
        | ~ hBOOL(hAPP_nat_bool(U_968,U_969)) )
      & ( hBOOL(hAPP_nat_bool(U_968,U_969))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_969),U_968)) ) ),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

fof(f_391_3,plain,
    ( ! [U_973,U_971] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_973),U_971))
        | ~ hBOOL(hAPP_nat_bool(U_971,U_973)) )
    & ! [U_972,U_970] :
        ( hBOOL(hAPP_nat_bool(U_970,U_972))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_972),U_970)) ) ),
    inference(miniscope,[status(thm)],[f_391_2]) ).

fof(f_391_4,plain,
    ( ! [U_971,U_973] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_973),U_971))
        | ~ hBOOL(hAPP_nat_bool(U_971,U_973)) )
    & ! [U_972,U_970] :
        ( hBOOL(hAPP_nat_bool(U_970,U_972))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_972),U_970)) ) ),
    inference(definitional_conversion,[status(esa)],[f_391_3]) ).

cnf(f_391_5,plain,
    ( hBOOL(hAPP_nat_bool(U_970,U_972))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_972),U_970)) ),
    inference(clausify,[status(thm)],[f_391_4]) ).

cnf(f_391_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_973),U_971))
    | ~ hBOOL(hAPP_nat_bool(U_971,U_973)) ),
    inference(clausify,[status(thm)],[f_391_4]) ).

fof(f_392_1,plain,
    ! [X_3,A_1] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1))
        | ~ hBOOL(hAPP_pname_bool(A_1,X_3)) )
      & ( hBOOL(hAPP_pname_bool(A_1,X_3))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_288_mem__def]) ).

fof(f_392_2,plain,
    ! [U_975,U_974] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_975),U_974))
        | ~ hBOOL(hAPP_pname_bool(U_974,U_975)) )
      & ( hBOOL(hAPP_pname_bool(U_974,U_975))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_975),U_974)) ) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ( ! [U_979,U_977] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_979),U_977))
        | ~ hBOOL(hAPP_pname_bool(U_977,U_979)) )
    & ! [U_978,U_976] :
        ( hBOOL(hAPP_pname_bool(U_976,U_978))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_978),U_976)) ) ),
    inference(miniscope,[status(thm)],[f_392_2]) ).

fof(f_392_4,plain,
    ( ! [U_977,U_979] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_979),U_977))
        | ~ hBOOL(hAPP_pname_bool(U_977,U_979)) )
    & ! [U_978,U_976] :
        ( hBOOL(hAPP_pname_bool(U_976,U_978))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_978),U_976)) ) ),
    inference(definitional_conversion,[status(esa)],[f_392_3]) ).

cnf(f_392_5,plain,
    ( hBOOL(hAPP_pname_bool(U_976,U_978))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_978),U_976)) ),
    inference(clausify,[status(thm)],[f_392_4]) ).

cnf(f_392_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_979),U_977))
    | ~ hBOOL(hAPP_pname_bool(U_977,U_979)) ),
    inference(clausify,[status(thm)],[f_392_4]) ).

fof(f_393_1,plain,
    ! [X_3,A_1] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1))
        | ~ hBOOL(hAPP_a_bool(A_1,X_3)) )
      & ( hBOOL(hAPP_a_bool(A_1,X_3))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_289_mem__def]) ).

fof(f_393_2,plain,
    ! [U_981,U_980] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_981),U_980))
        | ~ hBOOL(hAPP_a_bool(U_980,U_981)) )
      & ( hBOOL(hAPP_a_bool(U_980,U_981))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_981),U_980)) ) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

fof(f_393_3,plain,
    ( ! [U_985,U_983] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_985),U_983))
        | ~ hBOOL(hAPP_a_bool(U_983,U_985)) )
    & ! [U_984,U_982] :
        ( hBOOL(hAPP_a_bool(U_982,U_984))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_984),U_982)) ) ),
    inference(miniscope,[status(thm)],[f_393_2]) ).

fof(f_393_4,plain,
    ( ! [U_983,U_985] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_985),U_983))
        | ~ hBOOL(hAPP_a_bool(U_983,U_985)) )
    & ! [U_984,U_982] :
        ( hBOOL(hAPP_a_bool(U_982,U_984))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_984),U_982)) ) ),
    inference(definitional_conversion,[status(esa)],[f_393_3]) ).

cnf(f_393_5,plain,
    ( hBOOL(hAPP_a_bool(U_982,U_984))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_984),U_982)) ),
    inference(clausify,[status(thm)],[f_393_4]) ).

cnf(f_393_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_985),U_983))
    | ~ hBOOL(hAPP_a_bool(U_983,U_985)) ),
    inference(clausify,[status(thm)],[f_393_4]) ).

fof(f_394_1,plain,
    ! [Pa] :
      ( collect_a(Pa) = Pa
      | ~ is_fun_a_bool(Pa) ),
    inference(fof_nnf,[status(thm)],[fact_290_Collect__def]) ).

fof(f_394_2,plain,
    ! [U_986] :
      ( collect_a(U_986) = U_986
      | ~ is_fun_a_bool(U_986) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

fof(f_394_3,plain,
    ! [U_986] :
      ( collect_a(U_986) = U_986
      | ~ is_fun_a_bool(U_986) ),
    inference(definitional_conversion,[status(esa)],[f_394_2]) ).

cnf(f_394_4,plain,
    ( collect_a(U_986) = U_986
    | ~ is_fun_a_bool(U_986) ),
    inference(clausify,[status(thm)],[f_394_3]) ).

fof(f_395_1,plain,
    ! [Pa] :
      ( collect_pname(Pa) = Pa
      | ~ is_fun_pname_bool(Pa) ),
    inference(fof_nnf,[status(thm)],[fact_291_Collect__def]) ).

fof(f_395_2,plain,
    ! [U_987] :
      ( collect_pname(U_987) = U_987
      | ~ is_fun_pname_bool(U_987) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

fof(f_395_3,plain,
    ! [U_987] :
      ( collect_pname(U_987) = U_987
      | ~ is_fun_pname_bool(U_987) ),
    inference(definitional_conversion,[status(esa)],[f_395_2]) ).

cnf(f_395_4,plain,
    ( collect_pname(U_987) = U_987
    | ~ is_fun_pname_bool(U_987) ),
    inference(clausify,[status(thm)],[f_395_3]) ).

fof(f_396_1,plain,
    ! [Pa] : collect_fun_nat_bool(Pa) = Pa,
    inference(fof_nnf,[status(thm)],[fact_292_Collect__def]) ).

fof(f_396_2,plain,
    ! [U_988] : collect_fun_nat_bool(U_988) = U_988,
    inference(variable_rename,[status(thm)],[f_396_1]) ).

fof(f_396_3,plain,
    ! [U_988] : collect_fun_nat_bool(U_988) = U_988,
    inference(definitional_conversion,[status(esa)],[f_396_2]) ).

cnf(f_396_4,plain,
    collect_fun_nat_bool(U_988) = U_988,
    inference(clausify,[status(thm)],[f_396_3]) ).

fof(f_397_1,plain,
    ! [Pa] :
      ( collec1974731493e_bool(Pa) = Pa
      | ~ is_fun1661590463l_bool(Pa) ),
    inference(fof_nnf,[status(thm)],[fact_293_Collect__def]) ).

fof(f_397_2,plain,
    ! [U_989] :
      ( collec1974731493e_bool(U_989) = U_989
      | ~ is_fun1661590463l_bool(U_989) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

fof(f_397_3,plain,
    ! [U_989] :
      ( collec1974731493e_bool(U_989) = U_989
      | ~ is_fun1661590463l_bool(U_989) ),
    inference(definitional_conversion,[status(esa)],[f_397_2]) ).

cnf(f_397_4,plain,
    ( collec1974731493e_bool(U_989) = U_989
    | ~ is_fun1661590463l_bool(U_989) ),
    inference(clausify,[status(thm)],[f_397_3]) ).

fof(f_398_1,plain,
    ! [Pa] :
      ( collect_fun_a_bool(Pa) = Pa
      | ~ is_fun949378684l_bool(Pa) ),
    inference(fof_nnf,[status(thm)],[fact_294_Collect__def]) ).

fof(f_398_2,plain,
    ! [U_990] :
      ( collect_fun_a_bool(U_990) = U_990
      | ~ is_fun949378684l_bool(U_990) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

fof(f_398_3,plain,
    ! [U_990] :
      ( collect_fun_a_bool(U_990) = U_990
      | ~ is_fun949378684l_bool(U_990) ),
    inference(definitional_conversion,[status(esa)],[f_398_2]) ).

cnf(f_398_4,plain,
    ( collect_fun_a_bool(U_990) = U_990
    | ~ is_fun949378684l_bool(U_990) ),
    inference(clausify,[status(thm)],[f_398_3]) ).

fof(f_399_1,plain,
    ! [Pa] : collect_nat(Pa) = Pa,
    inference(fof_nnf,[status(thm)],[fact_295_Collect__def]) ).

fof(f_399_2,plain,
    ! [U_991] : collect_nat(U_991) = U_991,
    inference(variable_rename,[status(thm)],[f_399_1]) ).

fof(f_399_3,plain,
    ! [U_991] : collect_nat(U_991) = U_991,
    inference(definitional_conversion,[status(esa)],[f_399_2]) ).

cnf(f_399_4,plain,
    collect_nat(U_991) = U_991,
    inference(clausify,[status(thm)],[f_399_3]) ).

fof(f_400_1,plain,
    ! [C_6,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),C_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),C_6))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_296_subset__trans]) ).

fof(f_400_2,plain,
    ! [U_994,U_993,U_992] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_993),U_994))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_992),U_994))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_993),U_992)) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

fof(f_400_3,plain,
    ! [U_992,U_993,U_994] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_993),U_994))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_992),U_994))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_993),U_992)) ),
    inference(definitional_conversion,[status(esa)],[f_400_2]) ).

cnf(f_400_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_993),U_994))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_992),U_994))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_993),U_992)) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

fof(f_401_1,plain,
    ! [C_6,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),C_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),C_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_297_subset__trans]) ).

fof(f_401_2,plain,
    ! [U_997,U_996,U_995] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_996),U_997))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_995),U_997))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_996),U_995)) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

fof(f_401_3,plain,
    ! [U_995,U_996,U_997] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_996),U_997))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_995),U_997))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_996),U_995)) ),
    inference(definitional_conversion,[status(esa)],[f_401_2]) ).

cnf(f_401_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_996),U_997))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_995),U_997))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_996),U_995)) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

fof(f_402_1,plain,
    ! [C_6,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),C_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),C_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_298_subset__trans]) ).

fof(f_402_2,plain,
    ! [U_1000,U_999,U_998] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_999),U_1000))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_998),U_1000))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_999),U_998)) ),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

fof(f_402_3,plain,
    ! [U_998,U_999,U_1000] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_999),U_1000))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_998),U_1000))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_999),U_998)) ),
    inference(definitional_conversion,[status(esa)],[f_402_2]) ).

cnf(f_402_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_999),U_1000))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_998),U_1000))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_999),U_998)) ),
    inference(clausify,[status(thm)],[f_402_3]) ).

fof(f_403_1,plain,
    ! [A_1,B_6] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),A_1))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) )
      | A_1 != B_6 ),
    inference(fof_nnf,[status(thm)],[fact_299_equalityE]) ).

fof(f_403_2,plain,
    ! [U_1002,U_1001] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1001),U_1002))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1002),U_1001)) )
      | U_1002 != U_1001 ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

fof(f_403_3,plain,
    ( ! [U_1001,U_1002] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1001),U_1002))
        | ~ sP94(U_1001,U_1002) )
    & ! [U_1001,U_1002] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1002),U_1001))
        | ~ sP94(U_1001,U_1002) )
    & ! [U_1001,U_1002] :
        ( sP94(U_1001,U_1002)
        | U_1002 != U_1001 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94])],[f_403_2]) ).

cnf(f_403_4,plain,
    ( sP94(U_1001,U_1002)
    | U_1002 != U_1001 ),
    inference(clausify,[status(thm)],[f_403_3]) ).

cnf(f_403_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1002),U_1001))
    | ~ sP94(U_1001,U_1002) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

cnf(f_403_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1001),U_1002))
    | ~ sP94(U_1001,U_1002) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

fof(f_404_1,plain,
    ! [A_1,B_6] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),A_1))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) )
      | A_1 != B_6 ),
    inference(fof_nnf,[status(thm)],[fact_300_equalityE]) ).

fof(f_404_2,plain,
    ! [U_1004,U_1003] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1003),U_1004))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1004),U_1003)) )
      | U_1004 != U_1003 ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

fof(f_404_3,plain,
    ( ! [U_1003,U_1004] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1003),U_1004))
        | ~ sP95(U_1003,U_1004) )
    & ! [U_1003,U_1004] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1004),U_1003))
        | ~ sP95(U_1003,U_1004) )
    & ! [U_1003,U_1004] :
        ( sP95(U_1003,U_1004)
        | U_1004 != U_1003 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95])],[f_404_2]) ).

cnf(f_404_4,plain,
    ( sP95(U_1003,U_1004)
    | U_1004 != U_1003 ),
    inference(clausify,[status(thm)],[f_404_3]) ).

cnf(f_404_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1004),U_1003))
    | ~ sP95(U_1003,U_1004) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

cnf(f_404_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1003),U_1004))
    | ~ sP95(U_1003,U_1004) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

fof(f_405_1,plain,
    ! [A_1,B_6] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),A_1))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) )
      | A_1 != B_6 ),
    inference(fof_nnf,[status(thm)],[fact_301_equalityE]) ).

fof(f_405_2,plain,
    ! [U_1006,U_1005] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1005),U_1006))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1006),U_1005)) )
      | U_1006 != U_1005 ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

fof(f_405_3,plain,
    ( ! [U_1006,U_1005] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1005),U_1006))
        | ~ sP96(U_1006,U_1005) )
    & ! [U_1006,U_1005] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1006),U_1005))
        | ~ sP96(U_1006,U_1005) )
    & ! [U_1006,U_1005] :
        ( sP96(U_1006,U_1005)
        | U_1006 != U_1005 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96])],[f_405_2]) ).

cnf(f_405_4,plain,
    ( sP96(U_1006,U_1005)
    | U_1006 != U_1005 ),
    inference(clausify,[status(thm)],[f_405_3]) ).

cnf(f_405_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1006),U_1005))
    | ~ sP96(U_1006,U_1005) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

cnf(f_405_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1005),U_1006))
    | ~ sP96(U_1006,U_1005) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

fof(f_406_1,plain,
    ! [Z_1,F,A_1] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z_1),image_pname_a(F,A_1)))
          | ! [X_1] :
              ( Z_1 != hAPP_pname_a(F,X_1)
              | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
              | ~ is_pname(X_1) ) )
        & ( ? [X_1] :
              ( Z_1 = hAPP_pname_a(F,X_1)
              & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
              & is_pname(X_1) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z_1),image_pname_a(F,A_1))) ) )
      | ~ is_a(Z_1) ),
    inference(fof_nnf,[status(thm)],[fact_302_image__iff]) ).

fof(f_406_2,plain,
    ! [U_1011,U_1010,U_1009] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1011),image_pname_a(U_1010,U_1009)))
          | ! [U_1008] :
              ( U_1011 != hAPP_pname_a(U_1010,U_1008)
              | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1008),U_1009))
              | ~ is_pname(U_1008) ) )
        & ( ? [U_1007] :
              ( U_1011 = hAPP_pname_a(U_1010,U_1007)
              & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1007),U_1009))
              & is_pname(U_1007) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1011),image_pname_a(U_1010,U_1009))) ) )
      | ~ is_a(U_1011) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ! [U_1011] :
      ( ( ! [U_1015,U_1013] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1011),image_pname_a(U_1015,U_1013)))
            | ! [U_1008] :
                ( U_1011 != hAPP_pname_a(U_1015,U_1008)
                | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1008),U_1013))
                | ~ is_pname(U_1008) ) )
        & ! [U_1014,U_1012] :
            ( ? [U_1007] :
                ( U_1011 = hAPP_pname_a(U_1014,U_1007)
                & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1007),U_1012))
                & is_pname(U_1007) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1011),image_pname_a(U_1014,U_1012))) ) )
      | ~ is_a(U_1011) ),
    inference(miniscope,[status(thm)],[f_406_2]) ).

fof(f_406_4,plain,
    ! [U_1011] :
      ( ( ! [U_1015,U_1013] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1011),image_pname_a(U_1015,U_1013)))
            | ! [U_1008] :
                ( U_1011 != hAPP_pname_a(U_1015,U_1008)
                | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1008),U_1013))
                | ~ is_pname(U_1008) ) )
        & ! [U_1014,U_1012] :
            ( ( U_1011 = hAPP_pname_a(U_1014,sK59(U_1011,U_1014,U_1012))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK59(U_1011,U_1014,U_1012)),U_1012))
              & is_pname(sK59(U_1011,U_1014,U_1012)) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1011),image_pname_a(U_1014,U_1012))) ) )
      | ~ is_a(U_1011) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_1007,sK59(U_1011,U_1014,U_1012))],[f_406_3]) ).

fof(f_406_5,plain,
    ( ! [U_1011,U_1012,U_1014] :
        ( U_1011 = hAPP_pname_a(U_1014,sK59(U_1011,U_1014,U_1012))
        | ~ sP97(U_1011,U_1012,U_1014) )
    & ! [U_1011,U_1012,U_1014] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK59(U_1011,U_1014,U_1012)),U_1012))
        | ~ sP97(U_1011,U_1012,U_1014) )
    & ! [U_1011,U_1012,U_1014] :
        ( is_pname(sK59(U_1011,U_1014,U_1012))
        | ~ sP97(U_1011,U_1012,U_1014) )
    & ! [U_1008,U_1011,U_1012,U_1014,U_1013,U_1015] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1011),image_pname_a(U_1015,U_1013)))
        | U_1011 != hAPP_pname_a(U_1015,U_1008)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1008),U_1013))
        | ~ is_pname(U_1008)
        | ~ sP98(U_1008,U_1011,U_1012,U_1014,U_1013,U_1015) )
    & ! [U_1008,U_1011,U_1012,U_1014,U_1013,U_1015] :
        ( sP97(U_1011,U_1012,U_1014)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1011),image_pname_a(U_1014,U_1012)))
        | ~ sP98(U_1008,U_1011,U_1012,U_1014,U_1013,U_1015) )
    & ! [U_1008,U_1011,U_1012,U_1014,U_1013,U_1015] :
        ( sP98(U_1008,U_1011,U_1012,U_1014,U_1013,U_1015)
        | ~ is_a(U_1011) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP97,sP98])],[f_406_4]) ).

cnf(f_406_6,plain,
    ( sP98(U_1008,U_1011,U_1012,U_1014,U_1013,U_1015)
    | ~ is_a(U_1011) ),
    inference(clausify,[status(thm)],[f_406_5]) ).

cnf(f_406_7,plain,
    ( sP97(U_1011,U_1012,U_1014)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1011),image_pname_a(U_1014,U_1012)))
    | ~ sP98(U_1008,U_1011,U_1012,U_1014,U_1013,U_1015) ),
    inference(clausify,[status(thm)],[f_406_5]) ).

cnf(f_406_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1011),image_pname_a(U_1015,U_1013)))
    | U_1011 != hAPP_pname_a(U_1015,U_1008)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1008),U_1013))
    | ~ is_pname(U_1008)
    | ~ sP98(U_1008,U_1011,U_1012,U_1014,U_1013,U_1015) ),
    inference(clausify,[status(thm)],[f_406_5]) ).

cnf(f_406_9,plain,
    ( is_pname(sK59(U_1011,U_1014,U_1012))
    | ~ sP97(U_1011,U_1012,U_1014) ),
    inference(clausify,[status(thm)],[f_406_5]) ).

cnf(f_406_10,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK59(U_1011,U_1014,U_1012)),U_1012))
    | ~ sP97(U_1011,U_1012,U_1014) ),
    inference(clausify,[status(thm)],[f_406_5]) ).

cnf(f_406_11,plain,
    ( U_1011 = hAPP_pname_a(U_1014,sK59(U_1011,U_1014,U_1012))
    | ~ sP97(U_1011,U_1012,U_1014) ),
    inference(clausify,[status(thm)],[f_406_5]) ).

fof(f_407_1,plain,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(F,X_3)),image_pname_nat(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_303_imageI]) ).

fof(f_407_2,plain,
    ! [U_1018,U_1017,U_1016] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(U_1018,U_1017)),image_pname_nat(U_1018,U_1016)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1017),U_1016)) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ! [U_1017,U_1018,U_1016] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(U_1018,U_1017)),image_pname_nat(U_1018,U_1016)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1017),U_1016)) ),
    inference(definitional_conversion,[status(esa)],[f_407_2]) ).

cnf(f_407_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(U_1018,U_1017)),image_pname_nat(U_1018,U_1016)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1017),U_1016)) ),
    inference(clausify,[status(thm)],[f_407_3]) ).

fof(f_408_1,plain,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(F,X_3)),image_a_nat(F,A_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_304_imageI]) ).

fof(f_408_2,plain,
    ! [U_1021,U_1020,U_1019] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(U_1021,U_1020)),image_a_nat(U_1021,U_1019)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1020),U_1019)) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

fof(f_408_3,plain,
    ! [U_1021,U_1020,U_1019] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(U_1021,U_1020)),image_a_nat(U_1021,U_1019)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1020),U_1019)) ),
    inference(definitional_conversion,[status(esa)],[f_408_2]) ).

cnf(f_408_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(U_1021,U_1020)),image_a_nat(U_1021,U_1019)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1020),U_1019)) ),
    inference(clausify,[status(thm)],[f_408_3]) ).

fof(f_409_1,plain,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(F,X_3)),image_nat_pname(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_305_imageI]) ).

fof(f_409_2,plain,
    ! [U_1024,U_1023,U_1022] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(U_1024,U_1023)),image_nat_pname(U_1024,U_1022)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1023),U_1022)) ),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

fof(f_409_3,plain,
    ! [U_1023,U_1022,U_1024] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(U_1024,U_1023)),image_nat_pname(U_1024,U_1022)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1023),U_1022)) ),
    inference(definitional_conversion,[status(esa)],[f_409_2]) ).

cnf(f_409_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(U_1024,U_1023)),image_nat_pname(U_1024,U_1022)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1023),U_1022)) ),
    inference(clausify,[status(thm)],[f_409_3]) ).

fof(f_410_1,plain,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(F,X_3)),image_nat_a(F,A_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_306_imageI]) ).

fof(f_410_2,plain,
    ! [U_1027,U_1026,U_1025] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(U_1027,U_1026)),image_nat_a(U_1027,U_1025)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1026),U_1025)) ),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

fof(f_410_3,plain,
    ! [U_1025,U_1026,U_1027] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(U_1027,U_1026)),image_nat_a(U_1027,U_1025)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1026),U_1025)) ),
    inference(definitional_conversion,[status(esa)],[f_410_2]) ).

cnf(f_410_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(U_1027,U_1026)),image_nat_a(U_1027,U_1025)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1026),U_1025)) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

fof(f_411_1,plain,
    ! [F,X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_3)),image_pname_a(F,A_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_307_imageI]) ).

fof(f_411_2,plain,
    ! [U_1030,U_1029,U_1028] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1030,U_1029)),image_pname_a(U_1030,U_1028)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1029),U_1028)) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

fof(f_411_3,plain,
    ! [U_1028,U_1029,U_1030] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1030,U_1029)),image_pname_a(U_1030,U_1028)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1029),U_1028)) ),
    inference(definitional_conversion,[status(esa)],[f_411_2]) ).

cnf(f_411_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1030,U_1029)),image_pname_a(U_1030,U_1028)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1029),U_1028)) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

fof(f_412_1,plain,
    ! [B_1,F,X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_pname_nat(F,A_1)))
      | B_1 != hAPP_pname_nat(F,X_3)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_308_rev__image__eqI]) ).

fof(f_412_2,plain,
    ! [U_1034,U_1033,U_1032,U_1031] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1034),image_pname_nat(U_1033,U_1031)))
      | U_1034 != hAPP_pname_nat(U_1033,U_1032)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1032),U_1031)) ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

fof(f_412_3,plain,
    ! [U_1031,U_1032,U_1033,U_1034] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1034),image_pname_nat(U_1033,U_1031)))
      | U_1034 != hAPP_pname_nat(U_1033,U_1032)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1032),U_1031)) ),
    inference(definitional_conversion,[status(esa)],[f_412_2]) ).

cnf(f_412_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1034),image_pname_nat(U_1033,U_1031)))
    | U_1034 != hAPP_pname_nat(U_1033,U_1032)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1032),U_1031)) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

fof(f_413_1,plain,
    ! [B_1,F,X_3,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_a_nat(F,A_1)))
      | B_1 != hAPP_a_nat(F,X_3)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_309_rev__image__eqI]) ).

fof(f_413_2,plain,
    ! [U_1038,U_1037,U_1036,U_1035] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1038),image_a_nat(U_1037,U_1035)))
      | U_1038 != hAPP_a_nat(U_1037,U_1036)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1036),U_1035)) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ! [U_1036,U_1035,U_1037,U_1038] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1038),image_a_nat(U_1037,U_1035)))
      | U_1038 != hAPP_a_nat(U_1037,U_1036)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1036),U_1035)) ),
    inference(definitional_conversion,[status(esa)],[f_413_2]) ).

cnf(f_413_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1038),image_a_nat(U_1037,U_1035)))
    | U_1038 != hAPP_a_nat(U_1037,U_1036)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1036),U_1035)) ),
    inference(clausify,[status(thm)],[f_413_3]) ).

fof(f_414_1,plain,
    ! [B_1,F,X_3,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_nat_pname(F,A_1)))
      | B_1 != hAPP_nat_pname(F,X_3)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_310_rev__image__eqI]) ).

fof(f_414_2,plain,
    ! [U_1042,U_1041,U_1040,U_1039] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1042),image_nat_pname(U_1041,U_1039)))
      | U_1042 != hAPP_nat_pname(U_1041,U_1040)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1040),U_1039)) ),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

fof(f_414_3,plain,
    ! [U_1040,U_1039,U_1041,U_1042] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1042),image_nat_pname(U_1041,U_1039)))
      | U_1042 != hAPP_nat_pname(U_1041,U_1040)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1040),U_1039)) ),
    inference(definitional_conversion,[status(esa)],[f_414_2]) ).

cnf(f_414_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1042),image_nat_pname(U_1041,U_1039)))
    | U_1042 != hAPP_nat_pname(U_1041,U_1040)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1040),U_1039)) ),
    inference(clausify,[status(thm)],[f_414_3]) ).

fof(f_415_1,plain,
    ! [B_1,F,X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_nat_a(F,A_1)))
      | B_1 != hAPP_nat_a(F,X_3)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_311_rev__image__eqI]) ).

fof(f_415_2,plain,
    ! [U_1046,U_1045,U_1044,U_1043] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1046),image_nat_a(U_1045,U_1043)))
      | U_1046 != hAPP_nat_a(U_1045,U_1044)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1044),U_1043)) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

fof(f_415_3,plain,
    ! [U_1044,U_1043,U_1045,U_1046] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1046),image_nat_a(U_1045,U_1043)))
      | U_1046 != hAPP_nat_a(U_1045,U_1044)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1044),U_1043)) ),
    inference(definitional_conversion,[status(esa)],[f_415_2]) ).

cnf(f_415_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1046),image_nat_a(U_1045,U_1043)))
    | U_1046 != hAPP_nat_a(U_1045,U_1044)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1044),U_1043)) ),
    inference(clausify,[status(thm)],[f_415_3]) ).

fof(f_416_1,plain,
    ! [B_1,F,X_3,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
      | B_1 != hAPP_pname_a(F,X_3)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_312_rev__image__eqI]) ).

fof(f_416_2,plain,
    ! [U_1050,U_1049,U_1048,U_1047] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1050),image_pname_a(U_1049,U_1047)))
      | U_1050 != hAPP_pname_a(U_1049,U_1048)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1048),U_1047)) ),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

fof(f_416_3,plain,
    ! [U_1048,U_1047,U_1049,U_1050] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1050),image_pname_a(U_1049,U_1047)))
      | U_1050 != hAPP_pname_a(U_1049,U_1048)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1048),U_1047)) ),
    inference(definitional_conversion,[status(esa)],[f_416_2]) ).

cnf(f_416_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1050),image_pname_a(U_1049,U_1047)))
    | U_1050 != hAPP_pname_a(U_1049,U_1048)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1048),U_1047)) ),
    inference(clausify,[status(thm)],[f_416_3]) ).

fof(f_417_1,plain,
    ! [X_1,Xa] : insert_fun_nat_bool(X_1,Xa) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X_1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),Xa))),
    inference(fof_nnf,[status(thm)],[fact_313_insert__compr__raw]) ).

fof(f_417_2,plain,
    ! [U_1052,U_1051] : insert_fun_nat_bool(U_1052,U_1051) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1052)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_1051))),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

fof(f_417_3,plain,
    ! [U_1052,U_1051] : insert_fun_nat_bool(U_1052,U_1051) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1052)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_1051))),
    inference(definitional_conversion,[status(esa)],[f_417_2]) ).

cnf(f_417_4,plain,
    insert_fun_nat_bool(U_1052,U_1051) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1052)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_1051))),
    inference(clausify,[status(thm)],[f_417_3]) ).

fof(f_418_1,plain,
    ! [X_1,Xa] : insert1325755072e_bool(X_1,Xa) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),Xa))),
    inference(fof_nnf,[status(thm)],[fact_314_insert__compr__raw]) ).

fof(f_418_2,plain,
    ! [U_1054,U_1053] : insert1325755072e_bool(U_1054,U_1053) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1054)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_1053))),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

fof(f_418_3,plain,
    ! [U_1053,U_1054] : insert1325755072e_bool(U_1054,U_1053) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1054)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_1053))),
    inference(definitional_conversion,[status(esa)],[f_418_2]) ).

cnf(f_418_4,plain,
    insert1325755072e_bool(U_1054,U_1053) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1054)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_1053))),
    inference(clausify,[status(thm)],[f_418_3]) ).

fof(f_419_1,plain,
    ! [X_1,Xa] : insert_fun_a_bool(X_1,Xa) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X_1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),Xa))),
    inference(fof_nnf,[status(thm)],[fact_315_insert__compr__raw]) ).

fof(f_419_2,plain,
    ! [U_1056,U_1055] : insert_fun_a_bool(U_1056,U_1055) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1056)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_1055))),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

fof(f_419_3,plain,
    ! [U_1055,U_1056] : insert_fun_a_bool(U_1056,U_1055) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1056)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_1055))),
    inference(definitional_conversion,[status(esa)],[f_419_2]) ).

cnf(f_419_4,plain,
    insert_fun_a_bool(U_1056,U_1055) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1056)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_1055))),
    inference(clausify,[status(thm)],[f_419_3]) ).

fof(f_420_1,plain,
    ! [X_1,Xa] : insert_nat(X_1,Xa) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),Xa))),
    inference(fof_nnf,[status(thm)],[fact_316_insert__compr__raw]) ).

fof(f_420_2,plain,
    ! [U_1058,U_1057] : insert_nat(U_1058,U_1057) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1058)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_1057))),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

fof(f_420_3,plain,
    ! [U_1057,U_1058] : insert_nat(U_1058,U_1057) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1058)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_1057))),
    inference(definitional_conversion,[status(esa)],[f_420_2]) ).

cnf(f_420_4,plain,
    insert_nat(U_1058,U_1057) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1058)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_1057))),
    inference(clausify,[status(thm)],[f_420_3]) ).

fof(f_421_1,plain,
    ! [X_1,Xa] : insert_pname(X_1,Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),Xa))),
    inference(fof_nnf,[status(thm)],[fact_317_insert__compr__raw]) ).

fof(f_421_2,plain,
    ! [U_1060,U_1059] : insert_pname(U_1060,U_1059) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1060)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_1059))),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

fof(f_421_3,plain,
    ! [U_1059,U_1060] : insert_pname(U_1060,U_1059) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1060)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_1059))),
    inference(definitional_conversion,[status(esa)],[f_421_2]) ).

cnf(f_421_4,plain,
    insert_pname(U_1060,U_1059) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1060)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_1059))),
    inference(clausify,[status(thm)],[f_421_3]) ).

fof(f_422_1,plain,
    ! [X_1,Xa] : insert_a(X_1,Xa) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),Xa))),
    inference(fof_nnf,[status(thm)],[fact_318_insert__compr__raw]) ).

fof(f_422_2,plain,
    ! [U_1062,U_1061] : insert_a(U_1062,U_1061) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1062)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_1061))),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

fof(f_422_3,plain,
    ! [U_1061,U_1062] : insert_a(U_1062,U_1061) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1062)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_1061))),
    inference(definitional_conversion,[status(esa)],[f_422_2]) ).

cnf(f_422_4,plain,
    insert_a(U_1062,U_1061) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1062)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_1061))),
    inference(clausify,[status(thm)],[f_422_3]) ).

fof(f_423_1,plain,
    ! [B_6,A_3] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),insert_pname(A_3,B_6))),
    inference(fof_nnf,[status(thm)],[fact_319_subset__insertI]) ).

fof(f_423_2,plain,
    ! [U_1064,U_1063] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1064),insert_pname(U_1063,U_1064))),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

fof(f_423_3,plain,
    ! [U_1063,U_1064] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1064),insert_pname(U_1063,U_1064))),
    inference(definitional_conversion,[status(esa)],[f_423_2]) ).

cnf(f_423_4,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1064),insert_pname(U_1063,U_1064))),
    inference(clausify,[status(thm)],[f_423_3]) ).

fof(f_424_1,plain,
    ! [B_6,A_3] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),insert_nat(A_3,B_6))),
    inference(fof_nnf,[status(thm)],[fact_320_subset__insertI]) ).

fof(f_424_2,plain,
    ! [U_1066,U_1065] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1066),insert_nat(U_1065,U_1066))),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

fof(f_424_3,plain,
    ! [U_1065,U_1066] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1066),insert_nat(U_1065,U_1066))),
    inference(definitional_conversion,[status(esa)],[f_424_2]) ).

cnf(f_424_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1066),insert_nat(U_1065,U_1066))),
    inference(clausify,[status(thm)],[f_424_3]) ).

fof(f_425_1,plain,
    ! [B_6,A_3] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),insert_a(A_3,B_6))),
    inference(fof_nnf,[status(thm)],[fact_321_subset__insertI]) ).

fof(f_425_2,plain,
    ! [U_1068,U_1067] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1068),insert_a(U_1067,U_1068))),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

fof(f_425_3,plain,
    ! [U_1067,U_1068] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1068),insert_a(U_1067,U_1068))),
    inference(definitional_conversion,[status(esa)],[f_425_2]) ).

cnf(f_425_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1068),insert_a(U_1067,U_1068))),
    inference(clausify,[status(thm)],[f_425_3]) ).

fof(f_426_1,plain,
    ! [X_3,A_1,B_6] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X_3,A_1)),B_6))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),B_6)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X_3,A_1)),B_6)) ) ),
    inference(fof_nnf,[status(thm)],[fact_322_insert__subset]) ).

fof(f_426_2,plain,
    ! [U_1071,U_1070,U_1069] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_1071,U_1070)),U_1069))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1070),U_1069))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1071),U_1069)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1070),U_1069))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1071),U_1069)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_1071,U_1070)),U_1069)) ) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

fof(f_426_3,plain,
    ( ! [U_1077,U_1075,U_1073] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_1077,U_1075)),U_1073))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1075),U_1073))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1077),U_1073)) )
    & ! [U_1076,U_1074,U_1072] :
        ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1074),U_1072))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1076),U_1072)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_1076,U_1074)),U_1072)) ) ),
    inference(miniscope,[status(thm)],[f_426_2]) ).

fof(f_426_4,plain,
    ( ! [U_1074,U_1072,U_1076] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1074),U_1072))
        | ~ sP99(U_1074,U_1072,U_1076) )
    & ! [U_1074,U_1072,U_1076] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1076),U_1072))
        | ~ sP99(U_1074,U_1072,U_1076) )
    & ! [U_1077,U_1075,U_1073] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_1077,U_1075)),U_1073))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1075),U_1073))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1077),U_1073)) )
    & ! [U_1074,U_1072,U_1076] :
        ( sP99(U_1074,U_1072,U_1076)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_1076,U_1074)),U_1072)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99])],[f_426_3]) ).

cnf(f_426_5,plain,
    ( sP99(U_1074,U_1072,U_1076)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_1076,U_1074)),U_1072)) ),
    inference(clausify,[status(thm)],[f_426_4]) ).

cnf(f_426_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_1077,U_1075)),U_1073))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1075),U_1073))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1077),U_1073)) ),
    inference(clausify,[status(thm)],[f_426_4]) ).

cnf(f_426_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1076),U_1072))
    | ~ sP99(U_1074,U_1072,U_1076) ),
    inference(clausify,[status(thm)],[f_426_4]) ).

cnf(f_426_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1074),U_1072))
    | ~ sP99(U_1074,U_1072,U_1076) ),
    inference(clausify,[status(thm)],[f_426_4]) ).

fof(f_427_1,plain,
    ! [X_3,A_1,B_6] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_3,A_1)),B_6))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),B_6)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_3,A_1)),B_6)) ) ),
    inference(fof_nnf,[status(thm)],[fact_323_insert__subset]) ).

fof(f_427_2,plain,
    ! [U_1080,U_1079,U_1078] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_1080,U_1079)),U_1078))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1079),U_1078))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1080),U_1078)) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1079),U_1078))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1080),U_1078)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_1080,U_1079)),U_1078)) ) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

fof(f_427_3,plain,
    ( ! [U_1086,U_1084,U_1082] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_1086,U_1084)),U_1082))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1084),U_1082))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1086),U_1082)) )
    & ! [U_1085,U_1083,U_1081] :
        ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1083),U_1081))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1085),U_1081)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_1085,U_1083)),U_1081)) ) ),
    inference(miniscope,[status(thm)],[f_427_2]) ).

fof(f_427_4,plain,
    ( ! [U_1081,U_1085,U_1083] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1083),U_1081))
        | ~ sP100(U_1081,U_1085,U_1083) )
    & ! [U_1081,U_1085,U_1083] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1085),U_1081))
        | ~ sP100(U_1081,U_1085,U_1083) )
    & ! [U_1086,U_1084,U_1082] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_1086,U_1084)),U_1082))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1084),U_1082))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1086),U_1082)) )
    & ! [U_1081,U_1085,U_1083] :
        ( sP100(U_1081,U_1085,U_1083)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_1085,U_1083)),U_1081)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100])],[f_427_3]) ).

cnf(f_427_5,plain,
    ( sP100(U_1081,U_1085,U_1083)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_1085,U_1083)),U_1081)) ),
    inference(clausify,[status(thm)],[f_427_4]) ).

cnf(f_427_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_1086,U_1084)),U_1082))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1084),U_1082))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1086),U_1082)) ),
    inference(clausify,[status(thm)],[f_427_4]) ).

cnf(f_427_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1085),U_1081))
    | ~ sP100(U_1081,U_1085,U_1083) ),
    inference(clausify,[status(thm)],[f_427_4]) ).

cnf(f_427_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1083),U_1081))
    | ~ sP100(U_1081,U_1085,U_1083) ),
    inference(clausify,[status(thm)],[f_427_4]) ).

fof(f_428_1,plain,
    ! [X_3,A_1,B_6] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_3,A_1)),B_6))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),B_6)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_3,A_1)),B_6)) ) ),
    inference(fof_nnf,[status(thm)],[fact_324_insert__subset]) ).

fof(f_428_2,plain,
    ! [U_1089,U_1088,U_1087] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_1089,U_1088)),U_1087))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1088),U_1087))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1089),U_1087)) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1088),U_1087))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1089),U_1087)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_1089,U_1088)),U_1087)) ) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

fof(f_428_3,plain,
    ( ! [U_1095,U_1093,U_1091] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_1095,U_1093)),U_1091))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1093),U_1091))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1095),U_1091)) )
    & ! [U_1094,U_1092,U_1090] :
        ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1092),U_1090))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1094),U_1090)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_1094,U_1092)),U_1090)) ) ),
    inference(miniscope,[status(thm)],[f_428_2]) ).

fof(f_428_4,plain,
    ( ! [U_1090,U_1092,U_1094] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1092),U_1090))
        | ~ sP101(U_1090,U_1092,U_1094) )
    & ! [U_1090,U_1092,U_1094] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1094),U_1090))
        | ~ sP101(U_1090,U_1092,U_1094) )
    & ! [U_1095,U_1091,U_1093] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_1095,U_1093)),U_1091))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1093),U_1091))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1095),U_1091)) )
    & ! [U_1090,U_1092,U_1094] :
        ( sP101(U_1090,U_1092,U_1094)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_1094,U_1092)),U_1090)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_428_3]) ).

cnf(f_428_5,plain,
    ( sP101(U_1090,U_1092,U_1094)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_1094,U_1092)),U_1090)) ),
    inference(clausify,[status(thm)],[f_428_4]) ).

cnf(f_428_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_1095,U_1093)),U_1091))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1093),U_1091))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1095),U_1091)) ),
    inference(clausify,[status(thm)],[f_428_4]) ).

cnf(f_428_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1094),U_1090))
    | ~ sP101(U_1090,U_1092,U_1094) ),
    inference(clausify,[status(thm)],[f_428_4]) ).

cnf(f_428_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1092),U_1090))
    | ~ sP101(U_1090,U_1092,U_1094) ),
    inference(clausify,[status(thm)],[f_428_4]) ).

fof(f_429_1,plain,
    ! [B_6,X_3,A_1] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(X_3,B_6)))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(X_3,B_6))) ) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_325_subset__insert]) ).

fof(f_429_2,plain,
    ! [U_1098,U_1097,U_1096] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),insert_nat(U_1097,U_1098)))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),U_1098)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),U_1098))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),insert_nat(U_1097,U_1098))) ) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1097),U_1096)) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

fof(f_429_3,plain,
    ( ! [U_1097,U_1096,U_1098] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),insert_nat(U_1097,U_1098)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),U_1098))
        | ~ sP102(U_1097,U_1096,U_1098) )
    & ! [U_1097,U_1096,U_1098] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),U_1098))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),insert_nat(U_1097,U_1098)))
        | ~ sP102(U_1097,U_1096,U_1098) )
    & ! [U_1097,U_1096,U_1098] :
        ( sP102(U_1097,U_1096,U_1098)
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1097),U_1096)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_429_2]) ).

cnf(f_429_4,plain,
    ( sP102(U_1097,U_1096,U_1098)
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1097),U_1096)) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

cnf(f_429_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),U_1098))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),insert_nat(U_1097,U_1098)))
    | ~ sP102(U_1097,U_1096,U_1098) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

cnf(f_429_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),insert_nat(U_1097,U_1098)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),U_1098))
    | ~ sP102(U_1097,U_1096,U_1098) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

fof(f_430_1,plain,
    ! [B_6,X_3,A_1] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(X_3,B_6)))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(X_3,B_6))) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_326_subset__insert]) ).

fof(f_430_2,plain,
    ! [U_1101,U_1100,U_1099] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1099),insert_pname(U_1100,U_1101)))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1099),U_1101)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1099),U_1101))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1099),insert_pname(U_1100,U_1101))) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1100),U_1099)) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

fof(f_430_3,plain,
    ( ! [U_1101,U_1099,U_1100] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1099),insert_pname(U_1100,U_1101)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1099),U_1101))
        | ~ sP103(U_1101,U_1099,U_1100) )
    & ! [U_1101,U_1099,U_1100] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1099),U_1101))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1099),insert_pname(U_1100,U_1101)))
        | ~ sP103(U_1101,U_1099,U_1100) )
    & ! [U_1101,U_1099,U_1100] :
        ( sP103(U_1101,U_1099,U_1100)
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1100),U_1099)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103])],[f_430_2]) ).

cnf(f_430_4,plain,
    ( sP103(U_1101,U_1099,U_1100)
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1100),U_1099)) ),
    inference(clausify,[status(thm)],[f_430_3]) ).

cnf(f_430_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1099),U_1101))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1099),insert_pname(U_1100,U_1101)))
    | ~ sP103(U_1101,U_1099,U_1100) ),
    inference(clausify,[status(thm)],[f_430_3]) ).

cnf(f_430_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1099),insert_pname(U_1100,U_1101)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1099),U_1101))
    | ~ sP103(U_1101,U_1099,U_1100) ),
    inference(clausify,[status(thm)],[f_430_3]) ).

fof(f_431_1,plain,
    ! [B_6,X_3,A_1] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(X_3,B_6)))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(X_3,B_6))) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_327_subset__insert]) ).

fof(f_431_2,plain,
    ! [U_1104,U_1103,U_1102] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1102),insert_a(U_1103,U_1104)))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1102),U_1104)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1102),U_1104))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1102),insert_a(U_1103,U_1104))) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1103),U_1102)) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

fof(f_431_3,plain,
    ( ! [U_1104,U_1102,U_1103] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1102),insert_a(U_1103,U_1104)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1102),U_1104))
        | ~ sP104(U_1104,U_1102,U_1103) )
    & ! [U_1104,U_1102,U_1103] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1102),U_1104))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1102),insert_a(U_1103,U_1104)))
        | ~ sP104(U_1104,U_1102,U_1103) )
    & ! [U_1104,U_1102,U_1103] :
        ( sP104(U_1104,U_1102,U_1103)
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1103),U_1102)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104])],[f_431_2]) ).

cnf(f_431_4,plain,
    ( sP104(U_1104,U_1102,U_1103)
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1103),U_1102)) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

cnf(f_431_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1102),U_1104))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1102),insert_a(U_1103,U_1104)))
    | ~ sP104(U_1104,U_1102,U_1103) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

cnf(f_431_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1102),insert_a(U_1103,U_1104)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1102),U_1104))
    | ~ sP104(U_1104,U_1102,U_1103) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

fof(f_432_1,plain,
    ! [B_1,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(B_1,B_6)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_328_subset__insertI2]) ).

fof(f_432_2,plain,
    ! [U_1107,U_1106,U_1105] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1106),insert_pname(U_1107,U_1105)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1106),U_1105)) ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

fof(f_432_3,plain,
    ! [U_1107,U_1106,U_1105] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1106),insert_pname(U_1107,U_1105)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1106),U_1105)) ),
    inference(definitional_conversion,[status(esa)],[f_432_2]) ).

cnf(f_432_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1106),insert_pname(U_1107,U_1105)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1106),U_1105)) ),
    inference(clausify,[status(thm)],[f_432_3]) ).

fof(f_433_1,plain,
    ! [B_1,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(B_1,B_6)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_329_subset__insertI2]) ).

fof(f_433_2,plain,
    ! [U_1110,U_1109,U_1108] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1109),insert_nat(U_1110,U_1108)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1109),U_1108)) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

fof(f_433_3,plain,
    ! [U_1108,U_1109,U_1110] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1109),insert_nat(U_1110,U_1108)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1109),U_1108)) ),
    inference(definitional_conversion,[status(esa)],[f_433_2]) ).

cnf(f_433_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1109),insert_nat(U_1110,U_1108)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1109),U_1108)) ),
    inference(clausify,[status(thm)],[f_433_3]) ).

fof(f_434_1,plain,
    ! [B_1,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(B_1,B_6)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_330_subset__insertI2]) ).

fof(f_434_2,plain,
    ! [U_1113,U_1112,U_1111] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1112),insert_a(U_1113,U_1111)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1112),U_1111)) ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

fof(f_434_3,plain,
    ! [U_1111,U_1112,U_1113] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1112),insert_a(U_1113,U_1111)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1112),U_1111)) ),
    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_1112),insert_a(U_1113,U_1111)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1112),U_1111)) ),
    inference(clausify,[status(thm)],[f_434_3]) ).

fof(f_435_1,plain,
    ! [A_3,C_6,D_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(A_3,C_6)),insert_pname(A_3,D_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_6),D_1)) ),
    inference(fof_nnf,[status(thm)],[fact_331_insert__mono]) ).

fof(f_435_2,plain,
    ! [U_1116,U_1115,U_1114] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_1116,U_1115)),insert_pname(U_1116,U_1114)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1115),U_1114)) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

fof(f_435_3,plain,
    ! [U_1114,U_1115,U_1116] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_1116,U_1115)),insert_pname(U_1116,U_1114)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1115),U_1114)) ),
    inference(definitional_conversion,[status(esa)],[f_435_2]) ).

cnf(f_435_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_1116,U_1115)),insert_pname(U_1116,U_1114)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1115),U_1114)) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

fof(f_436_1,plain,
    ! [A_3,C_6,D_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(A_3,C_6)),insert_nat(A_3,D_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),D_1)) ),
    inference(fof_nnf,[status(thm)],[fact_332_insert__mono]) ).

fof(f_436_2,plain,
    ! [U_1119,U_1118,U_1117] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_1119,U_1118)),insert_nat(U_1119,U_1117)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1118),U_1117)) ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

fof(f_436_3,plain,
    ! [U_1117,U_1118,U_1119] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_1119,U_1118)),insert_nat(U_1119,U_1117)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1118),U_1117)) ),
    inference(definitional_conversion,[status(esa)],[f_436_2]) ).

cnf(f_436_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_1119,U_1118)),insert_nat(U_1119,U_1117)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1118),U_1117)) ),
    inference(clausify,[status(thm)],[f_436_3]) ).

fof(f_437_1,plain,
    ! [A_3,C_6,D_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_3,C_6)),insert_a(A_3,D_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),D_1)) ),
    inference(fof_nnf,[status(thm)],[fact_333_insert__mono]) ).

fof(f_437_2,plain,
    ! [U_1122,U_1121,U_1120] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_1122,U_1121)),insert_a(U_1122,U_1120)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1121),U_1120)) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

fof(f_437_3,plain,
    ! [U_1120,U_1121,U_1122] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_1122,U_1121)),insert_a(U_1122,U_1120)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1121),U_1120)) ),
    inference(definitional_conversion,[status(esa)],[f_437_2]) ).

cnf(f_437_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_1122,U_1121)),insert_a(U_1122,U_1120)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1121),U_1120)) ),
    inference(clausify,[status(thm)],[f_437_3]) ).

fof(f_438_1,plain,
    ! [F,A_3,B_6] : image_a_pname(F,insert_a(A_3,B_6)) = insert_pname(hAPP_a_pname(F,A_3),image_a_pname(F,B_6)),
    inference(fof_nnf,[status(thm)],[fact_334_image__insert]) ).

fof(f_438_2,plain,
    ! [U_1125,U_1124,U_1123] : image_a_pname(U_1125,insert_a(U_1124,U_1123)) = insert_pname(hAPP_a_pname(U_1125,U_1124),image_a_pname(U_1125,U_1123)),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

fof(f_438_3,plain,
    ! [U_1123,U_1124,U_1125] : image_a_pname(U_1125,insert_a(U_1124,U_1123)) = insert_pname(hAPP_a_pname(U_1125,U_1124),image_a_pname(U_1125,U_1123)),
    inference(definitional_conversion,[status(esa)],[f_438_2]) ).

cnf(f_438_4,plain,
    image_a_pname(U_1125,insert_a(U_1124,U_1123)) = insert_pname(hAPP_a_pname(U_1125,U_1124),image_a_pname(U_1125,U_1123)),
    inference(clausify,[status(thm)],[f_438_3]) ).

fof(f_439_1,plain,
    ! [F,A_3,B_6] : image_a_nat(F,insert_a(A_3,B_6)) = insert_nat(hAPP_a_nat(F,A_3),image_a_nat(F,B_6)),
    inference(fof_nnf,[status(thm)],[fact_335_image__insert]) ).

fof(f_439_2,plain,
    ! [U_1128,U_1127,U_1126] : image_a_nat(U_1128,insert_a(U_1127,U_1126)) = insert_nat(hAPP_a_nat(U_1128,U_1127),image_a_nat(U_1128,U_1126)),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

fof(f_439_3,plain,
    ! [U_1126,U_1127,U_1128] : image_a_nat(U_1128,insert_a(U_1127,U_1126)) = insert_nat(hAPP_a_nat(U_1128,U_1127),image_a_nat(U_1128,U_1126)),
    inference(definitional_conversion,[status(esa)],[f_439_2]) ).

cnf(f_439_4,plain,
    image_a_nat(U_1128,insert_a(U_1127,U_1126)) = insert_nat(hAPP_a_nat(U_1128,U_1127),image_a_nat(U_1128,U_1126)),
    inference(clausify,[status(thm)],[f_439_3]) ).

fof(f_440_1,plain,
    ! [F,A_3,B_6] : image_nat_a(F,insert_nat(A_3,B_6)) = insert_a(hAPP_nat_a(F,A_3),image_nat_a(F,B_6)),
    inference(fof_nnf,[status(thm)],[fact_336_image__insert]) ).

fof(f_440_2,plain,
    ! [U_1131,U_1130,U_1129] : image_nat_a(U_1131,insert_nat(U_1130,U_1129)) = insert_a(hAPP_nat_a(U_1131,U_1130),image_nat_a(U_1131,U_1129)),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

fof(f_440_3,plain,
    ! [U_1129,U_1130,U_1131] : image_nat_a(U_1131,insert_nat(U_1130,U_1129)) = insert_a(hAPP_nat_a(U_1131,U_1130),image_nat_a(U_1131,U_1129)),
    inference(definitional_conversion,[status(esa)],[f_440_2]) ).

cnf(f_440_4,plain,
    image_nat_a(U_1131,insert_nat(U_1130,U_1129)) = insert_a(hAPP_nat_a(U_1131,U_1130),image_nat_a(U_1131,U_1129)),
    inference(clausify,[status(thm)],[f_440_3]) ).

fof(f_441_1,plain,
    ! [F,A_3,B_6] : image_pname_a(F,insert_pname(A_3,B_6)) = insert_a(hAPP_pname_a(F,A_3),image_pname_a(F,B_6)),
    inference(fof_nnf,[status(thm)],[fact_337_image__insert]) ).

fof(f_441_2,plain,
    ! [U_1134,U_1133,U_1132] : image_pname_a(U_1134,insert_pname(U_1133,U_1132)) = insert_a(hAPP_pname_a(U_1134,U_1133),image_pname_a(U_1134,U_1132)),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

fof(f_441_3,plain,
    ! [U_1132,U_1133,U_1134] : image_pname_a(U_1134,insert_pname(U_1133,U_1132)) = insert_a(hAPP_pname_a(U_1134,U_1133),image_pname_a(U_1134,U_1132)),
    inference(definitional_conversion,[status(esa)],[f_441_2]) ).

cnf(f_441_4,plain,
    image_pname_a(U_1134,insert_pname(U_1133,U_1132)) = insert_a(hAPP_pname_a(U_1134,U_1133),image_pname_a(U_1134,U_1132)),
    inference(clausify,[status(thm)],[f_441_3]) ).

fof(f_442_1,plain,
    ! [F,X_3,A_1] :
      ( insert_pname(hAPP_pname_pname(F,X_3),image_pname_pname(F,A_1)) = image_pname_pname(F,A_1)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_338_insert__image]) ).

fof(f_442_2,plain,
    ! [U_1137,U_1136,U_1135] :
      ( insert_pname(hAPP_pname_pname(U_1137,U_1136),image_pname_pname(U_1137,U_1135)) = image_pname_pname(U_1137,U_1135)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1136),U_1135)) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

fof(f_442_3,plain,
    ! [U_1135,U_1136,U_1137] :
      ( insert_pname(hAPP_pname_pname(U_1137,U_1136),image_pname_pname(U_1137,U_1135)) = image_pname_pname(U_1137,U_1135)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1136),U_1135)) ),
    inference(definitional_conversion,[status(esa)],[f_442_2]) ).

cnf(f_442_4,plain,
    ( insert_pname(hAPP_pname_pname(U_1137,U_1136),image_pname_pname(U_1137,U_1135)) = image_pname_pname(U_1137,U_1135)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1136),U_1135)) ),
    inference(clausify,[status(thm)],[f_442_3]) ).

fof(f_443_1,plain,
    ! [F,X_3,A_1] :
      ( insert_nat(hAPP_pname_nat(F,X_3),image_pname_nat(F,A_1)) = image_pname_nat(F,A_1)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_339_insert__image]) ).

fof(f_443_2,plain,
    ! [U_1140,U_1139,U_1138] :
      ( insert_nat(hAPP_pname_nat(U_1140,U_1139),image_pname_nat(U_1140,U_1138)) = image_pname_nat(U_1140,U_1138)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1139),U_1138)) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

fof(f_443_3,plain,
    ! [U_1138,U_1139,U_1140] :
      ( insert_nat(hAPP_pname_nat(U_1140,U_1139),image_pname_nat(U_1140,U_1138)) = image_pname_nat(U_1140,U_1138)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1139),U_1138)) ),
    inference(definitional_conversion,[status(esa)],[f_443_2]) ).

cnf(f_443_4,plain,
    ( insert_nat(hAPP_pname_nat(U_1140,U_1139),image_pname_nat(U_1140,U_1138)) = image_pname_nat(U_1140,U_1138)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1139),U_1138)) ),
    inference(clausify,[status(thm)],[f_443_3]) ).

fof(f_444_1,plain,
    ! [F,X_3,A_1] :
      ( insert_pname(hAPP_a_pname(F,X_3),image_a_pname(F,A_1)) = image_a_pname(F,A_1)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_340_insert__image]) ).

fof(f_444_2,plain,
    ! [U_1143,U_1142,U_1141] :
      ( insert_pname(hAPP_a_pname(U_1143,U_1142),image_a_pname(U_1143,U_1141)) = image_a_pname(U_1143,U_1141)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1142),U_1141)) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

fof(f_444_3,plain,
    ! [U_1141,U_1142,U_1143] :
      ( insert_pname(hAPP_a_pname(U_1143,U_1142),image_a_pname(U_1143,U_1141)) = image_a_pname(U_1143,U_1141)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1142),U_1141)) ),
    inference(definitional_conversion,[status(esa)],[f_444_2]) ).

cnf(f_444_4,plain,
    ( insert_pname(hAPP_a_pname(U_1143,U_1142),image_a_pname(U_1143,U_1141)) = image_a_pname(U_1143,U_1141)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1142),U_1141)) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

fof(f_445_1,plain,
    ! [F,X_3,A_1] :
      ( insert_nat(hAPP_a_nat(F,X_3),image_a_nat(F,A_1)) = image_a_nat(F,A_1)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_341_insert__image]) ).

fof(f_445_2,plain,
    ! [U_1146,U_1145,U_1144] :
      ( insert_nat(hAPP_a_nat(U_1146,U_1145),image_a_nat(U_1146,U_1144)) = image_a_nat(U_1146,U_1144)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1145),U_1144)) ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

fof(f_445_3,plain,
    ! [U_1144,U_1145,U_1146] :
      ( insert_nat(hAPP_a_nat(U_1146,U_1145),image_a_nat(U_1146,U_1144)) = image_a_nat(U_1146,U_1144)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1145),U_1144)) ),
    inference(definitional_conversion,[status(esa)],[f_445_2]) ).

cnf(f_445_4,plain,
    ( insert_nat(hAPP_a_nat(U_1146,U_1145),image_a_nat(U_1146,U_1144)) = image_a_nat(U_1146,U_1144)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1145),U_1144)) ),
    inference(clausify,[status(thm)],[f_445_3]) ).

fof(f_446_1,plain,
    ! [F,X_3,A_1] :
      ( insert_a(hAPP_nat_a(F,X_3),image_nat_a(F,A_1)) = image_nat_a(F,A_1)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_342_insert__image]) ).

fof(f_446_2,plain,
    ! [U_1149,U_1148,U_1147] :
      ( insert_a(hAPP_nat_a(U_1149,U_1148),image_nat_a(U_1149,U_1147)) = image_nat_a(U_1149,U_1147)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1148),U_1147)) ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

fof(f_446_3,plain,
    ! [U_1147,U_1148,U_1149] :
      ( insert_a(hAPP_nat_a(U_1149,U_1148),image_nat_a(U_1149,U_1147)) = image_nat_a(U_1149,U_1147)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1148),U_1147)) ),
    inference(definitional_conversion,[status(esa)],[f_446_2]) ).

cnf(f_446_4,plain,
    ( insert_a(hAPP_nat_a(U_1149,U_1148),image_nat_a(U_1149,U_1147)) = image_nat_a(U_1149,U_1147)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1148),U_1147)) ),
    inference(clausify,[status(thm)],[f_446_3]) ).

fof(f_447_1,plain,
    ! [F,X_3,A_1] :
      ( insert_a(hAPP_pname_a(F,X_3),image_pname_a(F,A_1)) = image_pname_a(F,A_1)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_343_insert__image]) ).

fof(f_447_2,plain,
    ! [U_1152,U_1151,U_1150] :
      ( insert_a(hAPP_pname_a(U_1152,U_1151),image_pname_a(U_1152,U_1150)) = image_pname_a(U_1152,U_1150)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1151),U_1150)) ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

fof(f_447_3,plain,
    ! [U_1150,U_1151,U_1152] :
      ( insert_a(hAPP_pname_a(U_1152,U_1151),image_pname_a(U_1152,U_1150)) = image_pname_a(U_1152,U_1150)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1151),U_1150)) ),
    inference(definitional_conversion,[status(esa)],[f_447_2]) ).

cnf(f_447_4,plain,
    ( insert_a(hAPP_pname_a(U_1152,U_1151),image_pname_a(U_1152,U_1150)) = image_pname_a(U_1152,U_1150)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1151),U_1150)) ),
    inference(clausify,[status(thm)],[f_447_3]) ).

fof(f_448_1,plain,
    ! [B_6,F,A_1] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1)))
          | ! [AA] :
              ( B_6 != image_nat_a(F,AA)
              | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,AA),A_1)) ) )
        & ( ? [AA] :
              ( B_6 = image_nat_a(F,AA)
              & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,AA),A_1)) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_nat_a(F,A_1))) ) )
      | ~ is_fun_a_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_344_subset__image__iff]) ).

fof(f_448_2,plain,
    ! [U_1157,U_1156,U_1155] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1157),image_nat_a(U_1156,U_1155)))
          | ! [U_1154] :
              ( U_1157 != image_nat_a(U_1156,U_1154)
              | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1154),U_1155)) ) )
        & ( ? [U_1153] :
              ( U_1157 = image_nat_a(U_1156,U_1153)
              & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1153),U_1155)) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1157),image_nat_a(U_1156,U_1155))) ) )
      | ~ is_fun_a_bool(U_1157) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

fof(f_448_3,plain,
    ! [U_1157] :
      ( ( ! [U_1161,U_1159] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1157),image_nat_a(U_1161,U_1159)))
            | ! [U_1154] :
                ( U_1157 != image_nat_a(U_1161,U_1154)
                | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1154),U_1159)) ) )
        & ! [U_1160,U_1158] :
            ( ? [U_1153] :
                ( U_1157 = image_nat_a(U_1160,U_1153)
                & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1153),U_1158)) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1157),image_nat_a(U_1160,U_1158))) ) )
      | ~ is_fun_a_bool(U_1157) ),
    inference(miniscope,[status(thm)],[f_448_2]) ).

fof(f_448_4,plain,
    ! [U_1157] :
      ( ( ! [U_1161,U_1159] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1157),image_nat_a(U_1161,U_1159)))
            | ! [U_1154] :
                ( U_1157 != image_nat_a(U_1161,U_1154)
                | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1154),U_1159)) ) )
        & ! [U_1160,U_1158] :
            ( ( U_1157 = image_nat_a(U_1160,sK60(U_1157,U_1160,U_1158))
              & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK60(U_1157,U_1160,U_1158)),U_1158)) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1157),image_nat_a(U_1160,U_1158))) ) )
      | ~ is_fun_a_bool(U_1157) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_1153,sK60(U_1157,U_1160,U_1158))],[f_448_3]) ).

fof(f_448_5,plain,
    ( ! [U_1157,U_1158,U_1160] :
        ( U_1157 = image_nat_a(U_1160,sK60(U_1157,U_1160,U_1158))
        | ~ sP105(U_1157,U_1158,U_1160) )
    & ! [U_1157,U_1158,U_1160] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK60(U_1157,U_1160,U_1158)),U_1158))
        | ~ sP105(U_1157,U_1158,U_1160) )
    & ! [U_1154,U_1157,U_1158,U_1160,U_1159,U_1161] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1157),image_nat_a(U_1161,U_1159)))
        | U_1157 != image_nat_a(U_1161,U_1154)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1154),U_1159))
        | ~ sP106(U_1154,U_1157,U_1158,U_1160,U_1159,U_1161) )
    & ! [U_1154,U_1157,U_1158,U_1160,U_1159,U_1161] :
        ( sP105(U_1157,U_1158,U_1160)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1157),image_nat_a(U_1160,U_1158)))
        | ~ sP106(U_1154,U_1157,U_1158,U_1160,U_1159,U_1161) )
    & ! [U_1154,U_1157,U_1158,U_1160,U_1159,U_1161] :
        ( sP106(U_1154,U_1157,U_1158,U_1160,U_1159,U_1161)
        | ~ is_fun_a_bool(U_1157) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105,sP106])],[f_448_4]) ).

cnf(f_448_6,plain,
    ( sP106(U_1154,U_1157,U_1158,U_1160,U_1159,U_1161)
    | ~ is_fun_a_bool(U_1157) ),
    inference(clausify,[status(thm)],[f_448_5]) ).

cnf(f_448_7,plain,
    ( sP105(U_1157,U_1158,U_1160)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1157),image_nat_a(U_1160,U_1158)))
    | ~ sP106(U_1154,U_1157,U_1158,U_1160,U_1159,U_1161) ),
    inference(clausify,[status(thm)],[f_448_5]) ).

cnf(f_448_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1157),image_nat_a(U_1161,U_1159)))
    | U_1157 != image_nat_a(U_1161,U_1154)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1154),U_1159))
    | ~ sP106(U_1154,U_1157,U_1158,U_1160,U_1159,U_1161) ),
    inference(clausify,[status(thm)],[f_448_5]) ).

cnf(f_448_9,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK60(U_1157,U_1160,U_1158)),U_1158))
    | ~ sP105(U_1157,U_1158,U_1160) ),
    inference(clausify,[status(thm)],[f_448_5]) ).

cnf(f_448_10,plain,
    ( U_1157 = image_nat_a(U_1160,sK60(U_1157,U_1160,U_1158))
    | ~ sP105(U_1157,U_1158,U_1160) ),
    inference(clausify,[status(thm)],[f_448_5]) ).

fof(f_449_1,plain,
    ! [B_6,F,A_1] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1)))
          | ! [AA] :
              ( B_6 != image_a_pname(F,AA)
              | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,AA),A_1))
              | ~ is_fun_a_bool(AA) ) )
        & ( ? [AA] :
              ( B_6 = image_a_pname(F,AA)
              & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,AA),A_1))
              & is_fun_a_bool(AA) )
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_6),image_a_pname(F,A_1))) ) )
      | ~ is_fun_pname_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_345_subset__image__iff]) ).

fof(f_449_2,plain,
    ! [U_1166,U_1165,U_1164] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1166),image_a_pname(U_1165,U_1164)))
          | ! [U_1163] :
              ( U_1166 != image_a_pname(U_1165,U_1163)
              | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1163),U_1164))
              | ~ is_fun_a_bool(U_1163) ) )
        & ( ? [U_1162] :
              ( U_1166 = image_a_pname(U_1165,U_1162)
              & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1162),U_1164))
              & is_fun_a_bool(U_1162) )
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1166),image_a_pname(U_1165,U_1164))) ) )
      | ~ is_fun_pname_bool(U_1166) ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

fof(f_449_3,plain,
    ! [U_1166] :
      ( ( ! [U_1170,U_1168] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1166),image_a_pname(U_1170,U_1168)))
            | ! [U_1163] :
                ( U_1166 != image_a_pname(U_1170,U_1163)
                | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1163),U_1168))
                | ~ is_fun_a_bool(U_1163) ) )
        & ! [U_1169,U_1167] :
            ( ? [U_1162] :
                ( U_1166 = image_a_pname(U_1169,U_1162)
                & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1162),U_1167))
                & is_fun_a_bool(U_1162) )
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1166),image_a_pname(U_1169,U_1167))) ) )
      | ~ is_fun_pname_bool(U_1166) ),
    inference(miniscope,[status(thm)],[f_449_2]) ).

fof(f_449_4,plain,
    ! [U_1166] :
      ( ( ! [U_1170,U_1168] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1166),image_a_pname(U_1170,U_1168)))
            | ! [U_1163] :
                ( U_1166 != image_a_pname(U_1170,U_1163)
                | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1163),U_1168))
                | ~ is_fun_a_bool(U_1163) ) )
        & ! [U_1169,U_1167] :
            ( ( U_1166 = image_a_pname(U_1169,sK61(U_1166,U_1169,U_1167))
              & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK61(U_1166,U_1169,U_1167)),U_1167))
              & is_fun_a_bool(sK61(U_1166,U_1169,U_1167)) )
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1166),image_a_pname(U_1169,U_1167))) ) )
      | ~ is_fun_pname_bool(U_1166) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_1162,sK61(U_1166,U_1169,U_1167))],[f_449_3]) ).

fof(f_449_5,plain,
    ( ! [U_1166,U_1167,U_1169] :
        ( U_1166 = image_a_pname(U_1169,sK61(U_1166,U_1169,U_1167))
        | ~ sP107(U_1166,U_1167,U_1169) )
    & ! [U_1166,U_1167,U_1169] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK61(U_1166,U_1169,U_1167)),U_1167))
        | ~ sP107(U_1166,U_1167,U_1169) )
    & ! [U_1166,U_1167,U_1169] :
        ( is_fun_a_bool(sK61(U_1166,U_1169,U_1167))
        | ~ sP107(U_1166,U_1167,U_1169) )
    & ! [U_1163,U_1166,U_1167,U_1169,U_1170,U_1168] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1166),image_a_pname(U_1170,U_1168)))
        | U_1166 != image_a_pname(U_1170,U_1163)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1163),U_1168))
        | ~ is_fun_a_bool(U_1163)
        | ~ sP108(U_1163,U_1166,U_1167,U_1169,U_1170,U_1168) )
    & ! [U_1163,U_1166,U_1167,U_1169,U_1170,U_1168] :
        ( sP107(U_1166,U_1167,U_1169)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1166),image_a_pname(U_1169,U_1167)))
        | ~ sP108(U_1163,U_1166,U_1167,U_1169,U_1170,U_1168) )
    & ! [U_1163,U_1166,U_1167,U_1169,U_1170,U_1168] :
        ( sP108(U_1163,U_1166,U_1167,U_1169,U_1170,U_1168)
        | ~ is_fun_pname_bool(U_1166) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107,sP108])],[f_449_4]) ).

cnf(f_449_6,plain,
    ( sP108(U_1163,U_1166,U_1167,U_1169,U_1170,U_1168)
    | ~ is_fun_pname_bool(U_1166) ),
    inference(clausify,[status(thm)],[f_449_5]) ).

cnf(f_449_7,plain,
    ( sP107(U_1166,U_1167,U_1169)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1166),image_a_pname(U_1169,U_1167)))
    | ~ sP108(U_1163,U_1166,U_1167,U_1169,U_1170,U_1168) ),
    inference(clausify,[status(thm)],[f_449_5]) ).

cnf(f_449_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1166),image_a_pname(U_1170,U_1168)))
    | U_1166 != image_a_pname(U_1170,U_1163)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1163),U_1168))
    | ~ is_fun_a_bool(U_1163)
    | ~ sP108(U_1163,U_1166,U_1167,U_1169,U_1170,U_1168) ),
    inference(clausify,[status(thm)],[f_449_5]) ).

cnf(f_449_9,plain,
    ( is_fun_a_bool(sK61(U_1166,U_1169,U_1167))
    | ~ sP107(U_1166,U_1167,U_1169) ),
    inference(clausify,[status(thm)],[f_449_5]) ).

cnf(f_449_10,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK61(U_1166,U_1169,U_1167)),U_1167))
    | ~ sP107(U_1166,U_1167,U_1169) ),
    inference(clausify,[status(thm)],[f_449_5]) ).

cnf(f_449_11,plain,
    ( U_1166 = image_a_pname(U_1169,sK61(U_1166,U_1169,U_1167))
    | ~ sP107(U_1166,U_1167,U_1169) ),
    inference(clausify,[status(thm)],[f_449_5]) ).

fof(f_450_1,plain,
    ! [B_6,F,A_1] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1)))
        | ! [AA] :
            ( B_6 != image_a_nat(F,AA)
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,AA),A_1))
            | ~ is_fun_a_bool(AA) ) )
      & ( ? [AA] :
            ( B_6 = image_a_nat(F,AA)
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,AA),A_1))
            & is_fun_a_bool(AA) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_6),image_a_nat(F,A_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_346_subset__image__iff]) ).

fof(f_450_2,plain,
    ! [U_1175,U_1174,U_1173] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1175),image_a_nat(U_1174,U_1173)))
        | ! [U_1172] :
            ( U_1175 != image_a_nat(U_1174,U_1172)
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1172),U_1173))
            | ~ is_fun_a_bool(U_1172) ) )
      & ( ? [U_1171] :
            ( U_1175 = image_a_nat(U_1174,U_1171)
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1171),U_1173))
            & is_fun_a_bool(U_1171) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1175),image_a_nat(U_1174,U_1173))) ) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

fof(f_450_3,plain,
    ( ! [U_1181,U_1179,U_1177] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1181),image_a_nat(U_1179,U_1177)))
        | ! [U_1172] :
            ( U_1181 != image_a_nat(U_1179,U_1172)
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1172),U_1177))
            | ~ is_fun_a_bool(U_1172) ) )
    & ! [U_1180,U_1178,U_1176] :
        ( ? [U_1171] :
            ( U_1180 = image_a_nat(U_1178,U_1171)
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1171),U_1176))
            & is_fun_a_bool(U_1171) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1180),image_a_nat(U_1178,U_1176))) ) ),
    inference(miniscope,[status(thm)],[f_450_2]) ).

fof(f_450_4,plain,
    ( ! [U_1181,U_1179,U_1177] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1181),image_a_nat(U_1179,U_1177)))
        | ! [U_1172] :
            ( U_1181 != image_a_nat(U_1179,U_1172)
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1172),U_1177))
            | ~ is_fun_a_bool(U_1172) ) )
    & ! [U_1180,U_1178,U_1176] :
        ( ( U_1180 = image_a_nat(U_1178,sK62(U_1180,U_1178,U_1176))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK62(U_1180,U_1178,U_1176)),U_1176))
          & is_fun_a_bool(sK62(U_1180,U_1178,U_1176)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1180),image_a_nat(U_1178,U_1176))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_1171,sK62(U_1180,U_1178,U_1176))],[f_450_3]) ).

fof(f_450_5,plain,
    ( ! [U_1176,U_1178,U_1180] :
        ( U_1180 = image_a_nat(U_1178,sK62(U_1180,U_1178,U_1176))
        | ~ sP109(U_1176,U_1178,U_1180) )
    & ! [U_1176,U_1178,U_1180] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK62(U_1180,U_1178,U_1176)),U_1176))
        | ~ sP109(U_1176,U_1178,U_1180) )
    & ! [U_1176,U_1178,U_1180] :
        ( is_fun_a_bool(sK62(U_1180,U_1178,U_1176))
        | ~ sP109(U_1176,U_1178,U_1180) )
    & ! [U_1172,U_1177,U_1179,U_1181] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1181),image_a_nat(U_1179,U_1177)))
        | U_1181 != image_a_nat(U_1179,U_1172)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1172),U_1177))
        | ~ is_fun_a_bool(U_1172) )
    & ! [U_1176,U_1178,U_1180] :
        ( sP109(U_1176,U_1178,U_1180)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1180),image_a_nat(U_1178,U_1176))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_450_4]) ).

cnf(f_450_6,plain,
    ( sP109(U_1176,U_1178,U_1180)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1180),image_a_nat(U_1178,U_1176))) ),
    inference(clausify,[status(thm)],[f_450_5]) ).

cnf(f_450_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1181),image_a_nat(U_1179,U_1177)))
    | U_1181 != image_a_nat(U_1179,U_1172)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1172),U_1177))
    | ~ is_fun_a_bool(U_1172) ),
    inference(clausify,[status(thm)],[f_450_5]) ).

cnf(f_450_8,plain,
    ( is_fun_a_bool(sK62(U_1180,U_1178,U_1176))
    | ~ sP109(U_1176,U_1178,U_1180) ),
    inference(clausify,[status(thm)],[f_450_5]) ).

cnf(f_450_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK62(U_1180,U_1178,U_1176)),U_1176))
    | ~ sP109(U_1176,U_1178,U_1180) ),
    inference(clausify,[status(thm)],[f_450_5]) ).

cnf(f_450_10,plain,
    ( U_1180 = image_a_nat(U_1178,sK62(U_1180,U_1178,U_1176))
    | ~ sP109(U_1176,U_1178,U_1180) ),
    inference(clausify,[status(thm)],[f_450_5]) ).

fof(f_451_1,plain,
    ! [B_6,F,A_1] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1)))
          | ! [AA] :
              ( B_6 != image_pname_a(F,AA)
              | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A_1))
              | ~ is_fun_pname_bool(AA) ) )
        & ( ? [AA] :
              ( B_6 = image_pname_a(F,AA)
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A_1))
              & is_fun_pname_bool(AA) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_6),image_pname_a(F,A_1))) ) )
      | ~ is_fun_a_bool(B_6) ),
    inference(fof_nnf,[status(thm)],[fact_347_subset__image__iff]) ).

fof(f_451_2,plain,
    ! [U_1186,U_1185,U_1184] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1186),image_pname_a(U_1185,U_1184)))
          | ! [U_1183] :
              ( U_1186 != image_pname_a(U_1185,U_1183)
              | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1183),U_1184))
              | ~ is_fun_pname_bool(U_1183) ) )
        & ( ? [U_1182] :
              ( U_1186 = image_pname_a(U_1185,U_1182)
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1182),U_1184))
              & is_fun_pname_bool(U_1182) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1186),image_pname_a(U_1185,U_1184))) ) )
      | ~ is_fun_a_bool(U_1186) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

fof(f_451_3,plain,
    ! [U_1186] :
      ( ( ! [U_1190,U_1188] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1186),image_pname_a(U_1190,U_1188)))
            | ! [U_1183] :
                ( U_1186 != image_pname_a(U_1190,U_1183)
                | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1183),U_1188))
                | ~ is_fun_pname_bool(U_1183) ) )
        & ! [U_1189,U_1187] :
            ( ? [U_1182] :
                ( U_1186 = image_pname_a(U_1189,U_1182)
                & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1182),U_1187))
                & is_fun_pname_bool(U_1182) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1186),image_pname_a(U_1189,U_1187))) ) )
      | ~ is_fun_a_bool(U_1186) ),
    inference(miniscope,[status(thm)],[f_451_2]) ).

fof(f_451_4,plain,
    ! [U_1186] :
      ( ( ! [U_1190,U_1188] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1186),image_pname_a(U_1190,U_1188)))
            | ! [U_1183] :
                ( U_1186 != image_pname_a(U_1190,U_1183)
                | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1183),U_1188))
                | ~ is_fun_pname_bool(U_1183) ) )
        & ! [U_1189,U_1187] :
            ( ( U_1186 = image_pname_a(U_1189,sK63(U_1186,U_1189,U_1187))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK63(U_1186,U_1189,U_1187)),U_1187))
              & is_fun_pname_bool(sK63(U_1186,U_1189,U_1187)) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1186),image_pname_a(U_1189,U_1187))) ) )
      | ~ is_fun_a_bool(U_1186) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_1182,sK63(U_1186,U_1189,U_1187))],[f_451_3]) ).

fof(f_451_5,plain,
    ( ! [U_1186,U_1189,U_1187] :
        ( U_1186 = image_pname_a(U_1189,sK63(U_1186,U_1189,U_1187))
        | ~ sP110(U_1186,U_1189,U_1187) )
    & ! [U_1186,U_1189,U_1187] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK63(U_1186,U_1189,U_1187)),U_1187))
        | ~ sP110(U_1186,U_1189,U_1187) )
    & ! [U_1186,U_1189,U_1187] :
        ( is_fun_pname_bool(sK63(U_1186,U_1189,U_1187))
        | ~ sP110(U_1186,U_1189,U_1187) )
    & ! [U_1186,U_1183,U_1189,U_1187,U_1188,U_1190] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1186),image_pname_a(U_1190,U_1188)))
        | U_1186 != image_pname_a(U_1190,U_1183)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1183),U_1188))
        | ~ is_fun_pname_bool(U_1183)
        | ~ sP111(U_1186,U_1183,U_1189,U_1187,U_1188,U_1190) )
    & ! [U_1186,U_1183,U_1189,U_1187,U_1188,U_1190] :
        ( sP110(U_1186,U_1189,U_1187)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1186),image_pname_a(U_1189,U_1187)))
        | ~ sP111(U_1186,U_1183,U_1189,U_1187,U_1188,U_1190) )
    & ! [U_1186,U_1183,U_1189,U_1187,U_1188,U_1190] :
        ( sP111(U_1186,U_1183,U_1189,U_1187,U_1188,U_1190)
        | ~ is_fun_a_bool(U_1186) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110,sP111])],[f_451_4]) ).

cnf(f_451_6,plain,
    ( sP111(U_1186,U_1183,U_1189,U_1187,U_1188,U_1190)
    | ~ is_fun_a_bool(U_1186) ),
    inference(clausify,[status(thm)],[f_451_5]) ).

cnf(f_451_7,plain,
    ( sP110(U_1186,U_1189,U_1187)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1186),image_pname_a(U_1189,U_1187)))
    | ~ sP111(U_1186,U_1183,U_1189,U_1187,U_1188,U_1190) ),
    inference(clausify,[status(thm)],[f_451_5]) ).

cnf(f_451_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1186),image_pname_a(U_1190,U_1188)))
    | U_1186 != image_pname_a(U_1190,U_1183)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1183),U_1188))
    | ~ is_fun_pname_bool(U_1183)
    | ~ sP111(U_1186,U_1183,U_1189,U_1187,U_1188,U_1190) ),
    inference(clausify,[status(thm)],[f_451_5]) ).

cnf(f_451_9,plain,
    ( is_fun_pname_bool(sK63(U_1186,U_1189,U_1187))
    | ~ sP110(U_1186,U_1189,U_1187) ),
    inference(clausify,[status(thm)],[f_451_5]) ).

cnf(f_451_10,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK63(U_1186,U_1189,U_1187)),U_1187))
    | ~ sP110(U_1186,U_1189,U_1187) ),
    inference(clausify,[status(thm)],[f_451_5]) ).

cnf(f_451_11,plain,
    ( U_1186 = image_pname_a(U_1189,sK63(U_1186,U_1189,U_1187))
    | ~ sP110(U_1186,U_1189,U_1187) ),
    inference(clausify,[status(thm)],[f_451_5]) ).

fof(f_452_1,plain,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(F,A_1)),image_a_pname(F,B_6)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_348_image__mono]) ).

fof(f_452_2,plain,
    ! [U_1193,U_1192,U_1191] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(U_1193,U_1192)),image_a_pname(U_1193,U_1191)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1192),U_1191)) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

fof(f_452_3,plain,
    ! [U_1191,U_1193,U_1192] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(U_1193,U_1192)),image_a_pname(U_1193,U_1191)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1192),U_1191)) ),
    inference(definitional_conversion,[status(esa)],[f_452_2]) ).

cnf(f_452_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(U_1193,U_1192)),image_a_pname(U_1193,U_1191)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1192),U_1191)) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

fof(f_453_1,plain,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(F,A_1)),image_a_nat(F,B_6)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_349_image__mono]) ).

fof(f_453_2,plain,
    ! [U_1196,U_1195,U_1194] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(U_1196,U_1195)),image_a_nat(U_1196,U_1194)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1195),U_1194)) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

fof(f_453_3,plain,
    ! [U_1196,U_1194,U_1195] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(U_1196,U_1195)),image_a_nat(U_1196,U_1194)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1195),U_1194)) ),
    inference(definitional_conversion,[status(esa)],[f_453_2]) ).

cnf(f_453_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(U_1196,U_1195)),image_a_nat(U_1196,U_1194)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1195),U_1194)) ),
    inference(clausify,[status(thm)],[f_453_3]) ).

fof(f_454_1,plain,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(F,A_1)),image_nat_a(F,B_6)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_350_image__mono]) ).

fof(f_454_2,plain,
    ! [U_1199,U_1198,U_1197] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(U_1199,U_1198)),image_nat_a(U_1199,U_1197)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1198),U_1197)) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

fof(f_454_3,plain,
    ! [U_1198,U_1197,U_1199] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(U_1199,U_1198)),image_nat_a(U_1199,U_1197)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1198),U_1197)) ),
    inference(definitional_conversion,[status(esa)],[f_454_2]) ).

cnf(f_454_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(U_1199,U_1198)),image_nat_a(U_1199,U_1197)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1198),U_1197)) ),
    inference(clausify,[status(thm)],[f_454_3]) ).

fof(f_455_1,plain,
    ! [F,A_1,B_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A_1)),image_pname_a(F,B_6)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6)) ),
    inference(fof_nnf,[status(thm)],[fact_351_image__mono]) ).

fof(f_455_2,plain,
    ! [U_1202,U_1201,U_1200] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1202,U_1201)),image_pname_a(U_1202,U_1200)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1201),U_1200)) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

fof(f_455_3,plain,
    ! [U_1200,U_1201,U_1202] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1202,U_1201)),image_pname_a(U_1202,U_1200)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1201),U_1200)) ),
    inference(definitional_conversion,[status(esa)],[f_455_2]) ).

cnf(f_455_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1202,U_1201)),image_pname_a(U_1202,U_1200)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1201),U_1200)) ),
    inference(clausify,[status(thm)],[f_455_3]) ).

fof(f_456_1,plain,
    ! [B_1,F,A_1] :
      ( ? [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
          & B_1 = hAPP_nat_pname(F,X_1) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_nat_pname(F,A_1)))
      | ~ is_pname(B_1) ),
    inference(fof_nnf,[status(thm)],[fact_352_imageE]) ).

fof(f_456_2,plain,
    ! [U_1206,U_1205,U_1204] :
      ( ? [U_1203] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1203),U_1204))
          & U_1206 = hAPP_nat_pname(U_1205,U_1203) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1206),image_nat_pname(U_1205,U_1204)))
      | ~ is_pname(U_1206) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

fof(f_456_3,plain,
    ! [U_1206] :
      ( ! [U_1205,U_1204] :
          ( ? [U_1203] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1203),U_1204))
              & U_1206 = hAPP_nat_pname(U_1205,U_1203) )
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1206),image_nat_pname(U_1205,U_1204))) )
      | ~ is_pname(U_1206) ),
    inference(miniscope,[status(thm)],[f_456_2]) ).

fof(f_456_4,plain,
    ! [U_1206] :
      ( ! [U_1205,U_1204] :
          ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK64(U_1206,U_1205,U_1204)),U_1204))
            & U_1206 = hAPP_nat_pname(U_1205,sK64(U_1206,U_1205,U_1204)) )
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1206),image_nat_pname(U_1205,U_1204))) )
      | ~ is_pname(U_1206) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_1203,sK64(U_1206,U_1205,U_1204))],[f_456_3]) ).

fof(f_456_5,plain,
    ( ! [U_1204,U_1205,U_1206] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK64(U_1206,U_1205,U_1204)),U_1204))
        | ~ sP112(U_1204,U_1205,U_1206) )
    & ! [U_1204,U_1205,U_1206] :
        ( U_1206 = hAPP_nat_pname(U_1205,sK64(U_1206,U_1205,U_1204))
        | ~ sP112(U_1204,U_1205,U_1206) )
    & ! [U_1204,U_1205,U_1206] :
        ( sP112(U_1204,U_1205,U_1206)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1206),image_nat_pname(U_1205,U_1204)))
        | ~ is_pname(U_1206) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112])],[f_456_4]) ).

cnf(f_456_6,plain,
    ( sP112(U_1204,U_1205,U_1206)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1206),image_nat_pname(U_1205,U_1204)))
    | ~ is_pname(U_1206) ),
    inference(clausify,[status(thm)],[f_456_5]) ).

cnf(f_456_7,plain,
    ( U_1206 = hAPP_nat_pname(U_1205,sK64(U_1206,U_1205,U_1204))
    | ~ sP112(U_1204,U_1205,U_1206) ),
    inference(clausify,[status(thm)],[f_456_5]) ).

cnf(f_456_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK64(U_1206,U_1205,U_1204)),U_1204))
    | ~ sP112(U_1204,U_1205,U_1206) ),
    inference(clausify,[status(thm)],[f_456_5]) ).

fof(f_457_1,plain,
    ! [B_1,F,A_1] :
      ( ? [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
          & B_1 = hAPP_nat_a(F,X_1) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_nat_a(F,A_1)))
      | ~ is_a(B_1) ),
    inference(fof_nnf,[status(thm)],[fact_353_imageE]) ).

fof(f_457_2,plain,
    ! [U_1210,U_1209,U_1208] :
      ( ? [U_1207] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1207),U_1208))
          & U_1210 = hAPP_nat_a(U_1209,U_1207) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1210),image_nat_a(U_1209,U_1208)))
      | ~ is_a(U_1210) ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

fof(f_457_3,plain,
    ! [U_1210] :
      ( ! [U_1209,U_1208] :
          ( ? [U_1207] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1207),U_1208))
              & U_1210 = hAPP_nat_a(U_1209,U_1207) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1210),image_nat_a(U_1209,U_1208))) )
      | ~ is_a(U_1210) ),
    inference(miniscope,[status(thm)],[f_457_2]) ).

fof(f_457_4,plain,
    ! [U_1210] :
      ( ! [U_1209,U_1208] :
          ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK65(U_1210,U_1209,U_1208)),U_1208))
            & U_1210 = hAPP_nat_a(U_1209,sK65(U_1210,U_1209,U_1208)) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1210),image_nat_a(U_1209,U_1208))) )
      | ~ is_a(U_1210) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_1207,sK65(U_1210,U_1209,U_1208))],[f_457_3]) ).

fof(f_457_5,plain,
    ( ! [U_1208,U_1209,U_1210] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK65(U_1210,U_1209,U_1208)),U_1208))
        | ~ sP113(U_1208,U_1209,U_1210) )
    & ! [U_1208,U_1209,U_1210] :
        ( U_1210 = hAPP_nat_a(U_1209,sK65(U_1210,U_1209,U_1208))
        | ~ sP113(U_1208,U_1209,U_1210) )
    & ! [U_1208,U_1209,U_1210] :
        ( sP113(U_1208,U_1209,U_1210)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1210),image_nat_a(U_1209,U_1208)))
        | ~ is_a(U_1210) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113])],[f_457_4]) ).

cnf(f_457_6,plain,
    ( sP113(U_1208,U_1209,U_1210)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1210),image_nat_a(U_1209,U_1208)))
    | ~ is_a(U_1210) ),
    inference(clausify,[status(thm)],[f_457_5]) ).

cnf(f_457_7,plain,
    ( U_1210 = hAPP_nat_a(U_1209,sK65(U_1210,U_1209,U_1208))
    | ~ sP113(U_1208,U_1209,U_1210) ),
    inference(clausify,[status(thm)],[f_457_5]) ).

cnf(f_457_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK65(U_1210,U_1209,U_1208)),U_1208))
    | ~ sP113(U_1208,U_1209,U_1210) ),
    inference(clausify,[status(thm)],[f_457_5]) ).

fof(f_458_1,plain,
    ! [B_1,F,A_1] :
      ( ? [X_1] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
          & B_1 = hAPP_pname_nat(F,X_1)
          & is_pname(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_pname_nat(F,A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_354_imageE]) ).

fof(f_458_2,plain,
    ! [U_1214,U_1213,U_1212] :
      ( ? [U_1211] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1211),U_1212))
          & U_1214 = hAPP_pname_nat(U_1213,U_1211)
          & is_pname(U_1211) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1214),image_pname_nat(U_1213,U_1212))) ),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

fof(f_458_3,plain,
    ! [U_1214,U_1213,U_1212] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK66(U_1214,U_1213,U_1212)),U_1212))
        & U_1214 = hAPP_pname_nat(U_1213,sK66(U_1214,U_1213,U_1212))
        & is_pname(sK66(U_1214,U_1213,U_1212)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1214),image_pname_nat(U_1213,U_1212))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_1211,sK66(U_1214,U_1213,U_1212))],[f_458_2]) ).

fof(f_458_4,plain,
    ( ! [U_1213,U_1212,U_1214] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK66(U_1214,U_1213,U_1212)),U_1212))
        | ~ sP114(U_1213,U_1212,U_1214) )
    & ! [U_1213,U_1212,U_1214] :
        ( U_1214 = hAPP_pname_nat(U_1213,sK66(U_1214,U_1213,U_1212))
        | ~ sP114(U_1213,U_1212,U_1214) )
    & ! [U_1213,U_1212,U_1214] :
        ( is_pname(sK66(U_1214,U_1213,U_1212))
        | ~ sP114(U_1213,U_1212,U_1214) )
    & ! [U_1213,U_1212,U_1214] :
        ( sP114(U_1213,U_1212,U_1214)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1214),image_pname_nat(U_1213,U_1212))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114])],[f_458_3]) ).

cnf(f_458_5,plain,
    ( sP114(U_1213,U_1212,U_1214)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1214),image_pname_nat(U_1213,U_1212))) ),
    inference(clausify,[status(thm)],[f_458_4]) ).

cnf(f_458_6,plain,
    ( is_pname(sK66(U_1214,U_1213,U_1212))
    | ~ sP114(U_1213,U_1212,U_1214) ),
    inference(clausify,[status(thm)],[f_458_4]) ).

cnf(f_458_7,plain,
    ( U_1214 = hAPP_pname_nat(U_1213,sK66(U_1214,U_1213,U_1212))
    | ~ sP114(U_1213,U_1212,U_1214) ),
    inference(clausify,[status(thm)],[f_458_4]) ).

cnf(f_458_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK66(U_1214,U_1213,U_1212)),U_1212))
    | ~ sP114(U_1213,U_1212,U_1214) ),
    inference(clausify,[status(thm)],[f_458_4]) ).

fof(f_459_1,plain,
    ! [B_1,F,A_1] :
      ( ? [X_1] :
          ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
          & B_1 = hAPP_a_nat(F,X_1)
          & is_a(X_1) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),image_a_nat(F,A_1))) ),
    inference(fof_nnf,[status(thm)],[fact_355_imageE]) ).

fof(f_459_2,plain,
    ! [U_1218,U_1217,U_1216] :
      ( ? [U_1215] :
          ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1215),U_1216))
          & U_1218 = hAPP_a_nat(U_1217,U_1215)
          & is_a(U_1215) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1218),image_a_nat(U_1217,U_1216))) ),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

fof(f_459_3,plain,
    ! [U_1218,U_1217,U_1216] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK67(U_1218,U_1217,U_1216)),U_1216))
        & U_1218 = hAPP_a_nat(U_1217,sK67(U_1218,U_1217,U_1216))
        & is_a(sK67(U_1218,U_1217,U_1216)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1218),image_a_nat(U_1217,U_1216))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_1215,sK67(U_1218,U_1217,U_1216))],[f_459_2]) ).

fof(f_459_4,plain,
    ( ! [U_1218,U_1217,U_1216] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK67(U_1218,U_1217,U_1216)),U_1216))
        | ~ sP115(U_1218,U_1217,U_1216) )
    & ! [U_1218,U_1217,U_1216] :
        ( U_1218 = hAPP_a_nat(U_1217,sK67(U_1218,U_1217,U_1216))
        | ~ sP115(U_1218,U_1217,U_1216) )
    & ! [U_1218,U_1217,U_1216] :
        ( is_a(sK67(U_1218,U_1217,U_1216))
        | ~ sP115(U_1218,U_1217,U_1216) )
    & ! [U_1218,U_1217,U_1216] :
        ( sP115(U_1218,U_1217,U_1216)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1218),image_a_nat(U_1217,U_1216))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115])],[f_459_3]) ).

cnf(f_459_5,plain,
    ( sP115(U_1218,U_1217,U_1216)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1218),image_a_nat(U_1217,U_1216))) ),
    inference(clausify,[status(thm)],[f_459_4]) ).

cnf(f_459_6,plain,
    ( is_a(sK67(U_1218,U_1217,U_1216))
    | ~ sP115(U_1218,U_1217,U_1216) ),
    inference(clausify,[status(thm)],[f_459_4]) ).

cnf(f_459_7,plain,
    ( U_1218 = hAPP_a_nat(U_1217,sK67(U_1218,U_1217,U_1216))
    | ~ sP115(U_1218,U_1217,U_1216) ),
    inference(clausify,[status(thm)],[f_459_4]) ).

cnf(f_459_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK67(U_1218,U_1217,U_1216)),U_1216))
    | ~ sP115(U_1218,U_1217,U_1216) ),
    inference(clausify,[status(thm)],[f_459_4]) ).

fof(f_460_1,plain,
    ! [B_1,F,A_1] :
      ( ? [X_1] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
          & B_1 = hAPP_pname_a(F,X_1)
          & is_pname(X_1) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A_1)))
      | ~ is_a(B_1) ),
    inference(fof_nnf,[status(thm)],[fact_356_imageE]) ).

fof(f_460_2,plain,
    ! [U_1222,U_1221,U_1220] :
      ( ? [U_1219] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1219),U_1220))
          & U_1222 = hAPP_pname_a(U_1221,U_1219)
          & is_pname(U_1219) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1222),image_pname_a(U_1221,U_1220)))
      | ~ is_a(U_1222) ),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

fof(f_460_3,plain,
    ! [U_1222] :
      ( ! [U_1221,U_1220] :
          ( ? [U_1219] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1219),U_1220))
              & U_1222 = hAPP_pname_a(U_1221,U_1219)
              & is_pname(U_1219) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1222),image_pname_a(U_1221,U_1220))) )
      | ~ is_a(U_1222) ),
    inference(miniscope,[status(thm)],[f_460_2]) ).

fof(f_460_4,plain,
    ! [U_1222] :
      ( ! [U_1221,U_1220] :
          ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK68(U_1222,U_1221,U_1220)),U_1220))
            & U_1222 = hAPP_pname_a(U_1221,sK68(U_1222,U_1221,U_1220))
            & is_pname(sK68(U_1222,U_1221,U_1220)) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1222),image_pname_a(U_1221,U_1220))) )
      | ~ is_a(U_1222) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_1219,sK68(U_1222,U_1221,U_1220))],[f_460_3]) ).

fof(f_460_5,plain,
    ( ! [U_1221,U_1220,U_1222] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK68(U_1222,U_1221,U_1220)),U_1220))
        | ~ sP116(U_1221,U_1220,U_1222) )
    & ! [U_1221,U_1220,U_1222] :
        ( U_1222 = hAPP_pname_a(U_1221,sK68(U_1222,U_1221,U_1220))
        | ~ sP116(U_1221,U_1220,U_1222) )
    & ! [U_1221,U_1220,U_1222] :
        ( is_pname(sK68(U_1222,U_1221,U_1220))
        | ~ sP116(U_1221,U_1220,U_1222) )
    & ! [U_1221,U_1220,U_1222] :
        ( sP116(U_1221,U_1220,U_1222)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1222),image_pname_a(U_1221,U_1220)))
        | ~ is_a(U_1222) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116])],[f_460_4]) ).

cnf(f_460_6,plain,
    ( sP116(U_1221,U_1220,U_1222)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1222),image_pname_a(U_1221,U_1220)))
    | ~ is_a(U_1222) ),
    inference(clausify,[status(thm)],[f_460_5]) ).

cnf(f_460_7,plain,
    ( is_pname(sK68(U_1222,U_1221,U_1220))
    | ~ sP116(U_1221,U_1220,U_1222) ),
    inference(clausify,[status(thm)],[f_460_5]) ).

cnf(f_460_8,plain,
    ( U_1222 = hAPP_pname_a(U_1221,sK68(U_1222,U_1221,U_1220))
    | ~ sP116(U_1221,U_1220,U_1222) ),
    inference(clausify,[status(thm)],[f_460_5]) ).

cnf(f_460_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK68(U_1222,U_1221,U_1220)),U_1220))
    | ~ sP116(U_1221,U_1220,U_1222) ),
    inference(clausify,[status(thm)],[f_460_5]) ).

fof(f_461_1,plain,
    ! [B_6,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),B_6))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_6))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_357_subsetI]) ).

fof(f_461_2,plain,
    ! [U_1225,U_1224] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1224),U_1225))
      | ? [U_1223] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1223),U_1225))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1223),U_1224)) ) ),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

fof(f_461_3,plain,
    ! [U_1225,U_1224] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1224),U_1225))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK69(U_1225,U_1224)),U_1225))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK69(U_1225,U_1224)),U_1224)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_1223,sK69(U_1225,U_1224))],[f_461_2]) ).

fof(f_461_4,plain,
    ( ! [U_1224,U_1225] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK69(U_1225,U_1224)),U_1225))
        | ~ sP117(U_1224,U_1225) )
    & ! [U_1224,U_1225] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK69(U_1225,U_1224)),U_1224))
        | ~ sP117(U_1224,U_1225) )
    & ! [U_1224,U_1225] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1224),U_1225))
        | sP117(U_1224,U_1225) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117])],[f_461_3]) ).

cnf(f_461_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1224),U_1225))
    | sP117(U_1224,U_1225) ),
    inference(clausify,[status(thm)],[f_461_4]) ).

cnf(f_461_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK69(U_1225,U_1224)),U_1224))
    | ~ sP117(U_1224,U_1225) ),
    inference(clausify,[status(thm)],[f_461_4]) ).

cnf(f_461_7,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK69(U_1225,U_1224)),U_1225))
    | ~ sP117(U_1224,U_1225) ),
    inference(clausify,[status(thm)],[f_461_4]) ).

fof(f_462_1,plain,
    ! [B_6,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),B_6))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B_6))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
          & is_pname(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_358_subsetI]) ).

fof(f_462_2,plain,
    ! [U_1228,U_1227] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1227),U_1228))
      | ? [U_1226] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1226),U_1228))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1226),U_1227))
          & is_pname(U_1226) ) ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

fof(f_462_3,plain,
    ! [U_1228,U_1227] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1227),U_1228))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK70(U_1228,U_1227)),U_1228))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK70(U_1228,U_1227)),U_1227))
        & is_pname(sK70(U_1228,U_1227)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_1226,sK70(U_1228,U_1227))],[f_462_2]) ).

fof(f_462_4,plain,
    ( ! [U_1227,U_1228] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK70(U_1228,U_1227)),U_1228))
        | ~ sP118(U_1227,U_1228) )
    & ! [U_1227,U_1228] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK70(U_1228,U_1227)),U_1227))
        | ~ sP118(U_1227,U_1228) )
    & ! [U_1227,U_1228] :
        ( is_pname(sK70(U_1228,U_1227))
        | ~ sP118(U_1227,U_1228) )
    & ! [U_1227,U_1228] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1227),U_1228))
        | sP118(U_1227,U_1228) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP118])],[f_462_3]) ).

cnf(f_462_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1227),U_1228))
    | sP118(U_1227,U_1228) ),
    inference(clausify,[status(thm)],[f_462_4]) ).

cnf(f_462_6,plain,
    ( is_pname(sK70(U_1228,U_1227))
    | ~ sP118(U_1227,U_1228) ),
    inference(clausify,[status(thm)],[f_462_4]) ).

cnf(f_462_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK70(U_1228,U_1227)),U_1227))
    | ~ sP118(U_1227,U_1228) ),
    inference(clausify,[status(thm)],[f_462_4]) ).

cnf(f_462_8,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK70(U_1228,U_1227)),U_1228))
    | ~ sP118(U_1227,U_1228) ),
    inference(clausify,[status(thm)],[f_462_4]) ).

fof(f_463_1,plain,
    ! [B_6,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),B_6))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B_6))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
          & is_a(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_359_subsetI]) ).

fof(f_463_2,plain,
    ! [U_1231,U_1230] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1230),U_1231))
      | ? [U_1229] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1229),U_1231))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1229),U_1230))
          & is_a(U_1229) ) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

fof(f_463_3,plain,
    ! [U_1231,U_1230] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1230),U_1231))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK71(U_1231,U_1230)),U_1231))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK71(U_1231,U_1230)),U_1230))
        & is_a(sK71(U_1231,U_1230)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_1229,sK71(U_1231,U_1230))],[f_463_2]) ).

fof(f_463_4,plain,
    ( ! [U_1230,U_1231] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK71(U_1231,U_1230)),U_1231))
        | ~ sP119(U_1230,U_1231) )
    & ! [U_1230,U_1231] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK71(U_1231,U_1230)),U_1230))
        | ~ sP119(U_1230,U_1231) )
    & ! [U_1230,U_1231] :
        ( is_a(sK71(U_1231,U_1230))
        | ~ sP119(U_1230,U_1231) )
    & ! [U_1230,U_1231] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1230),U_1231))
        | sP119(U_1230,U_1231) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119])],[f_463_3]) ).

cnf(f_463_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1230),U_1231))
    | sP119(U_1230,U_1231) ),
    inference(clausify,[status(thm)],[f_463_4]) ).

cnf(f_463_6,plain,
    ( is_a(sK71(U_1231,U_1230))
    | ~ sP119(U_1230,U_1231) ),
    inference(clausify,[status(thm)],[f_463_4]) ).

cnf(f_463_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK71(U_1231,U_1230)),U_1230))
    | ~ sP119(U_1230,U_1231) ),
    inference(clausify,[status(thm)],[f_463_4]) ).

cnf(f_463_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK71(U_1231,U_1230)),U_1231))
    | ~ sP119(U_1230,U_1231) ),
    inference(clausify,[status(thm)],[f_463_4]) ).

fof(f_464_1,plain,
    ! [F,B_6,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(F,A_1)),B_6))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(F,X_1)),B_6))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
          & is_pname(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_360_image__subsetI]) ).

fof(f_464_2,plain,
    ! [U_1235,U_1234,U_1233] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(U_1235,U_1233)),U_1234))
      | ? [U_1232] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(U_1235,U_1232)),U_1234))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1232),U_1233))
          & is_pname(U_1232) ) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

fof(f_464_3,plain,
    ! [U_1235,U_1234,U_1233] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(U_1235,U_1233)),U_1234))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(U_1235,sK72(U_1235,U_1234,U_1233))),U_1234))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK72(U_1235,U_1234,U_1233)),U_1233))
        & is_pname(sK72(U_1235,U_1234,U_1233)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_1232,sK72(U_1235,U_1234,U_1233))],[f_464_2]) ).

fof(f_464_4,plain,
    ( ! [U_1233,U_1234,U_1235] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(U_1235,sK72(U_1235,U_1234,U_1233))),U_1234))
        | ~ sP120(U_1233,U_1234,U_1235) )
    & ! [U_1233,U_1234,U_1235] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK72(U_1235,U_1234,U_1233)),U_1233))
        | ~ sP120(U_1233,U_1234,U_1235) )
    & ! [U_1233,U_1234,U_1235] :
        ( is_pname(sK72(U_1235,U_1234,U_1233))
        | ~ sP120(U_1233,U_1234,U_1235) )
    & ! [U_1233,U_1234,U_1235] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(U_1235,U_1233)),U_1234))
        | sP120(U_1233,U_1234,U_1235) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP120])],[f_464_3]) ).

cnf(f_464_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(U_1235,U_1233)),U_1234))
    | sP120(U_1233,U_1234,U_1235) ),
    inference(clausify,[status(thm)],[f_464_4]) ).

cnf(f_464_6,plain,
    ( is_pname(sK72(U_1235,U_1234,U_1233))
    | ~ sP120(U_1233,U_1234,U_1235) ),
    inference(clausify,[status(thm)],[f_464_4]) ).

cnf(f_464_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK72(U_1235,U_1234,U_1233)),U_1233))
    | ~ sP120(U_1233,U_1234,U_1235) ),
    inference(clausify,[status(thm)],[f_464_4]) ).

cnf(f_464_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(U_1235,sK72(U_1235,U_1234,U_1233))),U_1234))
    | ~ sP120(U_1233,U_1234,U_1235) ),
    inference(clausify,[status(thm)],[f_464_4]) ).

fof(f_465_1,plain,
    ! [F,B_6,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(F,A_1)),B_6))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(F,X_1)),B_6))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
          & is_pname(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_361_image__subsetI]) ).

fof(f_465_2,plain,
    ! [U_1239,U_1238,U_1237] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(U_1239,U_1237)),U_1238))
      | ? [U_1236] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(U_1239,U_1236)),U_1238))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1236),U_1237))
          & is_pname(U_1236) ) ),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

fof(f_465_3,plain,
    ! [U_1239,U_1238,U_1237] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(U_1239,U_1237)),U_1238))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(U_1239,sK73(U_1239,U_1238,U_1237))),U_1238))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK73(U_1239,U_1238,U_1237)),U_1237))
        & is_pname(sK73(U_1239,U_1238,U_1237)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_1236,sK73(U_1239,U_1238,U_1237))],[f_465_2]) ).

fof(f_465_4,plain,
    ( ! [U_1237,U_1238,U_1239] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(U_1239,sK73(U_1239,U_1238,U_1237))),U_1238))
        | ~ sP121(U_1237,U_1238,U_1239) )
    & ! [U_1237,U_1238,U_1239] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK73(U_1239,U_1238,U_1237)),U_1237))
        | ~ sP121(U_1237,U_1238,U_1239) )
    & ! [U_1237,U_1238,U_1239] :
        ( is_pname(sK73(U_1239,U_1238,U_1237))
        | ~ sP121(U_1237,U_1238,U_1239) )
    & ! [U_1237,U_1238,U_1239] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(U_1239,U_1237)),U_1238))
        | sP121(U_1237,U_1238,U_1239) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP121])],[f_465_3]) ).

cnf(f_465_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(U_1239,U_1237)),U_1238))
    | sP121(U_1237,U_1238,U_1239) ),
    inference(clausify,[status(thm)],[f_465_4]) ).

cnf(f_465_6,plain,
    ( is_pname(sK73(U_1239,U_1238,U_1237))
    | ~ sP121(U_1237,U_1238,U_1239) ),
    inference(clausify,[status(thm)],[f_465_4]) ).

cnf(f_465_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK73(U_1239,U_1238,U_1237)),U_1237))
    | ~ sP121(U_1237,U_1238,U_1239) ),
    inference(clausify,[status(thm)],[f_465_4]) ).

cnf(f_465_8,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(U_1239,sK73(U_1239,U_1238,U_1237))),U_1238))
    | ~ sP121(U_1237,U_1238,U_1239) ),
    inference(clausify,[status(thm)],[f_465_4]) ).

fof(f_466_1,plain,
    ! [F,B_6,A_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(F,A_1)),B_6))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(F,X_1)),B_6))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
          & is_a(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_362_image__subsetI]) ).

fof(f_466_2,plain,
    ! [U_1243,U_1242,U_1241] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(U_1243,U_1241)),U_1242))
      | ? [U_1240] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(U_1243,U_1240)),U_1242))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1240),U_1241))
          & is_a(U_1240) ) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

fof(f_466_3,plain,
    ! [U_1243,U_1242,U_1241] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(U_1243,U_1241)),U_1242))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(U_1243,sK74(U_1243,U_1242,U_1241))),U_1242))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK74(U_1243,U_1242,U_1241)),U_1241))
        & is_a(sK74(U_1243,U_1242,U_1241)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_1240,sK74(U_1243,U_1242,U_1241))],[f_466_2]) ).

fof(f_466_4,plain,
    ( ! [U_1243,U_1242,U_1241] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(U_1243,sK74(U_1243,U_1242,U_1241))),U_1242))
        | ~ sP122(U_1243,U_1242,U_1241) )
    & ! [U_1243,U_1242,U_1241] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK74(U_1243,U_1242,U_1241)),U_1241))
        | ~ sP122(U_1243,U_1242,U_1241) )
    & ! [U_1243,U_1242,U_1241] :
        ( is_a(sK74(U_1243,U_1242,U_1241))
        | ~ sP122(U_1243,U_1242,U_1241) )
    & ! [U_1243,U_1242,U_1241] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(U_1243,U_1241)),U_1242))
        | sP122(U_1243,U_1242,U_1241) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122])],[f_466_3]) ).

cnf(f_466_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(U_1243,U_1241)),U_1242))
    | sP122(U_1243,U_1242,U_1241) ),
    inference(clausify,[status(thm)],[f_466_4]) ).

cnf(f_466_6,plain,
    ( is_a(sK74(U_1243,U_1242,U_1241))
    | ~ sP122(U_1243,U_1242,U_1241) ),
    inference(clausify,[status(thm)],[f_466_4]) ).

cnf(f_466_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK74(U_1243,U_1242,U_1241)),U_1241))
    | ~ sP122(U_1243,U_1242,U_1241) ),
    inference(clausify,[status(thm)],[f_466_4]) ).

cnf(f_466_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(U_1243,sK74(U_1243,U_1242,U_1241))),U_1242))
    | ~ sP122(U_1243,U_1242,U_1241) ),
    inference(clausify,[status(thm)],[f_466_4]) ).

fof(f_467_1,plain,
    ! [F,B_6,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(F,A_1)),B_6))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_a_pname(F,X_1)),B_6))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
          & is_a(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_363_image__subsetI]) ).

fof(f_467_2,plain,
    ! [U_1247,U_1246,U_1245] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(U_1247,U_1245)),U_1246))
      | ? [U_1244] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_a_pname(U_1247,U_1244)),U_1246))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1244),U_1245))
          & is_a(U_1244) ) ),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

fof(f_467_3,plain,
    ! [U_1247,U_1246,U_1245] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(U_1247,U_1245)),U_1246))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_a_pname(U_1247,sK75(U_1247,U_1246,U_1245))),U_1246))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK75(U_1247,U_1246,U_1245)),U_1245))
        & is_a(sK75(U_1247,U_1246,U_1245)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_1244,sK75(U_1247,U_1246,U_1245))],[f_467_2]) ).

fof(f_467_4,plain,
    ( ! [U_1246,U_1245,U_1247] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_a_pname(U_1247,sK75(U_1247,U_1246,U_1245))),U_1246))
        | ~ sP123(U_1246,U_1245,U_1247) )
    & ! [U_1246,U_1245,U_1247] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK75(U_1247,U_1246,U_1245)),U_1245))
        | ~ sP123(U_1246,U_1245,U_1247) )
    & ! [U_1246,U_1245,U_1247] :
        ( is_a(sK75(U_1247,U_1246,U_1245))
        | ~ sP123(U_1246,U_1245,U_1247) )
    & ! [U_1246,U_1245,U_1247] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(U_1247,U_1245)),U_1246))
        | sP123(U_1246,U_1245,U_1247) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP123])],[f_467_3]) ).

cnf(f_467_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(U_1247,U_1245)),U_1246))
    | sP123(U_1246,U_1245,U_1247) ),
    inference(clausify,[status(thm)],[f_467_4]) ).

cnf(f_467_6,plain,
    ( is_a(sK75(U_1247,U_1246,U_1245))
    | ~ sP123(U_1246,U_1245,U_1247) ),
    inference(clausify,[status(thm)],[f_467_4]) ).

cnf(f_467_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK75(U_1247,U_1246,U_1245)),U_1245))
    | ~ sP123(U_1246,U_1245,U_1247) ),
    inference(clausify,[status(thm)],[f_467_4]) ).

cnf(f_467_8,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_a_pname(U_1247,sK75(U_1247,U_1246,U_1245))),U_1246))
    | ~ sP123(U_1246,U_1245,U_1247) ),
    inference(clausify,[status(thm)],[f_467_4]) ).

fof(f_468_1,plain,
    ! [F,B_6,A_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(F,A_1)),B_6))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(F,X_1)),B_6))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_364_image__subsetI]) ).

fof(f_468_2,plain,
    ! [U_1251,U_1250,U_1249] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(U_1251,U_1249)),U_1250))
      | ? [U_1248] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(U_1251,U_1248)),U_1250))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1248),U_1249)) ) ),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

fof(f_468_3,plain,
    ! [U_1251,U_1250,U_1249] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(U_1251,U_1249)),U_1250))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(U_1251,sK76(U_1251,U_1250,U_1249))),U_1250))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK76(U_1251,U_1250,U_1249)),U_1249)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_1248,sK76(U_1251,U_1250,U_1249))],[f_468_2]) ).

fof(f_468_4,plain,
    ( ! [U_1250,U_1249,U_1251] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(U_1251,sK76(U_1251,U_1250,U_1249))),U_1250))
        | ~ sP124(U_1250,U_1249,U_1251) )
    & ! [U_1250,U_1249,U_1251] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK76(U_1251,U_1250,U_1249)),U_1249))
        | ~ sP124(U_1250,U_1249,U_1251) )
    & ! [U_1250,U_1249,U_1251] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(U_1251,U_1249)),U_1250))
        | sP124(U_1250,U_1249,U_1251) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124])],[f_468_3]) ).

cnf(f_468_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(U_1251,U_1249)),U_1250))
    | sP124(U_1250,U_1249,U_1251) ),
    inference(clausify,[status(thm)],[f_468_4]) ).

cnf(f_468_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK76(U_1251,U_1250,U_1249)),U_1249))
    | ~ sP124(U_1250,U_1249,U_1251) ),
    inference(clausify,[status(thm)],[f_468_4]) ).

cnf(f_468_7,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(U_1251,sK76(U_1251,U_1250,U_1249))),U_1250))
    | ~ sP124(U_1250,U_1249,U_1251) ),
    inference(clausify,[status(thm)],[f_468_4]) ).

fof(f_469_1,plain,
    ! [F,B_6,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(F,A_1)),B_6))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(F,X_1)),B_6))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_365_image__subsetI]) ).

fof(f_469_2,plain,
    ! [U_1255,U_1254,U_1253] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(U_1255,U_1253)),U_1254))
      | ? [U_1252] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(U_1255,U_1252)),U_1254))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1252),U_1253)) ) ),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

fof(f_469_3,plain,
    ! [U_1255,U_1254,U_1253] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(U_1255,U_1253)),U_1254))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(U_1255,sK77(U_1255,U_1254,U_1253))),U_1254))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK77(U_1255,U_1254,U_1253)),U_1253)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_1252,sK77(U_1255,U_1254,U_1253))],[f_469_2]) ).

fof(f_469_4,plain,
    ( ! [U_1253,U_1254,U_1255] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(U_1255,sK77(U_1255,U_1254,U_1253))),U_1254))
        | ~ sP125(U_1253,U_1254,U_1255) )
    & ! [U_1253,U_1254,U_1255] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK77(U_1255,U_1254,U_1253)),U_1253))
        | ~ sP125(U_1253,U_1254,U_1255) )
    & ! [U_1253,U_1254,U_1255] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(U_1255,U_1253)),U_1254))
        | sP125(U_1253,U_1254,U_1255) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125])],[f_469_3]) ).

cnf(f_469_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(U_1255,U_1253)),U_1254))
    | sP125(U_1253,U_1254,U_1255) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK77(U_1255,U_1254,U_1253)),U_1253))
    | ~ sP125(U_1253,U_1254,U_1255) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_7,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(U_1255,sK77(U_1255,U_1254,U_1253))),U_1254))
    | ~ sP125(U_1253,U_1254,U_1255) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

fof(f_470_1,plain,
    ! [F,B_6,A_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A_1)),B_6))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_1)),B_6))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
          & is_pname(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_366_image__subsetI]) ).

fof(f_470_2,plain,
    ! [U_1259,U_1258,U_1257] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1259,U_1257)),U_1258))
      | ? [U_1256] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1259,U_1256)),U_1258))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1256),U_1257))
          & is_pname(U_1256) ) ),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

fof(f_470_3,plain,
    ! [U_1259,U_1258,U_1257] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1259,U_1257)),U_1258))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1259,sK78(U_1259,U_1258,U_1257))),U_1258))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(U_1259,U_1258,U_1257)),U_1257))
        & is_pname(sK78(U_1259,U_1258,U_1257)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_1256,sK78(U_1259,U_1258,U_1257))],[f_470_2]) ).

fof(f_470_4,plain,
    ( ! [U_1257,U_1258,U_1259] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1259,sK78(U_1259,U_1258,U_1257))),U_1258))
        | ~ sP126(U_1257,U_1258,U_1259) )
    & ! [U_1257,U_1258,U_1259] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(U_1259,U_1258,U_1257)),U_1257))
        | ~ sP126(U_1257,U_1258,U_1259) )
    & ! [U_1257,U_1258,U_1259] :
        ( is_pname(sK78(U_1259,U_1258,U_1257))
        | ~ sP126(U_1257,U_1258,U_1259) )
    & ! [U_1257,U_1258,U_1259] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1259,U_1257)),U_1258))
        | sP126(U_1257,U_1258,U_1259) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126])],[f_470_3]) ).

cnf(f_470_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1259,U_1257)),U_1258))
    | sP126(U_1257,U_1258,U_1259) ),
    inference(clausify,[status(thm)],[f_470_4]) ).

cnf(f_470_6,plain,
    ( is_pname(sK78(U_1259,U_1258,U_1257))
    | ~ sP126(U_1257,U_1258,U_1259) ),
    inference(clausify,[status(thm)],[f_470_4]) ).

cnf(f_470_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(U_1259,U_1258,U_1257)),U_1257))
    | ~ sP126(U_1257,U_1258,U_1259) ),
    inference(clausify,[status(thm)],[f_470_4]) ).

cnf(f_470_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1259,sK78(U_1259,U_1258,U_1257))),U_1258))
    | ~ sP126(U_1257,U_1258,U_1259) ),
    inference(clausify,[status(thm)],[f_470_4]) ).

fof(f_471_1,plain,
    ! [X_3] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),X_3)),
    inference(fof_nnf,[status(thm)],[fact_367_order__refl]) ).

fof(f_471_2,plain,
    ! [U_1260] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1260),U_1260)),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

fof(f_471_3,plain,
    ! [U_1260] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1260),U_1260)),
    inference(definitional_conversion,[status(esa)],[f_471_2]) ).

cnf(f_471_4,plain,
    hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1260),U_1260)),
    inference(clausify,[status(thm)],[f_471_3]) ).

fof(f_472_1,plain,
    ! [X_3] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),X_3)),
    inference(fof_nnf,[status(thm)],[fact_368_order__refl]) ).

fof(f_472_2,plain,
    ! [U_1261] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1261),U_1261)),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

fof(f_472_3,plain,
    ! [U_1261] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1261),U_1261)),
    inference(definitional_conversion,[status(esa)],[f_472_2]) ).

cnf(f_472_4,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1261),U_1261)),
    inference(clausify,[status(thm)],[f_472_3]) ).

fof(f_473_1,plain,
    ! [X_3] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),X_3)),
    inference(fof_nnf,[status(thm)],[fact_369_order__refl]) ).

fof(f_473_2,plain,
    ! [U_1262] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1262),U_1262)),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

fof(f_473_3,plain,
    ! [U_1262] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1262),U_1262)),
    inference(definitional_conversion,[status(esa)],[f_473_2]) ).

cnf(f_473_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1262),U_1262)),
    inference(clausify,[status(thm)],[f_473_3]) ).

fof(f_474_1,plain,
    ! [X_3] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),X_3)),
    inference(fof_nnf,[status(thm)],[fact_370_order__refl]) ).

fof(f_474_2,plain,
    ! [U_1263] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1263),U_1263)),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

fof(f_474_3,plain,
    ! [U_1263] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1263),U_1263)),
    inference(definitional_conversion,[status(esa)],[f_474_2]) ).

cnf(f_474_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1263),U_1263)),
    inference(clausify,[status(thm)],[f_474_3]) ).

fof(f_475_1,plain,
    ! [X_10] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_10),X_10)),
    inference(fof_nnf,[status(thm)],[fact_371_order__refl]) ).

fof(f_475_2,plain,
    ! [U_1264] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1264),U_1264)),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

fof(f_475_3,plain,
    ! [U_1264] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1264),U_1264)),
    inference(definitional_conversion,[status(esa)],[f_475_2]) ).

cnf(f_475_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1264),U_1264)),
    inference(clausify,[status(thm)],[f_475_3]) ).

fof(f_476_1,plain,
    ! [N_1] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1))
        | ! [M_2] :
          ? [X_1] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M_2))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1)) ) )
      & ( ? [M_2] :
          ! [X_1] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M_2))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_372_finite__nat__set__iff__bounded__le]) ).

fof(f_476_2,plain,
    ! [U_1269] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1269))
        | ! [U_1268] :
          ? [U_1267] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1267),U_1268))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1267),U_1269)) ) )
      & ( ? [U_1266] :
          ! [U_1265] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1265),U_1266))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1265),U_1269)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1269)) ) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

fof(f_476_3,plain,
    ( ! [U_1271] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1271))
        | ! [U_1268] :
          ? [U_1267] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1267),U_1268))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1267),U_1271)) ) )
    & ! [U_1270] :
        ( ? [U_1266] :
          ! [U_1265] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1265),U_1266))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1265),U_1270)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1270)) ) ),
    inference(miniscope,[status(thm)],[f_476_2]) ).

fof(f_476_4,plain,
    ( ! [U_1271] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1271))
        | ! [U_1268] :
          ? [U_1267] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1267),U_1268))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1267),U_1271)) ) )
    & ! [U_1270] :
        ( ! [U_1265] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1265),sK79(U_1270)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1265),U_1270)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1270)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_1266,sK79(U_1270))],[f_476_3]) ).

fof(f_476_5,plain,
    ( ! [U_1271] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1271))
        | ! [U_1268] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK80(U_1271,U_1268)),U_1268))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK80(U_1271,U_1268)),U_1271)) ) )
    & ! [U_1270] :
        ( ! [U_1265] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1265),sK79(U_1270)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1265),U_1270)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1270)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_1267,sK80(U_1271,U_1268))],[f_476_4]) ).

fof(f_476_6,plain,
    ( ! [U_1268,U_1271] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK80(U_1271,U_1268)),U_1268))
        | ~ sP127(U_1268,U_1271) )
    & ! [U_1268,U_1271] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK80(U_1271,U_1268)),U_1271))
        | ~ sP127(U_1268,U_1271) )
    & ! [U_1268,U_1271] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1271))
        | sP127(U_1268,U_1271) )
    & ! [U_1265,U_1270] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1265),sK79(U_1270)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1265),U_1270))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1270)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP127])],[f_476_5]) ).

cnf(f_476_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1265),sK79(U_1270)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1265),U_1270))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1270)) ),
    inference(clausify,[status(thm)],[f_476_6]) ).

cnf(f_476_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1271))
    | sP127(U_1268,U_1271) ),
    inference(clausify,[status(thm)],[f_476_6]) ).

cnf(f_476_9,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK80(U_1271,U_1268)),U_1271))
    | ~ sP127(U_1268,U_1271) ),
    inference(clausify,[status(thm)],[f_476_6]) ).

cnf(f_476_10,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK80(U_1271,U_1268)),U_1268))
    | ~ sP127(U_1268,U_1271) ),
    inference(clausify,[status(thm)],[f_476_6]) ).

fof(f_477_1,plain,
    ! [G,C_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(G),insert_a(mgt(C_1),bot_bot_fun_a_bool)))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(p(G),insert_a(hAPP_pname_a(mgt_call,X_1),bot_bot_fun_a_bool)))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),u))
          & is_pname(X_1) )
      | ~ hBOOL(wt(C_1)) ),
    inference(fof_nnf,[status(thm)],[fact_373_assms_I3_J]) ).

fof(f_477_2,plain,
    ! [U_1274,U_1273] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_1274),insert_a(mgt(U_1273),bot_bot_fun_a_bool)))
      | ? [U_1272] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(p(U_1274),insert_a(hAPP_pname_a(mgt_call,U_1272),bot_bot_fun_a_bool)))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1272),u))
          & is_pname(U_1272) )
      | ~ hBOOL(wt(U_1273)) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

fof(f_477_3,plain,
    ! [U_1274,U_1273] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_1274),insert_a(mgt(U_1273),bot_bot_fun_a_bool)))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(p(U_1274),insert_a(hAPP_pname_a(mgt_call,sK81(U_1274,U_1273)),bot_bot_fun_a_bool)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK81(U_1274,U_1273)),u))
        & is_pname(sK81(U_1274,U_1273)) )
      | ~ hBOOL(wt(U_1273)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_1272,sK81(U_1274,U_1273))],[f_477_2]) ).

fof(f_477_4,plain,
    ( ! [U_1273,U_1274] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(p(U_1274),insert_a(hAPP_pname_a(mgt_call,sK81(U_1274,U_1273)),bot_bot_fun_a_bool)))
        | ~ sP128(U_1273,U_1274) )
    & ! [U_1273,U_1274] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK81(U_1274,U_1273)),u))
        | ~ sP128(U_1273,U_1274) )
    & ! [U_1273,U_1274] :
        ( is_pname(sK81(U_1274,U_1273))
        | ~ sP128(U_1273,U_1274) )
    & ! [U_1273,U_1274] :
        ( hBOOL(hAPP_fun_a_bool_bool(p(U_1274),insert_a(mgt(U_1273),bot_bot_fun_a_bool)))
        | sP128(U_1273,U_1274)
        | ~ hBOOL(wt(U_1273)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128])],[f_477_3]) ).

cnf(f_477_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(p(U_1274),insert_a(mgt(U_1273),bot_bot_fun_a_bool)))
    | sP128(U_1273,U_1274)
    | ~ hBOOL(wt(U_1273)) ),
    inference(clausify,[status(thm)],[f_477_4]) ).

cnf(f_477_6,plain,
    ( is_pname(sK81(U_1274,U_1273))
    | ~ sP128(U_1273,U_1274) ),
    inference(clausify,[status(thm)],[f_477_4]) ).

cnf(f_477_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK81(U_1274,U_1273)),u))
    | ~ sP128(U_1273,U_1274) ),
    inference(clausify,[status(thm)],[f_477_4]) ).

cnf(f_477_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(p(U_1274),insert_a(hAPP_pname_a(mgt_call,sK81(U_1274,U_1273)),bot_bot_fun_a_bool)))
    | ~ sP128(U_1273,U_1274) ),
    inference(clausify,[status(thm)],[f_477_4]) ).

fof(f_478_1,plain,
    ! [F,G_1] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1))
        | ? [X_1] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G_1,X_1)))
            & is_pname(X_1) ) )
      & ( ! [X_1] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_1)),hAPP_pname_bool(G_1,X_1)))
            | ~ is_pname(X_1) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_374_le__fun__def]) ).

fof(f_478_2,plain,
    ! [U_1278,U_1277] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1278),U_1277))
        | ? [U_1276] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1278,U_1276)),hAPP_pname_bool(U_1277,U_1276)))
            & is_pname(U_1276) ) )
      & ( ! [U_1275] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1278,U_1275)),hAPP_pname_bool(U_1277,U_1275)))
            | ~ is_pname(U_1275) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1278),U_1277)) ) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

fof(f_478_3,plain,
    ( ! [U_1282,U_1280] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1282),U_1280))
        | ? [U_1276] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1282,U_1276)),hAPP_pname_bool(U_1280,U_1276)))
            & is_pname(U_1276) ) )
    & ! [U_1281,U_1279] :
        ( ! [U_1275] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1281,U_1275)),hAPP_pname_bool(U_1279,U_1275)))
            | ~ is_pname(U_1275) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1281),U_1279)) ) ),
    inference(miniscope,[status(thm)],[f_478_2]) ).

fof(f_478_4,plain,
    ( ! [U_1282,U_1280] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1282),U_1280))
        | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1282,sK82(U_1282,U_1280))),hAPP_pname_bool(U_1280,sK82(U_1282,U_1280))))
          & is_pname(sK82(U_1282,U_1280)) ) )
    & ! [U_1281,U_1279] :
        ( ! [U_1275] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1281,U_1275)),hAPP_pname_bool(U_1279,U_1275)))
            | ~ is_pname(U_1275) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1281),U_1279)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_1276,sK82(U_1282,U_1280))],[f_478_3]) ).

fof(f_478_5,plain,
    ( ! [U_1282,U_1280] :
        ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1282,sK82(U_1282,U_1280))),hAPP_pname_bool(U_1280,sK82(U_1282,U_1280))))
        | ~ sP129(U_1282,U_1280) )
    & ! [U_1282,U_1280] :
        ( is_pname(sK82(U_1282,U_1280))
        | ~ sP129(U_1282,U_1280) )
    & ! [U_1282,U_1280] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1282),U_1280))
        | sP129(U_1282,U_1280) )
    & ! [U_1281,U_1275,U_1279] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1281,U_1275)),hAPP_pname_bool(U_1279,U_1275)))
        | ~ is_pname(U_1275)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1281),U_1279)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129])],[f_478_4]) ).

cnf(f_478_6,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1281,U_1275)),hAPP_pname_bool(U_1279,U_1275)))
    | ~ is_pname(U_1275)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1281),U_1279)) ),
    inference(clausify,[status(thm)],[f_478_5]) ).

cnf(f_478_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1282),U_1280))
    | sP129(U_1282,U_1280) ),
    inference(clausify,[status(thm)],[f_478_5]) ).

cnf(f_478_8,plain,
    ( is_pname(sK82(U_1282,U_1280))
    | ~ sP129(U_1282,U_1280) ),
    inference(clausify,[status(thm)],[f_478_5]) ).

cnf(f_478_9,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1282,sK82(U_1282,U_1280))),hAPP_pname_bool(U_1280,sK82(U_1282,U_1280))))
    | ~ sP129(U_1282,U_1280) ),
    inference(clausify,[status(thm)],[f_478_5]) ).

fof(f_479_1,plain,
    ! [F,G_1] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1))
        | ? [X_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))) )
      & ( ! [X_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_375_le__fun__def]) ).

fof(f_479_2,plain,
    ! [U_1286,U_1285] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1286),U_1285))
        | ? [U_1284] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1286,U_1284)),hAPP_nat_bool(U_1285,U_1284))) )
      & ( ! [U_1283] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1286,U_1283)),hAPP_nat_bool(U_1285,U_1283)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1286),U_1285)) ) ),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

fof(f_479_3,plain,
    ( ! [U_1290,U_1288] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1290),U_1288))
        | ? [U_1284] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1290,U_1284)),hAPP_nat_bool(U_1288,U_1284))) )
    & ! [U_1289,U_1287] :
        ( ! [U_1283] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1289,U_1283)),hAPP_nat_bool(U_1287,U_1283)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1289),U_1287)) ) ),
    inference(miniscope,[status(thm)],[f_479_2]) ).

fof(f_479_4,plain,
    ( ! [U_1290,U_1288] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1290),U_1288))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1290,sK83(U_1290,U_1288))),hAPP_nat_bool(U_1288,sK83(U_1290,U_1288)))) )
    & ! [U_1289,U_1287] :
        ( ! [U_1283] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1289,U_1283)),hAPP_nat_bool(U_1287,U_1283)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1289),U_1287)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_1284,sK83(U_1290,U_1288))],[f_479_3]) ).

fof(f_479_5,plain,
    ( ! [U_1288,U_1290] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1290),U_1288))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1290,sK83(U_1290,U_1288))),hAPP_nat_bool(U_1288,sK83(U_1290,U_1288)))) )
    & ! [U_1283,U_1289,U_1287] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1289,U_1283)),hAPP_nat_bool(U_1287,U_1283)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1289),U_1287)) ) ),
    inference(definitional_conversion,[status(esa)],[f_479_4]) ).

cnf(f_479_6,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1289,U_1283)),hAPP_nat_bool(U_1287,U_1283)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1289),U_1287)) ),
    inference(clausify,[status(thm)],[f_479_5]) ).

cnf(f_479_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1290),U_1288))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1290,sK83(U_1290,U_1288))),hAPP_nat_bool(U_1288,sK83(U_1290,U_1288)))) ),
    inference(clausify,[status(thm)],[f_479_5]) ).

fof(f_480_1,plain,
    ! [F,G_1] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1))
        | ? [X_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)))
            & is_a(X_1) ) )
      & ( ! [X_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)))
            | ~ is_a(X_1) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_376_le__fun__def]) ).

fof(f_480_2,plain,
    ! [U_1294,U_1293] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1294),U_1293))
        | ? [U_1292] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1294,U_1292)),hAPP_a_bool(U_1293,U_1292)))
            & is_a(U_1292) ) )
      & ( ! [U_1291] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1294,U_1291)),hAPP_a_bool(U_1293,U_1291)))
            | ~ is_a(U_1291) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1294),U_1293)) ) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

fof(f_480_3,plain,
    ( ! [U_1298,U_1296] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1298),U_1296))
        | ? [U_1292] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1298,U_1292)),hAPP_a_bool(U_1296,U_1292)))
            & is_a(U_1292) ) )
    & ! [U_1297,U_1295] :
        ( ! [U_1291] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1297,U_1291)),hAPP_a_bool(U_1295,U_1291)))
            | ~ is_a(U_1291) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1297),U_1295)) ) ),
    inference(miniscope,[status(thm)],[f_480_2]) ).

fof(f_480_4,plain,
    ( ! [U_1298,U_1296] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1298),U_1296))
        | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1298,sK84(U_1298,U_1296))),hAPP_a_bool(U_1296,sK84(U_1298,U_1296))))
          & is_a(sK84(U_1298,U_1296)) ) )
    & ! [U_1297,U_1295] :
        ( ! [U_1291] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1297,U_1291)),hAPP_a_bool(U_1295,U_1291)))
            | ~ is_a(U_1291) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1297),U_1295)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_1292,sK84(U_1298,U_1296))],[f_480_3]) ).

fof(f_480_5,plain,
    ( ! [U_1296,U_1298] :
        ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1298,sK84(U_1298,U_1296))),hAPP_a_bool(U_1296,sK84(U_1298,U_1296))))
        | ~ sP130(U_1296,U_1298) )
    & ! [U_1296,U_1298] :
        ( is_a(sK84(U_1298,U_1296))
        | ~ sP130(U_1296,U_1298) )
    & ! [U_1296,U_1298] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1298),U_1296))
        | sP130(U_1296,U_1298) )
    & ! [U_1291,U_1295,U_1297] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1297,U_1291)),hAPP_a_bool(U_1295,U_1291)))
        | ~ is_a(U_1291)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1297),U_1295)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130])],[f_480_4]) ).

cnf(f_480_6,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1297,U_1291)),hAPP_a_bool(U_1295,U_1291)))
    | ~ is_a(U_1291)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1297),U_1295)) ),
    inference(clausify,[status(thm)],[f_480_5]) ).

cnf(f_480_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1298),U_1296))
    | sP130(U_1296,U_1298) ),
    inference(clausify,[status(thm)],[f_480_5]) ).

cnf(f_480_8,plain,
    ( is_a(sK84(U_1298,U_1296))
    | ~ sP130(U_1296,U_1298) ),
    inference(clausify,[status(thm)],[f_480_5]) ).

cnf(f_480_9,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1298,sK84(U_1298,U_1296))),hAPP_a_bool(U_1296,sK84(U_1298,U_1296))))
    | ~ sP130(U_1296,U_1298) ),
    inference(clausify,[status(thm)],[f_480_5]) ).

fof(f_481_1,plain,
    ! [X_3,F,G_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_3)),hAPP_pname_bool(G_1,X_3)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_377_le__funD]) ).

fof(f_481_2,plain,
    ! [U_1301,U_1300,U_1299] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1300,U_1301)),hAPP_pname_bool(U_1299,U_1301)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1300),U_1299)) ),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

fof(f_481_3,plain,
    ! [U_1301,U_1299,U_1300] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1300,U_1301)),hAPP_pname_bool(U_1299,U_1301)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1300),U_1299)) ),
    inference(definitional_conversion,[status(esa)],[f_481_2]) ).

cnf(f_481_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1300,U_1301)),hAPP_pname_bool(U_1299,U_1301)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1300),U_1299)) ),
    inference(clausify,[status(thm)],[f_481_3]) ).

fof(f_482_1,plain,
    ! [X_3,F,G_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_3)),hAPP_nat_bool(G_1,X_3)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_378_le__funD]) ).

fof(f_482_2,plain,
    ! [U_1304,U_1303,U_1302] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1303,U_1304)),hAPP_nat_bool(U_1302,U_1304)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1303),U_1302)) ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

fof(f_482_3,plain,
    ! [U_1302,U_1303,U_1304] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1303,U_1304)),hAPP_nat_bool(U_1302,U_1304)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1303),U_1302)) ),
    inference(definitional_conversion,[status(esa)],[f_482_2]) ).

cnf(f_482_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1303,U_1304)),hAPP_nat_bool(U_1302,U_1304)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1303),U_1302)) ),
    inference(clausify,[status(thm)],[f_482_3]) ).

fof(f_483_1,plain,
    ! [X_3,F,G_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_3)),hAPP_a_bool(G_1,X_3)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_379_le__funD]) ).

fof(f_483_2,plain,
    ! [U_1307,U_1306,U_1305] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1306,U_1307)),hAPP_a_bool(U_1305,U_1307)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1306),U_1305)) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

fof(f_483_3,plain,
    ! [U_1305,U_1306,U_1307] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1306,U_1307)),hAPP_a_bool(U_1305,U_1307)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1306),U_1305)) ),
    inference(definitional_conversion,[status(esa)],[f_483_2]) ).

cnf(f_483_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1306,U_1307)),hAPP_a_bool(U_1305,U_1307)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1306),U_1305)) ),
    inference(clausify,[status(thm)],[f_483_3]) ).

fof(f_484_1,plain,
    ! [X_3,F,G_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(F,X_3)),hAPP_pname_bool(G_1,X_3)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_380_le__funE]) ).

fof(f_484_2,plain,
    ! [U_1310,U_1309,U_1308] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1309,U_1310)),hAPP_pname_bool(U_1308,U_1310)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1309),U_1308)) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

fof(f_484_3,plain,
    ! [U_1308,U_1309,U_1310] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1309,U_1310)),hAPP_pname_bool(U_1308,U_1310)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1309),U_1308)) ),
    inference(definitional_conversion,[status(esa)],[f_484_2]) ).

cnf(f_484_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(U_1309,U_1310)),hAPP_pname_bool(U_1308,U_1310)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1309),U_1308)) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

fof(f_485_1,plain,
    ! [X_3,F,G_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_3)),hAPP_nat_bool(G_1,X_3)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_381_le__funE]) ).

fof(f_485_2,plain,
    ! [U_1313,U_1312,U_1311] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1312,U_1313)),hAPP_nat_bool(U_1311,U_1313)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1312),U_1311)) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

fof(f_485_3,plain,
    ! [U_1311,U_1312,U_1313] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1312,U_1313)),hAPP_nat_bool(U_1311,U_1313)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1312),U_1311)) ),
    inference(definitional_conversion,[status(esa)],[f_485_2]) ).

cnf(f_485_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1312,U_1313)),hAPP_nat_bool(U_1311,U_1313)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1312),U_1311)) ),
    inference(clausify,[status(thm)],[f_485_3]) ).

fof(f_486_1,plain,
    ! [X_3,F,G_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_3)),hAPP_a_bool(G_1,X_3)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_382_le__funE]) ).

fof(f_486_2,plain,
    ! [U_1316,U_1315,U_1314] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1315,U_1316)),hAPP_a_bool(U_1314,U_1316)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1315),U_1314)) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

fof(f_486_3,plain,
    ! [U_1314,U_1315,U_1316] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1315,U_1316)),hAPP_a_bool(U_1314,U_1316)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1315),U_1314)) ),
    inference(definitional_conversion,[status(esa)],[f_486_2]) ).

cnf(f_486_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1315,U_1316)),hAPP_a_bool(U_1314,U_1316)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1315),U_1314)) ),
    inference(clausify,[status(thm)],[f_486_3]) ).

fof(f_487_1,plain,
    ! [A_3] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),bot_bot_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_383_emptyE]) ).

fof(f_487_2,plain,
    ! [U_1317] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1317),bot_bot_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

fof(f_487_3,plain,
    ! [U_1317] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1317),bot_bot_fun_nat_bool)),
    inference(definitional_conversion,[status(esa)],[f_487_2]) ).

cnf(f_487_4,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1317),bot_bot_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_487_3]) ).

fof(f_488_1,plain,
    ! [A_3] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),bot_bo844097828e_bool)),
    inference(fof_nnf,[status(thm)],[fact_384_emptyE]) ).

fof(f_488_2,plain,
    ! [U_1318] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1318),bot_bo844097828e_bool)),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

fof(f_488_3,plain,
    ! [U_1318] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1318),bot_bo844097828e_bool)),
    inference(definitional_conversion,[status(esa)],[f_488_2]) ).

cnf(f_488_4,plain,
    ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1318),bot_bo844097828e_bool)),
    inference(clausify,[status(thm)],[f_488_3]) ).

fof(f_489_1,plain,
    ! [A_3] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),bot_bot_fun_a_bool)),
    inference(fof_nnf,[status(thm)],[fact_385_emptyE]) ).

fof(f_489_2,plain,
    ! [U_1319] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1319),bot_bot_fun_a_bool)),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

fof(f_489_3,plain,
    ! [U_1319] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1319),bot_bot_fun_a_bool)),
    inference(definitional_conversion,[status(esa)],[f_489_2]) ).

cnf(f_489_4,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1319),bot_bot_fun_a_bool)),
    inference(clausify,[status(thm)],[f_489_3]) ).

fof(f_490_1,plain,
    hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,bot_bo1701429464l_bool)),
    inference(fof_nnf,[status(thm)],[fact_386_finite_OemptyI]) ).

fof(f_490_2,plain,
    hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,bot_bo1701429464l_bool)),
    inference(definitional_conversion,[status(esa)],[f_490_1]) ).

cnf(f_490_3,plain,
    hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,bot_bo1701429464l_bool)),
    inference(clausify,[status(thm)],[f_490_2]) ).

fof(f_491_1,plain,
    hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)),
    inference(fof_nnf,[status(thm)],[fact_387_finite_OemptyI]) ).

fof(f_491_2,plain,
    hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)),
    inference(definitional_conversion,[status(esa)],[f_491_1]) ).

cnf(f_491_3,plain,
    hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)),
    inference(clausify,[status(thm)],[f_491_2]) ).

fof(f_492_1,plain,
    hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,bot_bo1389914601l_bool)),
    inference(fof_nnf,[status(thm)],[fact_388_finite_OemptyI]) ).

fof(f_492_2,plain,
    hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,bot_bo1389914601l_bool)),
    inference(definitional_conversion,[status(esa)],[f_492_1]) ).

cnf(f_492_3,plain,
    hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,bot_bo1389914601l_bool)),
    inference(clausify,[status(thm)],[f_492_2]) ).

fof(f_493_1,plain,
    hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
    inference(fof_nnf,[status(thm)],[fact_389_finite_OemptyI]) ).

fof(f_493_2,plain,
    hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
    inference(definitional_conversion,[status(esa)],[f_493_1]) ).

cnf(f_493_3,plain,
    hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
    inference(clausify,[status(thm)],[f_493_2]) ).

fof(f_494_1,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    inference(fof_nnf,[status(thm)],[fact_390_finite_OemptyI]) ).

fof(f_494_2,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    inference(definitional_conversion,[status(esa)],[f_494_1]) ).

cnf(f_494_3,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    inference(clausify,[status(thm)],[f_494_2]) ).

fof(f_495_1,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_391_finite_OemptyI]) ).

fof(f_495_2,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
    inference(definitional_conversion,[status(esa)],[f_495_1]) ).

cnf(f_495_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_495_2]) ).

fof(f_496_1,plain,
    ! [A_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_1)),
    inference(fof_nnf,[status(thm)],[fact_392_empty__subsetI]) ).

fof(f_496_2,plain,
    ! [U_1320] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),U_1320)),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

fof(f_496_3,plain,
    ! [U_1320] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),U_1320)),
    inference(definitional_conversion,[status(esa)],[f_496_2]) ).

cnf(f_496_4,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),U_1320)),
    inference(clausify,[status(thm)],[f_496_3]) ).

fof(f_497_1,plain,
    ! [A_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_1)),
    inference(fof_nnf,[status(thm)],[fact_393_empty__subsetI]) ).

fof(f_497_2,plain,
    ! [U_1321] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),U_1321)),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

fof(f_497_3,plain,
    ! [U_1321] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),U_1321)),
    inference(definitional_conversion,[status(esa)],[f_497_2]) ).

cnf(f_497_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),U_1321)),
    inference(clausify,[status(thm)],[f_497_3]) ).

fof(f_498_1,plain,
    ! [A_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A_1)),
    inference(fof_nnf,[status(thm)],[fact_394_empty__subsetI]) ).

fof(f_498_2,plain,
    ! [U_1322] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),U_1322)),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

fof(f_498_3,plain,
    ! [U_1322] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),U_1322)),
    inference(definitional_conversion,[status(esa)],[f_498_2]) ).

cnf(f_498_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),U_1322)),
    inference(clausify,[status(thm)],[f_498_3]) ).

fof(f_499_1,plain,
    ! [A_3,A_1] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_3),A_1))
      | A_1 != bot_bot_fun_nat_bool ),
    inference(fof_nnf,[status(thm)],[fact_395_equals0D]) ).

fof(f_499_2,plain,
    ! [U_1324,U_1323] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1324),U_1323))
      | U_1323 != bot_bot_fun_nat_bool ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

fof(f_499_3,plain,
    ! [U_1323,U_1324] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1324),U_1323))
      | U_1323 != bot_bot_fun_nat_bool ),
    inference(definitional_conversion,[status(esa)],[f_499_2]) ).

cnf(f_499_4,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1324),U_1323))
    | U_1323 != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_499_3]) ).

fof(f_500_1,plain,
    ! [A_3,A_1] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_3),A_1))
      | A_1 != bot_bo844097828e_bool ),
    inference(fof_nnf,[status(thm)],[fact_396_equals0D]) ).

fof(f_500_2,plain,
    ! [U_1326,U_1325] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1326),U_1325))
      | U_1325 != bot_bo844097828e_bool ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

fof(f_500_3,plain,
    ! [U_1325,U_1326] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1326),U_1325))
      | U_1325 != bot_bo844097828e_bool ),
    inference(definitional_conversion,[status(esa)],[f_500_2]) ).

cnf(f_500_4,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1326),U_1325))
    | U_1325 != bot_bo844097828e_bool ),
    inference(clausify,[status(thm)],[f_500_3]) ).

fof(f_501_1,plain,
    ! [A_3,A_1] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_3),A_1))
      | A_1 != bot_bot_fun_a_bool ),
    inference(fof_nnf,[status(thm)],[fact_397_equals0D]) ).

fof(f_501_2,plain,
    ! [U_1328,U_1327] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1328),U_1327))
      | U_1327 != bot_bot_fun_a_bool ),
    inference(variable_rename,[status(thm)],[f_501_1]) ).

fof(f_501_3,plain,
    ! [U_1327,U_1328] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1328),U_1327))
      | U_1327 != bot_bot_fun_a_bool ),
    inference(definitional_conversion,[status(esa)],[f_501_2]) ).

cnf(f_501_4,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1328),U_1327))
    | U_1327 != bot_bot_fun_a_bool ),
    inference(clausify,[status(thm)],[f_501_3]) ).

fof(f_502_1,plain,
    ! [Pa] :
      ( ( collect_pname(Pa) = bot_bo844097828e_bool
        | ? [X_1] :
            ( hBOOL(hAPP_pname_bool(Pa,X_1))
            & is_pname(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_pname_bool(Pa,X_1))
            | ~ is_pname(X_1) )
        | collect_pname(Pa) != bot_bo844097828e_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_398_Collect__empty__eq]) ).

fof(f_502_2,plain,
    ! [U_1331] :
      ( ( collect_pname(U_1331) = bot_bo844097828e_bool
        | ? [U_1330] :
            ( hBOOL(hAPP_pname_bool(U_1331,U_1330))
            & is_pname(U_1330) ) )
      & ( ! [U_1329] :
            ( ~ hBOOL(hAPP_pname_bool(U_1331,U_1329))
            | ~ is_pname(U_1329) )
        | collect_pname(U_1331) != bot_bo844097828e_bool ) ),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

fof(f_502_3,plain,
    ( ! [U_1333] :
        ( collect_pname(U_1333) = bot_bo844097828e_bool
        | ? [U_1330] :
            ( hBOOL(hAPP_pname_bool(U_1333,U_1330))
            & is_pname(U_1330) ) )
    & ! [U_1332] :
        ( ! [U_1329] :
            ( ~ hBOOL(hAPP_pname_bool(U_1332,U_1329))
            | ~ is_pname(U_1329) )
        | collect_pname(U_1332) != bot_bo844097828e_bool ) ),
    inference(miniscope,[status(thm)],[f_502_2]) ).

fof(f_502_4,plain,
    ( ! [U_1333] :
        ( collect_pname(U_1333) = bot_bo844097828e_bool
        | ( hBOOL(hAPP_pname_bool(U_1333,sK85(U_1333)))
          & is_pname(sK85(U_1333)) ) )
    & ! [U_1332] :
        ( ! [U_1329] :
            ( ~ hBOOL(hAPP_pname_bool(U_1332,U_1329))
            | ~ is_pname(U_1329) )
        | collect_pname(U_1332) != bot_bo844097828e_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_1330,sK85(U_1333))],[f_502_3]) ).

fof(f_502_5,plain,
    ( ! [U_1333] :
        ( hBOOL(hAPP_pname_bool(U_1333,sK85(U_1333)))
        | ~ sP131(U_1333) )
    & ! [U_1333] :
        ( is_pname(sK85(U_1333))
        | ~ sP131(U_1333) )
    & ! [U_1333] :
        ( collect_pname(U_1333) = bot_bo844097828e_bool
        | sP131(U_1333) )
    & ! [U_1329,U_1332] :
        ( ~ hBOOL(hAPP_pname_bool(U_1332,U_1329))
        | ~ is_pname(U_1329)
        | collect_pname(U_1332) != bot_bo844097828e_bool ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131])],[f_502_4]) ).

cnf(f_502_6,plain,
    ( ~ hBOOL(hAPP_pname_bool(U_1332,U_1329))
    | ~ is_pname(U_1329)
    | collect_pname(U_1332) != bot_bo844097828e_bool ),
    inference(clausify,[status(thm)],[f_502_5]) ).

cnf(f_502_7,plain,
    ( collect_pname(U_1333) = bot_bo844097828e_bool
    | sP131(U_1333) ),
    inference(clausify,[status(thm)],[f_502_5]) ).

cnf(f_502_8,plain,
    ( is_pname(sK85(U_1333))
    | ~ sP131(U_1333) ),
    inference(clausify,[status(thm)],[f_502_5]) ).

cnf(f_502_9,plain,
    ( hBOOL(hAPP_pname_bool(U_1333,sK85(U_1333)))
    | ~ sP131(U_1333) ),
    inference(clausify,[status(thm)],[f_502_5]) ).

fof(f_503_1,plain,
    ! [Pa] :
      ( ( collect_fun_nat_bool(Pa) = bot_bo1701429464l_bool
        | ? [X_1] : hBOOL(hAPP_f54304608l_bool(Pa,X_1)) )
      & ( ! [X_1] : ~ hBOOL(hAPP_f54304608l_bool(Pa,X_1))
        | collect_fun_nat_bool(Pa) != bot_bo1701429464l_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_399_Collect__empty__eq]) ).

fof(f_503_2,plain,
    ! [U_1336] :
      ( ( collect_fun_nat_bool(U_1336) = bot_bo1701429464l_bool
        | ? [U_1335] : hBOOL(hAPP_f54304608l_bool(U_1336,U_1335)) )
      & ( ! [U_1334] : ~ hBOOL(hAPP_f54304608l_bool(U_1336,U_1334))
        | collect_fun_nat_bool(U_1336) != bot_bo1701429464l_bool ) ),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

fof(f_503_3,plain,
    ( ! [U_1338] :
        ( collect_fun_nat_bool(U_1338) = bot_bo1701429464l_bool
        | ? [U_1335] : hBOOL(hAPP_f54304608l_bool(U_1338,U_1335)) )
    & ! [U_1337] :
        ( ! [U_1334] : ~ hBOOL(hAPP_f54304608l_bool(U_1337,U_1334))
        | collect_fun_nat_bool(U_1337) != bot_bo1701429464l_bool ) ),
    inference(miniscope,[status(thm)],[f_503_2]) ).

fof(f_503_4,plain,
    ( ! [U_1338] :
        ( collect_fun_nat_bool(U_1338) = bot_bo1701429464l_bool
        | hBOOL(hAPP_f54304608l_bool(U_1338,sK86(U_1338))) )
    & ! [U_1337] :
        ( ! [U_1334] : ~ hBOOL(hAPP_f54304608l_bool(U_1337,U_1334))
        | collect_fun_nat_bool(U_1337) != bot_bo1701429464l_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_1335,sK86(U_1338))],[f_503_3]) ).

fof(f_503_5,plain,
    ( ! [U_1338] :
        ( collect_fun_nat_bool(U_1338) = bot_bo1701429464l_bool
        | hBOOL(hAPP_f54304608l_bool(U_1338,sK86(U_1338))) )
    & ! [U_1334,U_1337] :
        ( ~ hBOOL(hAPP_f54304608l_bool(U_1337,U_1334))
        | collect_fun_nat_bool(U_1337) != bot_bo1701429464l_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_503_4]) ).

cnf(f_503_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(U_1337,U_1334))
    | collect_fun_nat_bool(U_1337) != bot_bo1701429464l_bool ),
    inference(clausify,[status(thm)],[f_503_5]) ).

cnf(f_503_7,plain,
    ( collect_fun_nat_bool(U_1338) = bot_bo1701429464l_bool
    | hBOOL(hAPP_f54304608l_bool(U_1338,sK86(U_1338))) ),
    inference(clausify,[status(thm)],[f_503_5]) ).

fof(f_504_1,plain,
    ! [Pa] :
      ( ( collec1974731493e_bool(Pa) = bot_bo1649642514l_bool
        | ? [X_1] :
            ( hBOOL(hAPP_f1664156314l_bool(Pa,X_1))
            & is_fun_pname_bool(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(Pa,X_1))
            | ~ is_fun_pname_bool(X_1) )
        | collec1974731493e_bool(Pa) != bot_bo1649642514l_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_400_Collect__empty__eq]) ).

fof(f_504_2,plain,
    ! [U_1341] :
      ( ( collec1974731493e_bool(U_1341) = bot_bo1649642514l_bool
        | ? [U_1340] :
            ( hBOOL(hAPP_f1664156314l_bool(U_1341,U_1340))
            & is_fun_pname_bool(U_1340) ) )
      & ( ! [U_1339] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(U_1341,U_1339))
            | ~ is_fun_pname_bool(U_1339) )
        | collec1974731493e_bool(U_1341) != bot_bo1649642514l_bool ) ),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

fof(f_504_3,plain,
    ( ! [U_1343] :
        ( collec1974731493e_bool(U_1343) = bot_bo1649642514l_bool
        | ? [U_1340] :
            ( hBOOL(hAPP_f1664156314l_bool(U_1343,U_1340))
            & is_fun_pname_bool(U_1340) ) )
    & ! [U_1342] :
        ( ! [U_1339] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(U_1342,U_1339))
            | ~ is_fun_pname_bool(U_1339) )
        | collec1974731493e_bool(U_1342) != bot_bo1649642514l_bool ) ),
    inference(miniscope,[status(thm)],[f_504_2]) ).

fof(f_504_4,plain,
    ( ! [U_1343] :
        ( collec1974731493e_bool(U_1343) = bot_bo1649642514l_bool
        | ( hBOOL(hAPP_f1664156314l_bool(U_1343,sK87(U_1343)))
          & is_fun_pname_bool(sK87(U_1343)) ) )
    & ! [U_1342] :
        ( ! [U_1339] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(U_1342,U_1339))
            | ~ is_fun_pname_bool(U_1339) )
        | collec1974731493e_bool(U_1342) != bot_bo1649642514l_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_1340,sK87(U_1343))],[f_504_3]) ).

fof(f_504_5,plain,
    ( ! [U_1343] :
        ( hBOOL(hAPP_f1664156314l_bool(U_1343,sK87(U_1343)))
        | ~ sP132(U_1343) )
    & ! [U_1343] :
        ( is_fun_pname_bool(sK87(U_1343))
        | ~ sP132(U_1343) )
    & ! [U_1343] :
        ( collec1974731493e_bool(U_1343) = bot_bo1649642514l_bool
        | sP132(U_1343) )
    & ! [U_1339,U_1342] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(U_1342,U_1339))
        | ~ is_fun_pname_bool(U_1339)
        | collec1974731493e_bool(U_1342) != bot_bo1649642514l_bool ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP132])],[f_504_4]) ).

cnf(f_504_6,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(U_1342,U_1339))
    | ~ is_fun_pname_bool(U_1339)
    | collec1974731493e_bool(U_1342) != bot_bo1649642514l_bool ),
    inference(clausify,[status(thm)],[f_504_5]) ).

cnf(f_504_7,plain,
    ( collec1974731493e_bool(U_1343) = bot_bo1649642514l_bool
    | sP132(U_1343) ),
    inference(clausify,[status(thm)],[f_504_5]) ).

cnf(f_504_8,plain,
    ( is_fun_pname_bool(sK87(U_1343))
    | ~ sP132(U_1343) ),
    inference(clausify,[status(thm)],[f_504_5]) ).

cnf(f_504_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_1343,sK87(U_1343)))
    | ~ sP132(U_1343) ),
    inference(clausify,[status(thm)],[f_504_5]) ).

fof(f_505_1,plain,
    ! [Pa] :
      ( ( collect_fun_a_bool(Pa) = bot_bo1389914601l_bool
        | ? [X_1] :
            ( hBOOL(hAPP_fun_a_bool_bool(Pa,X_1))
            & is_fun_a_bool(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(Pa,X_1))
            | ~ is_fun_a_bool(X_1) )
        | collect_fun_a_bool(Pa) != bot_bo1389914601l_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_401_Collect__empty__eq]) ).

fof(f_505_2,plain,
    ! [U_1346] :
      ( ( collect_fun_a_bool(U_1346) = bot_bo1389914601l_bool
        | ? [U_1345] :
            ( hBOOL(hAPP_fun_a_bool_bool(U_1346,U_1345))
            & is_fun_a_bool(U_1345) ) )
      & ( ! [U_1344] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1346,U_1344))
            | ~ is_fun_a_bool(U_1344) )
        | collect_fun_a_bool(U_1346) != bot_bo1389914601l_bool ) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

fof(f_505_3,plain,
    ( ! [U_1348] :
        ( collect_fun_a_bool(U_1348) = bot_bo1389914601l_bool
        | ? [U_1345] :
            ( hBOOL(hAPP_fun_a_bool_bool(U_1348,U_1345))
            & is_fun_a_bool(U_1345) ) )
    & ! [U_1347] :
        ( ! [U_1344] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1347,U_1344))
            | ~ is_fun_a_bool(U_1344) )
        | collect_fun_a_bool(U_1347) != bot_bo1389914601l_bool ) ),
    inference(miniscope,[status(thm)],[f_505_2]) ).

fof(f_505_4,plain,
    ( ! [U_1348] :
        ( collect_fun_a_bool(U_1348) = bot_bo1389914601l_bool
        | ( hBOOL(hAPP_fun_a_bool_bool(U_1348,sK88(U_1348)))
          & is_fun_a_bool(sK88(U_1348)) ) )
    & ! [U_1347] :
        ( ! [U_1344] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1347,U_1344))
            | ~ is_fun_a_bool(U_1344) )
        | collect_fun_a_bool(U_1347) != bot_bo1389914601l_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_1345,sK88(U_1348))],[f_505_3]) ).

fof(f_505_5,plain,
    ( ! [U_1348] :
        ( hBOOL(hAPP_fun_a_bool_bool(U_1348,sK88(U_1348)))
        | ~ sP133(U_1348) )
    & ! [U_1348] :
        ( is_fun_a_bool(sK88(U_1348))
        | ~ sP133(U_1348) )
    & ! [U_1348] :
        ( collect_fun_a_bool(U_1348) = bot_bo1389914601l_bool
        | sP133(U_1348) )
    & ! [U_1347,U_1344] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1347,U_1344))
        | ~ is_fun_a_bool(U_1344)
        | collect_fun_a_bool(U_1347) != bot_bo1389914601l_bool ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133])],[f_505_4]) ).

cnf(f_505_6,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1347,U_1344))
    | ~ is_fun_a_bool(U_1344)
    | collect_fun_a_bool(U_1347) != bot_bo1389914601l_bool ),
    inference(clausify,[status(thm)],[f_505_5]) ).

cnf(f_505_7,plain,
    ( collect_fun_a_bool(U_1348) = bot_bo1389914601l_bool
    | sP133(U_1348) ),
    inference(clausify,[status(thm)],[f_505_5]) ).

cnf(f_505_8,plain,
    ( is_fun_a_bool(sK88(U_1348))
    | ~ sP133(U_1348) ),
    inference(clausify,[status(thm)],[f_505_5]) ).

cnf(f_505_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(U_1348,sK88(U_1348)))
    | ~ sP133(U_1348) ),
    inference(clausify,[status(thm)],[f_505_5]) ).

fof(f_506_1,plain,
    ! [Pa] :
      ( ( collect_a(Pa) = bot_bot_fun_a_bool
        | ? [X_1] :
            ( hBOOL(hAPP_a_bool(Pa,X_1))
            & is_a(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_a_bool(Pa,X_1))
            | ~ is_a(X_1) )
        | collect_a(Pa) != bot_bot_fun_a_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_402_Collect__empty__eq]) ).

fof(f_506_2,plain,
    ! [U_1351] :
      ( ( collect_a(U_1351) = bot_bot_fun_a_bool
        | ? [U_1350] :
            ( hBOOL(hAPP_a_bool(U_1351,U_1350))
            & is_a(U_1350) ) )
      & ( ! [U_1349] :
            ( ~ hBOOL(hAPP_a_bool(U_1351,U_1349))
            | ~ is_a(U_1349) )
        | collect_a(U_1351) != bot_bot_fun_a_bool ) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

fof(f_506_3,plain,
    ( ! [U_1353] :
        ( collect_a(U_1353) = bot_bot_fun_a_bool
        | ? [U_1350] :
            ( hBOOL(hAPP_a_bool(U_1353,U_1350))
            & is_a(U_1350) ) )
    & ! [U_1352] :
        ( ! [U_1349] :
            ( ~ hBOOL(hAPP_a_bool(U_1352,U_1349))
            | ~ is_a(U_1349) )
        | collect_a(U_1352) != bot_bot_fun_a_bool ) ),
    inference(miniscope,[status(thm)],[f_506_2]) ).

fof(f_506_4,plain,
    ( ! [U_1353] :
        ( collect_a(U_1353) = bot_bot_fun_a_bool
        | ( hBOOL(hAPP_a_bool(U_1353,sK89(U_1353)))
          & is_a(sK89(U_1353)) ) )
    & ! [U_1352] :
        ( ! [U_1349] :
            ( ~ hBOOL(hAPP_a_bool(U_1352,U_1349))
            | ~ is_a(U_1349) )
        | collect_a(U_1352) != bot_bot_fun_a_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_1350,sK89(U_1353))],[f_506_3]) ).

fof(f_506_5,plain,
    ( ! [U_1353] :
        ( hBOOL(hAPP_a_bool(U_1353,sK89(U_1353)))
        | ~ sP134(U_1353) )
    & ! [U_1353] :
        ( is_a(sK89(U_1353))
        | ~ sP134(U_1353) )
    & ! [U_1353] :
        ( collect_a(U_1353) = bot_bot_fun_a_bool
        | sP134(U_1353) )
    & ! [U_1349,U_1352] :
        ( ~ hBOOL(hAPP_a_bool(U_1352,U_1349))
        | ~ is_a(U_1349)
        | collect_a(U_1352) != bot_bot_fun_a_bool ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134])],[f_506_4]) ).

cnf(f_506_6,plain,
    ( ~ hBOOL(hAPP_a_bool(U_1352,U_1349))
    | ~ is_a(U_1349)
    | collect_a(U_1352) != bot_bot_fun_a_bool ),
    inference(clausify,[status(thm)],[f_506_5]) ).

cnf(f_506_7,plain,
    ( collect_a(U_1353) = bot_bot_fun_a_bool
    | sP134(U_1353) ),
    inference(clausify,[status(thm)],[f_506_5]) ).

cnf(f_506_8,plain,
    ( is_a(sK89(U_1353))
    | ~ sP134(U_1353) ),
    inference(clausify,[status(thm)],[f_506_5]) ).

cnf(f_506_9,plain,
    ( hBOOL(hAPP_a_bool(U_1353,sK89(U_1353)))
    | ~ sP134(U_1353) ),
    inference(clausify,[status(thm)],[f_506_5]) ).

fof(f_507_1,plain,
    ! [Pa] :
      ( ( collect_nat(Pa) = bot_bot_fun_nat_bool
        | ? [X_1] : hBOOL(hAPP_nat_bool(Pa,X_1)) )
      & ( ! [X_1] : ~ hBOOL(hAPP_nat_bool(Pa,X_1))
        | collect_nat(Pa) != bot_bot_fun_nat_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_403_Collect__empty__eq]) ).

fof(f_507_2,plain,
    ! [U_1356] :
      ( ( collect_nat(U_1356) = bot_bot_fun_nat_bool
        | ? [U_1355] : hBOOL(hAPP_nat_bool(U_1356,U_1355)) )
      & ( ! [U_1354] : ~ hBOOL(hAPP_nat_bool(U_1356,U_1354))
        | collect_nat(U_1356) != bot_bot_fun_nat_bool ) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

fof(f_507_3,plain,
    ( ! [U_1358] :
        ( collect_nat(U_1358) = bot_bot_fun_nat_bool
        | ? [U_1355] : hBOOL(hAPP_nat_bool(U_1358,U_1355)) )
    & ! [U_1357] :
        ( ! [U_1354] : ~ hBOOL(hAPP_nat_bool(U_1357,U_1354))
        | collect_nat(U_1357) != bot_bot_fun_nat_bool ) ),
    inference(miniscope,[status(thm)],[f_507_2]) ).

fof(f_507_4,plain,
    ( ! [U_1358] :
        ( collect_nat(U_1358) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_1358,sK90(U_1358))) )
    & ! [U_1357] :
        ( ! [U_1354] : ~ hBOOL(hAPP_nat_bool(U_1357,U_1354))
        | collect_nat(U_1357) != bot_bot_fun_nat_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_1355,sK90(U_1358))],[f_507_3]) ).

fof(f_507_5,plain,
    ( ! [U_1358] :
        ( collect_nat(U_1358) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_1358,sK90(U_1358))) )
    & ! [U_1354,U_1357] :
        ( ~ hBOOL(hAPP_nat_bool(U_1357,U_1354))
        | collect_nat(U_1357) != bot_bot_fun_nat_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_507_4]) ).

cnf(f_507_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_1357,U_1354))
    | collect_nat(U_1357) != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_507_5]) ).

cnf(f_507_7,plain,
    ( collect_nat(U_1358) = bot_bot_fun_nat_bool
    | hBOOL(hAPP_nat_bool(U_1358,sK90(U_1358))) ),
    inference(clausify,[status(thm)],[f_507_5]) ).

fof(f_508_1,plain,
    ! [C_1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),bot_bot_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_404_empty__iff]) ).

fof(f_508_2,plain,
    ! [U_1359] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1359),bot_bot_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

fof(f_508_3,plain,
    ! [U_1359] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1359),bot_bot_fun_nat_bool)),
    inference(definitional_conversion,[status(esa)],[f_508_2]) ).

cnf(f_508_4,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1359),bot_bot_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_508_3]) ).

fof(f_509_1,plain,
    ! [C_1] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),bot_bo844097828e_bool)),
    inference(fof_nnf,[status(thm)],[fact_405_empty__iff]) ).

fof(f_509_2,plain,
    ! [U_1360] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1360),bot_bo844097828e_bool)),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

fof(f_509_3,plain,
    ! [U_1360] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1360),bot_bo844097828e_bool)),
    inference(definitional_conversion,[status(esa)],[f_509_2]) ).

cnf(f_509_4,plain,
    ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1360),bot_bo844097828e_bool)),
    inference(clausify,[status(thm)],[f_509_3]) ).

fof(f_510_1,plain,
    ! [C_1] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),bot_bot_fun_a_bool)),
    inference(fof_nnf,[status(thm)],[fact_406_empty__iff]) ).

fof(f_510_2,plain,
    ! [U_1361] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1361),bot_bot_fun_a_bool)),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

fof(f_510_3,plain,
    ! [U_1361] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1361),bot_bot_fun_a_bool)),
    inference(definitional_conversion,[status(esa)],[f_510_2]) ).

cnf(f_510_4,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1361),bot_bot_fun_a_bool)),
    inference(clausify,[status(thm)],[f_510_3]) ).

fof(f_511_1,plain,
    ! [Pa] :
      ( ( bot_bo844097828e_bool = collect_pname(Pa)
        | ? [X_1] :
            ( hBOOL(hAPP_pname_bool(Pa,X_1))
            & is_pname(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_pname_bool(Pa,X_1))
            | ~ is_pname(X_1) )
        | bot_bo844097828e_bool != collect_pname(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_407_empty__Collect__eq]) ).

fof(f_511_2,plain,
    ! [U_1364] :
      ( ( bot_bo844097828e_bool = collect_pname(U_1364)
        | ? [U_1363] :
            ( hBOOL(hAPP_pname_bool(U_1364,U_1363))
            & is_pname(U_1363) ) )
      & ( ! [U_1362] :
            ( ~ hBOOL(hAPP_pname_bool(U_1364,U_1362))
            | ~ is_pname(U_1362) )
        | bot_bo844097828e_bool != collect_pname(U_1364) ) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

fof(f_511_3,plain,
    ( ! [U_1366] :
        ( bot_bo844097828e_bool = collect_pname(U_1366)
        | ? [U_1363] :
            ( hBOOL(hAPP_pname_bool(U_1366,U_1363))
            & is_pname(U_1363) ) )
    & ! [U_1365] :
        ( ! [U_1362] :
            ( ~ hBOOL(hAPP_pname_bool(U_1365,U_1362))
            | ~ is_pname(U_1362) )
        | bot_bo844097828e_bool != collect_pname(U_1365) ) ),
    inference(miniscope,[status(thm)],[f_511_2]) ).

fof(f_511_4,plain,
    ( ! [U_1366] :
        ( bot_bo844097828e_bool = collect_pname(U_1366)
        | ( hBOOL(hAPP_pname_bool(U_1366,sK91(U_1366)))
          & is_pname(sK91(U_1366)) ) )
    & ! [U_1365] :
        ( ! [U_1362] :
            ( ~ hBOOL(hAPP_pname_bool(U_1365,U_1362))
            | ~ is_pname(U_1362) )
        | bot_bo844097828e_bool != collect_pname(U_1365) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_1363,sK91(U_1366))],[f_511_3]) ).

fof(f_511_5,plain,
    ( ! [U_1366] :
        ( hBOOL(hAPP_pname_bool(U_1366,sK91(U_1366)))
        | ~ sP135(U_1366) )
    & ! [U_1366] :
        ( is_pname(sK91(U_1366))
        | ~ sP135(U_1366) )
    & ! [U_1366] :
        ( bot_bo844097828e_bool = collect_pname(U_1366)
        | sP135(U_1366) )
    & ! [U_1362,U_1365] :
        ( ~ hBOOL(hAPP_pname_bool(U_1365,U_1362))
        | ~ is_pname(U_1362)
        | bot_bo844097828e_bool != collect_pname(U_1365) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP135])],[f_511_4]) ).

cnf(f_511_6,plain,
    ( ~ hBOOL(hAPP_pname_bool(U_1365,U_1362))
    | ~ is_pname(U_1362)
    | bot_bo844097828e_bool != collect_pname(U_1365) ),
    inference(clausify,[status(thm)],[f_511_5]) ).

cnf(f_511_7,plain,
    ( bot_bo844097828e_bool = collect_pname(U_1366)
    | sP135(U_1366) ),
    inference(clausify,[status(thm)],[f_511_5]) ).

cnf(f_511_8,plain,
    ( is_pname(sK91(U_1366))
    | ~ sP135(U_1366) ),
    inference(clausify,[status(thm)],[f_511_5]) ).

cnf(f_511_9,plain,
    ( hBOOL(hAPP_pname_bool(U_1366,sK91(U_1366)))
    | ~ sP135(U_1366) ),
    inference(clausify,[status(thm)],[f_511_5]) ).

fof(f_512_1,plain,
    ! [Pa] :
      ( ( bot_bo1701429464l_bool = collect_fun_nat_bool(Pa)
        | ? [X_1] : hBOOL(hAPP_f54304608l_bool(Pa,X_1)) )
      & ( ! [X_1] : ~ hBOOL(hAPP_f54304608l_bool(Pa,X_1))
        | bot_bo1701429464l_bool != collect_fun_nat_bool(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_408_empty__Collect__eq]) ).

fof(f_512_2,plain,
    ! [U_1369] :
      ( ( bot_bo1701429464l_bool = collect_fun_nat_bool(U_1369)
        | ? [U_1368] : hBOOL(hAPP_f54304608l_bool(U_1369,U_1368)) )
      & ( ! [U_1367] : ~ hBOOL(hAPP_f54304608l_bool(U_1369,U_1367))
        | bot_bo1701429464l_bool != collect_fun_nat_bool(U_1369) ) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

fof(f_512_3,plain,
    ( ! [U_1371] :
        ( bot_bo1701429464l_bool = collect_fun_nat_bool(U_1371)
        | ? [U_1368] : hBOOL(hAPP_f54304608l_bool(U_1371,U_1368)) )
    & ! [U_1370] :
        ( ! [U_1367] : ~ hBOOL(hAPP_f54304608l_bool(U_1370,U_1367))
        | bot_bo1701429464l_bool != collect_fun_nat_bool(U_1370) ) ),
    inference(miniscope,[status(thm)],[f_512_2]) ).

fof(f_512_4,plain,
    ( ! [U_1371] :
        ( bot_bo1701429464l_bool = collect_fun_nat_bool(U_1371)
        | hBOOL(hAPP_f54304608l_bool(U_1371,sK92(U_1371))) )
    & ! [U_1370] :
        ( ! [U_1367] : ~ hBOOL(hAPP_f54304608l_bool(U_1370,U_1367))
        | bot_bo1701429464l_bool != collect_fun_nat_bool(U_1370) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_1368,sK92(U_1371))],[f_512_3]) ).

fof(f_512_5,plain,
    ( ! [U_1371] :
        ( bot_bo1701429464l_bool = collect_fun_nat_bool(U_1371)
        | hBOOL(hAPP_f54304608l_bool(U_1371,sK92(U_1371))) )
    & ! [U_1367,U_1370] :
        ( ~ hBOOL(hAPP_f54304608l_bool(U_1370,U_1367))
        | bot_bo1701429464l_bool != collect_fun_nat_bool(U_1370) ) ),
    inference(definitional_conversion,[status(esa)],[f_512_4]) ).

cnf(f_512_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(U_1370,U_1367))
    | bot_bo1701429464l_bool != collect_fun_nat_bool(U_1370) ),
    inference(clausify,[status(thm)],[f_512_5]) ).

cnf(f_512_7,plain,
    ( bot_bo1701429464l_bool = collect_fun_nat_bool(U_1371)
    | hBOOL(hAPP_f54304608l_bool(U_1371,sK92(U_1371))) ),
    inference(clausify,[status(thm)],[f_512_5]) ).

fof(f_513_1,plain,
    ! [Pa] :
      ( ( bot_bo1649642514l_bool = collec1974731493e_bool(Pa)
        | ? [X_1] :
            ( hBOOL(hAPP_f1664156314l_bool(Pa,X_1))
            & is_fun_pname_bool(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(Pa,X_1))
            | ~ is_fun_pname_bool(X_1) )
        | bot_bo1649642514l_bool != collec1974731493e_bool(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_409_empty__Collect__eq]) ).

fof(f_513_2,plain,
    ! [U_1374] :
      ( ( bot_bo1649642514l_bool = collec1974731493e_bool(U_1374)
        | ? [U_1373] :
            ( hBOOL(hAPP_f1664156314l_bool(U_1374,U_1373))
            & is_fun_pname_bool(U_1373) ) )
      & ( ! [U_1372] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(U_1374,U_1372))
            | ~ is_fun_pname_bool(U_1372) )
        | bot_bo1649642514l_bool != collec1974731493e_bool(U_1374) ) ),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

fof(f_513_3,plain,
    ( ! [U_1376] :
        ( bot_bo1649642514l_bool = collec1974731493e_bool(U_1376)
        | ? [U_1373] :
            ( hBOOL(hAPP_f1664156314l_bool(U_1376,U_1373))
            & is_fun_pname_bool(U_1373) ) )
    & ! [U_1375] :
        ( ! [U_1372] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(U_1375,U_1372))
            | ~ is_fun_pname_bool(U_1372) )
        | bot_bo1649642514l_bool != collec1974731493e_bool(U_1375) ) ),
    inference(miniscope,[status(thm)],[f_513_2]) ).

fof(f_513_4,plain,
    ( ! [U_1376] :
        ( bot_bo1649642514l_bool = collec1974731493e_bool(U_1376)
        | ( hBOOL(hAPP_f1664156314l_bool(U_1376,sK93(U_1376)))
          & is_fun_pname_bool(sK93(U_1376)) ) )
    & ! [U_1375] :
        ( ! [U_1372] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(U_1375,U_1372))
            | ~ is_fun_pname_bool(U_1372) )
        | bot_bo1649642514l_bool != collec1974731493e_bool(U_1375) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_1373,sK93(U_1376))],[f_513_3]) ).

fof(f_513_5,plain,
    ( ! [U_1376] :
        ( hBOOL(hAPP_f1664156314l_bool(U_1376,sK93(U_1376)))
        | ~ sP136(U_1376) )
    & ! [U_1376] :
        ( is_fun_pname_bool(sK93(U_1376))
        | ~ sP136(U_1376) )
    & ! [U_1376] :
        ( bot_bo1649642514l_bool = collec1974731493e_bool(U_1376)
        | sP136(U_1376) )
    & ! [U_1372,U_1375] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(U_1375,U_1372))
        | ~ is_fun_pname_bool(U_1372)
        | bot_bo1649642514l_bool != collec1974731493e_bool(U_1375) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136])],[f_513_4]) ).

cnf(f_513_6,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(U_1375,U_1372))
    | ~ is_fun_pname_bool(U_1372)
    | bot_bo1649642514l_bool != collec1974731493e_bool(U_1375) ),
    inference(clausify,[status(thm)],[f_513_5]) ).

cnf(f_513_7,plain,
    ( bot_bo1649642514l_bool = collec1974731493e_bool(U_1376)
    | sP136(U_1376) ),
    inference(clausify,[status(thm)],[f_513_5]) ).

cnf(f_513_8,plain,
    ( is_fun_pname_bool(sK93(U_1376))
    | ~ sP136(U_1376) ),
    inference(clausify,[status(thm)],[f_513_5]) ).

cnf(f_513_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_1376,sK93(U_1376)))
    | ~ sP136(U_1376) ),
    inference(clausify,[status(thm)],[f_513_5]) ).

fof(f_514_1,plain,
    ! [Pa] :
      ( ( bot_bo1389914601l_bool = collect_fun_a_bool(Pa)
        | ? [X_1] :
            ( hBOOL(hAPP_fun_a_bool_bool(Pa,X_1))
            & is_fun_a_bool(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(Pa,X_1))
            | ~ is_fun_a_bool(X_1) )
        | bot_bo1389914601l_bool != collect_fun_a_bool(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_410_empty__Collect__eq]) ).

fof(f_514_2,plain,
    ! [U_1379] :
      ( ( bot_bo1389914601l_bool = collect_fun_a_bool(U_1379)
        | ? [U_1378] :
            ( hBOOL(hAPP_fun_a_bool_bool(U_1379,U_1378))
            & is_fun_a_bool(U_1378) ) )
      & ( ! [U_1377] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1379,U_1377))
            | ~ is_fun_a_bool(U_1377) )
        | bot_bo1389914601l_bool != collect_fun_a_bool(U_1379) ) ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

fof(f_514_3,plain,
    ( ! [U_1381] :
        ( bot_bo1389914601l_bool = collect_fun_a_bool(U_1381)
        | ? [U_1378] :
            ( hBOOL(hAPP_fun_a_bool_bool(U_1381,U_1378))
            & is_fun_a_bool(U_1378) ) )
    & ! [U_1380] :
        ( ! [U_1377] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1380,U_1377))
            | ~ is_fun_a_bool(U_1377) )
        | bot_bo1389914601l_bool != collect_fun_a_bool(U_1380) ) ),
    inference(miniscope,[status(thm)],[f_514_2]) ).

fof(f_514_4,plain,
    ( ! [U_1381] :
        ( bot_bo1389914601l_bool = collect_fun_a_bool(U_1381)
        | ( hBOOL(hAPP_fun_a_bool_bool(U_1381,sK94(U_1381)))
          & is_fun_a_bool(sK94(U_1381)) ) )
    & ! [U_1380] :
        ( ! [U_1377] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1380,U_1377))
            | ~ is_fun_a_bool(U_1377) )
        | bot_bo1389914601l_bool != collect_fun_a_bool(U_1380) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_1378,sK94(U_1381))],[f_514_3]) ).

fof(f_514_5,plain,
    ( ! [U_1381] :
        ( hBOOL(hAPP_fun_a_bool_bool(U_1381,sK94(U_1381)))
        | ~ sP137(U_1381) )
    & ! [U_1381] :
        ( is_fun_a_bool(sK94(U_1381))
        | ~ sP137(U_1381) )
    & ! [U_1381] :
        ( bot_bo1389914601l_bool = collect_fun_a_bool(U_1381)
        | sP137(U_1381) )
    & ! [U_1377,U_1380] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1380,U_1377))
        | ~ is_fun_a_bool(U_1377)
        | bot_bo1389914601l_bool != collect_fun_a_bool(U_1380) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137])],[f_514_4]) ).

cnf(f_514_6,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1380,U_1377))
    | ~ is_fun_a_bool(U_1377)
    | bot_bo1389914601l_bool != collect_fun_a_bool(U_1380) ),
    inference(clausify,[status(thm)],[f_514_5]) ).

cnf(f_514_7,plain,
    ( bot_bo1389914601l_bool = collect_fun_a_bool(U_1381)
    | sP137(U_1381) ),
    inference(clausify,[status(thm)],[f_514_5]) ).

cnf(f_514_8,plain,
    ( is_fun_a_bool(sK94(U_1381))
    | ~ sP137(U_1381) ),
    inference(clausify,[status(thm)],[f_514_5]) ).

cnf(f_514_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(U_1381,sK94(U_1381)))
    | ~ sP137(U_1381) ),
    inference(clausify,[status(thm)],[f_514_5]) ).

fof(f_515_1,plain,
    ! [Pa] :
      ( ( bot_bot_fun_a_bool = collect_a(Pa)
        | ? [X_1] :
            ( hBOOL(hAPP_a_bool(Pa,X_1))
            & is_a(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_a_bool(Pa,X_1))
            | ~ is_a(X_1) )
        | bot_bot_fun_a_bool != collect_a(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_411_empty__Collect__eq]) ).

fof(f_515_2,plain,
    ! [U_1384] :
      ( ( bot_bot_fun_a_bool = collect_a(U_1384)
        | ? [U_1383] :
            ( hBOOL(hAPP_a_bool(U_1384,U_1383))
            & is_a(U_1383) ) )
      & ( ! [U_1382] :
            ( ~ hBOOL(hAPP_a_bool(U_1384,U_1382))
            | ~ is_a(U_1382) )
        | bot_bot_fun_a_bool != collect_a(U_1384) ) ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

fof(f_515_3,plain,
    ( ! [U_1386] :
        ( bot_bot_fun_a_bool = collect_a(U_1386)
        | ? [U_1383] :
            ( hBOOL(hAPP_a_bool(U_1386,U_1383))
            & is_a(U_1383) ) )
    & ! [U_1385] :
        ( ! [U_1382] :
            ( ~ hBOOL(hAPP_a_bool(U_1385,U_1382))
            | ~ is_a(U_1382) )
        | bot_bot_fun_a_bool != collect_a(U_1385) ) ),
    inference(miniscope,[status(thm)],[f_515_2]) ).

fof(f_515_4,plain,
    ( ! [U_1386] :
        ( bot_bot_fun_a_bool = collect_a(U_1386)
        | ( hBOOL(hAPP_a_bool(U_1386,sK95(U_1386)))
          & is_a(sK95(U_1386)) ) )
    & ! [U_1385] :
        ( ! [U_1382] :
            ( ~ hBOOL(hAPP_a_bool(U_1385,U_1382))
            | ~ is_a(U_1382) )
        | bot_bot_fun_a_bool != collect_a(U_1385) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_1383,sK95(U_1386))],[f_515_3]) ).

fof(f_515_5,plain,
    ( ! [U_1386] :
        ( hBOOL(hAPP_a_bool(U_1386,sK95(U_1386)))
        | ~ sP138(U_1386) )
    & ! [U_1386] :
        ( is_a(sK95(U_1386))
        | ~ sP138(U_1386) )
    & ! [U_1386] :
        ( bot_bot_fun_a_bool = collect_a(U_1386)
        | sP138(U_1386) )
    & ! [U_1382,U_1385] :
        ( ~ hBOOL(hAPP_a_bool(U_1385,U_1382))
        | ~ is_a(U_1382)
        | bot_bot_fun_a_bool != collect_a(U_1385) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138])],[f_515_4]) ).

cnf(f_515_6,plain,
    ( ~ hBOOL(hAPP_a_bool(U_1385,U_1382))
    | ~ is_a(U_1382)
    | bot_bot_fun_a_bool != collect_a(U_1385) ),
    inference(clausify,[status(thm)],[f_515_5]) ).

cnf(f_515_7,plain,
    ( bot_bot_fun_a_bool = collect_a(U_1386)
    | sP138(U_1386) ),
    inference(clausify,[status(thm)],[f_515_5]) ).

cnf(f_515_8,plain,
    ( is_a(sK95(U_1386))
    | ~ sP138(U_1386) ),
    inference(clausify,[status(thm)],[f_515_5]) ).

cnf(f_515_9,plain,
    ( hBOOL(hAPP_a_bool(U_1386,sK95(U_1386)))
    | ~ sP138(U_1386) ),
    inference(clausify,[status(thm)],[f_515_5]) ).

fof(f_516_1,plain,
    ! [Pa] :
      ( ( bot_bot_fun_nat_bool = collect_nat(Pa)
        | ? [X_1] : hBOOL(hAPP_nat_bool(Pa,X_1)) )
      & ( ! [X_1] : ~ hBOOL(hAPP_nat_bool(Pa,X_1))
        | bot_bot_fun_nat_bool != collect_nat(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_412_empty__Collect__eq]) ).

fof(f_516_2,plain,
    ! [U_1389] :
      ( ( bot_bot_fun_nat_bool = collect_nat(U_1389)
        | ? [U_1388] : hBOOL(hAPP_nat_bool(U_1389,U_1388)) )
      & ( ! [U_1387] : ~ hBOOL(hAPP_nat_bool(U_1389,U_1387))
        | bot_bot_fun_nat_bool != collect_nat(U_1389) ) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

fof(f_516_3,plain,
    ( ! [U_1391] :
        ( bot_bot_fun_nat_bool = collect_nat(U_1391)
        | ? [U_1388] : hBOOL(hAPP_nat_bool(U_1391,U_1388)) )
    & ! [U_1390] :
        ( ! [U_1387] : ~ hBOOL(hAPP_nat_bool(U_1390,U_1387))
        | bot_bot_fun_nat_bool != collect_nat(U_1390) ) ),
    inference(miniscope,[status(thm)],[f_516_2]) ).

fof(f_516_4,plain,
    ( ! [U_1391] :
        ( bot_bot_fun_nat_bool = collect_nat(U_1391)
        | hBOOL(hAPP_nat_bool(U_1391,sK96(U_1391))) )
    & ! [U_1390] :
        ( ! [U_1387] : ~ hBOOL(hAPP_nat_bool(U_1390,U_1387))
        | bot_bot_fun_nat_bool != collect_nat(U_1390) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_1388,sK96(U_1391))],[f_516_3]) ).

fof(f_516_5,plain,
    ( ! [U_1391] :
        ( bot_bot_fun_nat_bool = collect_nat(U_1391)
        | hBOOL(hAPP_nat_bool(U_1391,sK96(U_1391))) )
    & ! [U_1390,U_1387] :
        ( ~ hBOOL(hAPP_nat_bool(U_1390,U_1387))
        | bot_bot_fun_nat_bool != collect_nat(U_1390) ) ),
    inference(definitional_conversion,[status(esa)],[f_516_4]) ).

cnf(f_516_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_1390,U_1387))
    | bot_bot_fun_nat_bool != collect_nat(U_1390) ),
    inference(clausify,[status(thm)],[f_516_5]) ).

cnf(f_516_7,plain,
    ( bot_bot_fun_nat_bool = collect_nat(U_1391)
    | hBOOL(hAPP_nat_bool(U_1391,sK96(U_1391))) ),
    inference(clausify,[status(thm)],[f_516_5]) ).

fof(f_517_1,plain,
    ! [A_1] :
      ( ( ? [X_1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
        | A_1 = bot_bot_fun_nat_bool )
      & ( A_1 != bot_bot_fun_nat_bool
        | ! [X_1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_413_ex__in__conv]) ).

fof(f_517_2,plain,
    ! [U_1394] :
      ( ( ? [U_1393] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1393),U_1394))
        | U_1394 = bot_bot_fun_nat_bool )
      & ( U_1394 != bot_bot_fun_nat_bool
        | ! [U_1392] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1392),U_1394)) ) ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

fof(f_517_3,plain,
    ( ! [U_1396] :
        ( ? [U_1393] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1393),U_1396))
        | U_1396 = bot_bot_fun_nat_bool )
    & ! [U_1395] :
        ( U_1395 != bot_bot_fun_nat_bool
        | ! [U_1392] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1392),U_1395)) ) ),
    inference(miniscope,[status(thm)],[f_517_2]) ).

fof(f_517_4,plain,
    ( ! [U_1396] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK97(U_1396)),U_1396))
        | U_1396 = bot_bot_fun_nat_bool )
    & ! [U_1395] :
        ( U_1395 != bot_bot_fun_nat_bool
        | ! [U_1392] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1392),U_1395)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_1393,sK97(U_1396))],[f_517_3]) ).

fof(f_517_5,plain,
    ( ! [U_1396] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK97(U_1396)),U_1396))
        | U_1396 = bot_bot_fun_nat_bool )
    & ! [U_1392,U_1395] :
        ( U_1395 != bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1392),U_1395)) ) ),
    inference(definitional_conversion,[status(esa)],[f_517_4]) ).

cnf(f_517_6,plain,
    ( U_1395 != bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1392),U_1395)) ),
    inference(clausify,[status(thm)],[f_517_5]) ).

cnf(f_517_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK97(U_1396)),U_1396))
    | U_1396 = bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_517_5]) ).

fof(f_518_1,plain,
    ! [A_1] :
      ( ( ( ? [X_1] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
              & is_pname(X_1) )
          | A_1 = bot_bo844097828e_bool )
        & ( A_1 != bot_bo844097828e_bool
          | ! [X_1] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
              | ~ is_pname(X_1) ) ) )
      | ~ is_fun_pname_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_414_ex__in__conv]) ).

fof(f_518_2,plain,
    ! [U_1399] :
      ( ( ( ? [U_1398] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1398),U_1399))
              & is_pname(U_1398) )
          | U_1399 = bot_bo844097828e_bool )
        & ( U_1399 != bot_bo844097828e_bool
          | ! [U_1397] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1397),U_1399))
              | ~ is_pname(U_1397) ) ) )
      | ~ is_fun_pname_bool(U_1399) ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

fof(f_518_3,plain,
    ! [U_1399] :
      ( ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK98(U_1399)),U_1399))
            & is_pname(sK98(U_1399)) )
          | U_1399 = bot_bo844097828e_bool )
        & ( U_1399 != bot_bo844097828e_bool
          | ! [U_1397] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1397),U_1399))
              | ~ is_pname(U_1397) ) ) )
      | ~ is_fun_pname_bool(U_1399) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_1398,sK98(U_1399))],[f_518_2]) ).

fof(f_518_4,plain,
    ( ! [U_1399] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK98(U_1399)),U_1399))
        | ~ sP139(U_1399) )
    & ! [U_1399] :
        ( is_pname(sK98(U_1399))
        | ~ sP139(U_1399) )
    & ! [U_1397,U_1399] :
        ( sP139(U_1399)
        | U_1399 = bot_bo844097828e_bool
        | ~ sP140(U_1397,U_1399) )
    & ! [U_1397,U_1399] :
        ( U_1399 != bot_bo844097828e_bool
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1397),U_1399))
        | ~ is_pname(U_1397)
        | ~ sP140(U_1397,U_1399) )
    & ! [U_1397,U_1399] :
        ( sP140(U_1397,U_1399)
        | ~ is_fun_pname_bool(U_1399) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP139,sP140])],[f_518_3]) ).

cnf(f_518_5,plain,
    ( sP140(U_1397,U_1399)
    | ~ is_fun_pname_bool(U_1399) ),
    inference(clausify,[status(thm)],[f_518_4]) ).

cnf(f_518_6,plain,
    ( U_1399 != bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1397),U_1399))
    | ~ is_pname(U_1397)
    | ~ sP140(U_1397,U_1399) ),
    inference(clausify,[status(thm)],[f_518_4]) ).

cnf(f_518_7,plain,
    ( sP139(U_1399)
    | U_1399 = bot_bo844097828e_bool
    | ~ sP140(U_1397,U_1399) ),
    inference(clausify,[status(thm)],[f_518_4]) ).

cnf(f_518_8,plain,
    ( is_pname(sK98(U_1399))
    | ~ sP139(U_1399) ),
    inference(clausify,[status(thm)],[f_518_4]) ).

cnf(f_518_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK98(U_1399)),U_1399))
    | ~ sP139(U_1399) ),
    inference(clausify,[status(thm)],[f_518_4]) ).

fof(f_519_1,plain,
    ! [A_1] :
      ( ( ( ? [X_1] :
              ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
              & is_a(X_1) )
          | A_1 = bot_bot_fun_a_bool )
        & ( A_1 != bot_bot_fun_a_bool
          | ! [X_1] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
              | ~ is_a(X_1) ) ) )
      | ~ is_fun_a_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_415_ex__in__conv]) ).

fof(f_519_2,plain,
    ! [U_1402] :
      ( ( ( ? [U_1401] :
              ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1401),U_1402))
              & is_a(U_1401) )
          | U_1402 = bot_bot_fun_a_bool )
        & ( U_1402 != bot_bot_fun_a_bool
          | ! [U_1400] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1400),U_1402))
              | ~ is_a(U_1400) ) ) )
      | ~ is_fun_a_bool(U_1402) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

fof(f_519_3,plain,
    ! [U_1402] :
      ( ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK99(U_1402)),U_1402))
            & is_a(sK99(U_1402)) )
          | U_1402 = bot_bot_fun_a_bool )
        & ( U_1402 != bot_bot_fun_a_bool
          | ! [U_1400] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1400),U_1402))
              | ~ is_a(U_1400) ) ) )
      | ~ is_fun_a_bool(U_1402) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_1401,sK99(U_1402))],[f_519_2]) ).

fof(f_519_4,plain,
    ( ! [U_1402] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK99(U_1402)),U_1402))
        | ~ sP141(U_1402) )
    & ! [U_1402] :
        ( is_a(sK99(U_1402))
        | ~ sP141(U_1402) )
    & ! [U_1402,U_1400] :
        ( sP141(U_1402)
        | U_1402 = bot_bot_fun_a_bool
        | ~ sP142(U_1402,U_1400) )
    & ! [U_1402,U_1400] :
        ( U_1402 != bot_bot_fun_a_bool
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1400),U_1402))
        | ~ is_a(U_1400)
        | ~ sP142(U_1402,U_1400) )
    & ! [U_1402,U_1400] :
        ( sP142(U_1402,U_1400)
        | ~ is_fun_a_bool(U_1402) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141,sP142])],[f_519_3]) ).

cnf(f_519_5,plain,
    ( sP142(U_1402,U_1400)
    | ~ is_fun_a_bool(U_1402) ),
    inference(clausify,[status(thm)],[f_519_4]) ).

cnf(f_519_6,plain,
    ( U_1402 != bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1400),U_1402))
    | ~ is_a(U_1400)
    | ~ sP142(U_1402,U_1400) ),
    inference(clausify,[status(thm)],[f_519_4]) ).

cnf(f_519_7,plain,
    ( sP141(U_1402)
    | U_1402 = bot_bot_fun_a_bool
    | ~ sP142(U_1402,U_1400) ),
    inference(clausify,[status(thm)],[f_519_4]) ).

cnf(f_519_8,plain,
    ( is_a(sK99(U_1402))
    | ~ sP141(U_1402) ),
    inference(clausify,[status(thm)],[f_519_4]) ).

cnf(f_519_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK99(U_1402)),U_1402))
    | ~ sP141(U_1402) ),
    inference(clausify,[status(thm)],[f_519_4]) ).

fof(f_520_1,plain,
    ! [A_1] :
      ( ( ! [X_1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1))
        | A_1 != bot_bot_fun_nat_bool )
      & ( A_1 = bot_bot_fun_nat_bool
        | ? [X_1] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_416_all__not__in__conv]) ).

fof(f_520_2,plain,
    ! [U_1405] :
      ( ( ! [U_1404] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1404),U_1405))
        | U_1405 != bot_bot_fun_nat_bool )
      & ( U_1405 = bot_bot_fun_nat_bool
        | ? [U_1403] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1403),U_1405)) ) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

fof(f_520_3,plain,
    ( ! [U_1407] :
        ( ! [U_1404] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1404),U_1407))
        | U_1407 != bot_bot_fun_nat_bool )
    & ! [U_1406] :
        ( U_1406 = bot_bot_fun_nat_bool
        | ? [U_1403] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1403),U_1406)) ) ),
    inference(miniscope,[status(thm)],[f_520_2]) ).

fof(f_520_4,plain,
    ( ! [U_1407] :
        ( ! [U_1404] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1404),U_1407))
        | U_1407 != bot_bot_fun_nat_bool )
    & ! [U_1406] :
        ( U_1406 = bot_bot_fun_nat_bool
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK100(U_1406)),U_1406)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_1403,sK100(U_1406))],[f_520_3]) ).

fof(f_520_5,plain,
    ( ! [U_1404,U_1407] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1404),U_1407))
        | U_1407 != bot_bot_fun_nat_bool )
    & ! [U_1406] :
        ( U_1406 = bot_bot_fun_nat_bool
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK100(U_1406)),U_1406)) ) ),
    inference(definitional_conversion,[status(esa)],[f_520_4]) ).

cnf(f_520_6,plain,
    ( U_1406 = bot_bot_fun_nat_bool
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK100(U_1406)),U_1406)) ),
    inference(clausify,[status(thm)],[f_520_5]) ).

cnf(f_520_7,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1404),U_1407))
    | U_1407 != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_520_5]) ).

fof(f_521_1,plain,
    ! [A_1] :
      ( ( ( ! [X_1] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
              | ~ is_pname(X_1) )
          | A_1 != bot_bo844097828e_bool )
        & ( A_1 = bot_bo844097828e_bool
          | ? [X_1] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A_1))
              & is_pname(X_1) ) ) )
      | ~ is_fun_pname_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_417_all__not__in__conv]) ).

fof(f_521_2,plain,
    ! [U_1410] :
      ( ( ( ! [U_1409] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1409),U_1410))
              | ~ is_pname(U_1409) )
          | U_1410 != bot_bo844097828e_bool )
        & ( U_1410 = bot_bo844097828e_bool
          | ? [U_1408] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1408),U_1410))
              & is_pname(U_1408) ) ) )
      | ~ is_fun_pname_bool(U_1410) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

fof(f_521_3,plain,
    ! [U_1410] :
      ( ( ( ! [U_1409] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1409),U_1410))
              | ~ is_pname(U_1409) )
          | U_1410 != bot_bo844097828e_bool )
        & ( U_1410 = bot_bo844097828e_bool
          | ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK101(U_1410)),U_1410))
            & is_pname(sK101(U_1410)) ) ) )
      | ~ is_fun_pname_bool(U_1410) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_1408,sK101(U_1410))],[f_521_2]) ).

fof(f_521_4,plain,
    ( ! [U_1410] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK101(U_1410)),U_1410))
        | ~ sP143(U_1410) )
    & ! [U_1410] :
        ( is_pname(sK101(U_1410))
        | ~ sP143(U_1410) )
    & ! [U_1409,U_1410] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1409),U_1410))
        | ~ is_pname(U_1409)
        | U_1410 != bot_bo844097828e_bool
        | ~ sP144(U_1409,U_1410) )
    & ! [U_1409,U_1410] :
        ( U_1410 = bot_bo844097828e_bool
        | sP143(U_1410)
        | ~ sP144(U_1409,U_1410) )
    & ! [U_1409,U_1410] :
        ( sP144(U_1409,U_1410)
        | ~ is_fun_pname_bool(U_1410) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP143,sP144])],[f_521_3]) ).

cnf(f_521_5,plain,
    ( sP144(U_1409,U_1410)
    | ~ is_fun_pname_bool(U_1410) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_6,plain,
    ( U_1410 = bot_bo844097828e_bool
    | sP143(U_1410)
    | ~ sP144(U_1409,U_1410) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_7,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1409),U_1410))
    | ~ is_pname(U_1409)
    | U_1410 != bot_bo844097828e_bool
    | ~ sP144(U_1409,U_1410) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_8,plain,
    ( is_pname(sK101(U_1410))
    | ~ sP143(U_1410) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK101(U_1410)),U_1410))
    | ~ sP143(U_1410) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

fof(f_522_1,plain,
    ! [A_1] :
      ( ( ( ! [X_1] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
              | ~ is_a(X_1) )
          | A_1 != bot_bot_fun_a_bool )
        & ( A_1 = bot_bot_fun_a_bool
          | ? [X_1] :
              ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A_1))
              & is_a(X_1) ) ) )
      | ~ is_fun_a_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_418_all__not__in__conv]) ).

fof(f_522_2,plain,
    ! [U_1413] :
      ( ( ( ! [U_1412] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1412),U_1413))
              | ~ is_a(U_1412) )
          | U_1413 != bot_bot_fun_a_bool )
        & ( U_1413 = bot_bot_fun_a_bool
          | ? [U_1411] :
              ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1411),U_1413))
              & is_a(U_1411) ) ) )
      | ~ is_fun_a_bool(U_1413) ),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

fof(f_522_3,plain,
    ! [U_1413] :
      ( ( ( ! [U_1412] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1412),U_1413))
              | ~ is_a(U_1412) )
          | U_1413 != bot_bot_fun_a_bool )
        & ( U_1413 = bot_bot_fun_a_bool
          | ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK102(U_1413)),U_1413))
            & is_a(sK102(U_1413)) ) ) )
      | ~ is_fun_a_bool(U_1413) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_1411,sK102(U_1413))],[f_522_2]) ).

fof(f_522_4,plain,
    ( ! [U_1413] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK102(U_1413)),U_1413))
        | ~ sP145(U_1413) )
    & ! [U_1413] :
        ( is_a(sK102(U_1413))
        | ~ sP145(U_1413) )
    & ! [U_1412,U_1413] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1412),U_1413))
        | ~ is_a(U_1412)
        | U_1413 != bot_bot_fun_a_bool
        | ~ sP146(U_1412,U_1413) )
    & ! [U_1412,U_1413] :
        ( U_1413 = bot_bot_fun_a_bool
        | sP145(U_1413)
        | ~ sP146(U_1412,U_1413) )
    & ! [U_1412,U_1413] :
        ( sP146(U_1412,U_1413)
        | ~ is_fun_a_bool(U_1413) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145,sP146])],[f_522_3]) ).

cnf(f_522_5,plain,
    ( sP146(U_1412,U_1413)
    | ~ is_fun_a_bool(U_1413) ),
    inference(clausify,[status(thm)],[f_522_4]) ).

cnf(f_522_6,plain,
    ( U_1413 = bot_bot_fun_a_bool
    | sP145(U_1413)
    | ~ sP146(U_1412,U_1413) ),
    inference(clausify,[status(thm)],[f_522_4]) ).

cnf(f_522_7,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1412),U_1413))
    | ~ is_a(U_1412)
    | U_1413 != bot_bot_fun_a_bool
    | ~ sP146(U_1412,U_1413) ),
    inference(clausify,[status(thm)],[f_522_4]) ).

cnf(f_522_8,plain,
    ( is_a(sK102(U_1413))
    | ~ sP145(U_1413) ),
    inference(clausify,[status(thm)],[f_522_4]) ).

cnf(f_522_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK102(U_1413)),U_1413))
    | ~ sP145(U_1413) ),
    inference(clausify,[status(thm)],[f_522_4]) ).

fof(f_523_1,plain,
    bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_419_empty__def]) ).

fof(f_523_2,plain,
    bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_523_1]) ).

cnf(f_523_3,plain,
    bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)),
    inference(clausify,[status(thm)],[f_523_2]) ).

fof(f_524_1,plain,
    bot_bo1701429464l_bool = collect_fun_nat_bool(cOMBK_1994329625t_bool(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_420_empty__def]) ).

fof(f_524_2,plain,
    bot_bo1701429464l_bool = collect_fun_nat_bool(cOMBK_1994329625t_bool(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_524_1]) ).

cnf(f_524_3,plain,
    bot_bo1701429464l_bool = collect_fun_nat_bool(cOMBK_1994329625t_bool(fFalse)),
    inference(clausify,[status(thm)],[f_524_2]) ).

fof(f_525_1,plain,
    bot_bo1649642514l_bool = collec1974731493e_bool(cOMBK_1857069011e_bool(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_421_empty__def]) ).

fof(f_525_2,plain,
    bot_bo1649642514l_bool = collec1974731493e_bool(cOMBK_1857069011e_bool(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_525_1]) ).

cnf(f_525_3,plain,
    bot_bo1649642514l_bool = collec1974731493e_bool(cOMBK_1857069011e_bool(fFalse)),
    inference(clausify,[status(thm)],[f_525_2]) ).

fof(f_526_1,plain,
    bot_bo1389914601l_bool = collect_fun_a_bool(cOMBK_324466864a_bool(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_422_empty__def]) ).

fof(f_526_2,plain,
    bot_bo1389914601l_bool = collect_fun_a_bool(cOMBK_324466864a_bool(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_526_1]) ).

cnf(f_526_3,plain,
    bot_bo1389914601l_bool = collect_fun_a_bool(cOMBK_324466864a_bool(fFalse)),
    inference(clausify,[status(thm)],[f_526_2]) ).

fof(f_527_1,plain,
    bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_423_empty__def]) ).

fof(f_527_2,plain,
    bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_527_1]) ).

cnf(f_527_3,plain,
    bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
    inference(clausify,[status(thm)],[f_527_2]) ).

fof(f_528_1,plain,
    bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_424_empty__def]) ).

fof(f_528_2,plain,
    bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_528_1]) ).

cnf(f_528_3,plain,
    bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
    inference(clausify,[status(thm)],[f_528_2]) ).

fof(f_529_1,plain,
    ! [X_1] :
      ( ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_1))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_425_bot__fun__def]) ).

fof(f_529_2,plain,
    ! [U_1414] :
      ( ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1414))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1414)) ) ),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

fof(f_529_3,plain,
    ( ( ! [U_1416] : hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1416))
      | ~ hBOOL(bot_bot_bool) )
    & ( ! [U_1415] : ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1415))
      | hBOOL(bot_bot_bool) ) ),
    inference(miniscope,[status(thm)],[f_529_2]) ).

fof(f_529_4,plain,
    ( ! [U_1416] :
        ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1416))
        | ~ hBOOL(bot_bot_bool) )
    & ! [U_1415] :
        ( ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1415))
        | hBOOL(bot_bot_bool) ) ),
    inference(definitional_conversion,[status(esa)],[f_529_3]) ).

cnf(f_529_5,plain,
    ( ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1415))
    | hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_529_4]) ).

cnf(f_529_6,plain,
    ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1416))
    | ~ hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_529_4]) ).

fof(f_530_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_426_bot__fun__def]) ).

fof(f_530_2,plain,
    ! [U_1417] :
      ( ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1417))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1417)) ) ),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

fof(f_530_3,plain,
    ( ( ! [U_1419] : hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1419))
      | ~ hBOOL(bot_bot_bool) )
    & ( ! [U_1418] : ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1418))
      | hBOOL(bot_bot_bool) ) ),
    inference(miniscope,[status(thm)],[f_530_2]) ).

fof(f_530_4,plain,
    ( ! [U_1419] :
        ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1419))
        | ~ hBOOL(bot_bot_bool) )
    & ! [U_1418] :
        ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1418))
        | hBOOL(bot_bot_bool) ) ),
    inference(definitional_conversion,[status(esa)],[f_530_3]) ).

cnf(f_530_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1418))
    | hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_530_4]) ).

cnf(f_530_6,plain,
    ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1419))
    | ~ hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_530_4]) ).

fof(f_531_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_427_bot__fun__def]) ).

fof(f_531_2,plain,
    ! [U_1420] :
      ( ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1420))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1420)) ) ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

fof(f_531_3,plain,
    ( ( ! [U_1422] : hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1422))
      | ~ hBOOL(bot_bot_bool) )
    & ( ! [U_1421] : ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1421))
      | hBOOL(bot_bot_bool) ) ),
    inference(miniscope,[status(thm)],[f_531_2]) ).

fof(f_531_4,plain,
    ( ! [U_1422] :
        ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1422))
        | ~ hBOOL(bot_bot_bool) )
    & ! [U_1421] :
        ( ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1421))
        | hBOOL(bot_bot_bool) ) ),
    inference(definitional_conversion,[status(esa)],[f_531_3]) ).

cnf(f_531_5,plain,
    ( ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1421))
    | hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_531_4]) ).

cnf(f_531_6,plain,
    ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1422))
    | ~ hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_531_4]) ).

fof(f_532_1,plain,
    ! [X_3] :
      ( ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_3))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_428_bot__apply]) ).

fof(f_532_2,plain,
    ! [U_1423] :
      ( ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1423))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1423)) ) ),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

fof(f_532_3,plain,
    ( ( ! [U_1425] : hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1425))
      | ~ hBOOL(bot_bot_bool) )
    & ( ! [U_1424] : ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1424))
      | hBOOL(bot_bot_bool) ) ),
    inference(miniscope,[status(thm)],[f_532_2]) ).

fof(f_532_4,plain,
    ( ! [U_1425] :
        ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1425))
        | ~ hBOOL(bot_bot_bool) )
    & ! [U_1424] :
        ( ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1424))
        | hBOOL(bot_bot_bool) ) ),
    inference(definitional_conversion,[status(esa)],[f_532_3]) ).

cnf(f_532_5,plain,
    ( ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1424))
    | hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_532_4]) ).

cnf(f_532_6,plain,
    ( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,U_1425))
    | ~ hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_532_4]) ).

fof(f_533_1,plain,
    ! [X_3] :
      ( ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_3))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_429_bot__apply]) ).

fof(f_533_2,plain,
    ! [U_1426] :
      ( ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1426))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1426)) ) ),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

fof(f_533_3,plain,
    ( ( ! [U_1428] : hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1428))
      | ~ hBOOL(bot_bot_bool) )
    & ( ! [U_1427] : ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1427))
      | hBOOL(bot_bot_bool) ) ),
    inference(miniscope,[status(thm)],[f_533_2]) ).

fof(f_533_4,plain,
    ( ! [U_1428] :
        ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1428))
        | ~ hBOOL(bot_bot_bool) )
    & ! [U_1427] :
        ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1427))
        | hBOOL(bot_bot_bool) ) ),
    inference(definitional_conversion,[status(esa)],[f_533_3]) ).

cnf(f_533_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1427))
    | hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_533_4]) ).

cnf(f_533_6,plain,
    ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1428))
    | ~ hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_533_4]) ).

fof(f_534_1,plain,
    ! [X_3] :
      ( ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_3))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_430_bot__apply]) ).

fof(f_534_2,plain,
    ! [U_1429] :
      ( ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1429))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1429)) ) ),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

fof(f_534_3,plain,
    ( ( ! [U_1431] : hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1431))
      | ~ hBOOL(bot_bot_bool) )
    & ( ! [U_1430] : ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1430))
      | hBOOL(bot_bot_bool) ) ),
    inference(miniscope,[status(thm)],[f_534_2]) ).

fof(f_534_4,plain,
    ( ! [U_1431] :
        ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1431))
        | ~ hBOOL(bot_bot_bool) )
    & ! [U_1430] :
        ( ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1430))
        | hBOOL(bot_bot_bool) ) ),
    inference(definitional_conversion,[status(esa)],[f_534_3]) ).

cnf(f_534_5,plain,
    ( ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1430))
    | hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_534_4]) ).

cnf(f_534_6,plain,
    ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1431))
    | ~ hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_534_4]) ).

fof(f_535_1,plain,
    ! [A_3] :
      ( A_3 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),bot_bo844097828e_bool))
      | ~ is_fun_pname_bool(A_3) ),
    inference(fof_nnf,[status(thm)],[fact_431_le__bot]) ).

fof(f_535_2,plain,
    ! [U_1432] :
      ( U_1432 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1432),bot_bo844097828e_bool))
      | ~ is_fun_pname_bool(U_1432) ),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

fof(f_535_3,plain,
    ! [U_1432] :
      ( U_1432 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1432),bot_bo844097828e_bool))
      | ~ is_fun_pname_bool(U_1432) ),
    inference(definitional_conversion,[status(esa)],[f_535_2]) ).

cnf(f_535_4,plain,
    ( U_1432 = bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1432),bot_bo844097828e_bool))
    | ~ is_fun_pname_bool(U_1432) ),
    inference(clausify,[status(thm)],[f_535_3]) ).

fof(f_536_1,plain,
    ! [A_3] :
      ( ( ( hBOOL(A_3)
          | ~ hBOOL(bot_bot_bool) )
        & ( hBOOL(bot_bot_bool)
          | ~ hBOOL(A_3) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),bot_bot_bool)) ),
    inference(fof_nnf,[status(thm)],[fact_432_le__bot]) ).

fof(f_536_2,plain,
    ! [U_1433] :
      ( ( ( hBOOL(U_1433)
          | ~ hBOOL(bot_bot_bool) )
        & ( hBOOL(bot_bot_bool)
          | ~ hBOOL(U_1433) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1433),bot_bot_bool)) ),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

fof(f_536_3,plain,
    ( ! [U_1433] :
        ( hBOOL(U_1433)
        | ~ hBOOL(bot_bot_bool)
        | ~ sP147(U_1433) )
    & ! [U_1433] :
        ( hBOOL(bot_bot_bool)
        | ~ hBOOL(U_1433)
        | ~ sP147(U_1433) )
    & ! [U_1433] :
        ( sP147(U_1433)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1433),bot_bot_bool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147])],[f_536_2]) ).

cnf(f_536_4,plain,
    ( sP147(U_1433)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1433),bot_bot_bool)) ),
    inference(clausify,[status(thm)],[f_536_3]) ).

cnf(f_536_5,plain,
    ( hBOOL(bot_bot_bool)
    | ~ hBOOL(U_1433)
    | ~ sP147(U_1433) ),
    inference(clausify,[status(thm)],[f_536_3]) ).

cnf(f_536_6,plain,
    ( hBOOL(U_1433)
    | ~ hBOOL(bot_bot_bool)
    | ~ sP147(U_1433) ),
    inference(clausify,[status(thm)],[f_536_3]) ).

fof(f_537_1,plain,
    ! [A_3] :
      ( A_3 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),bot_bot_fun_nat_bool)) ),
    inference(fof_nnf,[status(thm)],[fact_433_le__bot]) ).

fof(f_537_2,plain,
    ! [U_1434] :
      ( U_1434 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1434),bot_bot_fun_nat_bool)) ),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

fof(f_537_3,plain,
    ! [U_1434] :
      ( U_1434 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1434),bot_bot_fun_nat_bool)) ),
    inference(definitional_conversion,[status(esa)],[f_537_2]) ).

cnf(f_537_4,plain,
    ( U_1434 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1434),bot_bot_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_537_3]) ).

fof(f_538_1,plain,
    ! [A_3] :
      ( A_3 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),bot_bot_fun_a_bool))
      | ~ is_fun_a_bool(A_3) ),
    inference(fof_nnf,[status(thm)],[fact_434_le__bot]) ).

fof(f_538_2,plain,
    ! [U_1435] :
      ( U_1435 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1435),bot_bot_fun_a_bool))
      | ~ is_fun_a_bool(U_1435) ),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

fof(f_538_3,plain,
    ! [U_1435] :
      ( U_1435 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1435),bot_bot_fun_a_bool))
      | ~ is_fun_a_bool(U_1435) ),
    inference(definitional_conversion,[status(esa)],[f_538_2]) ).

cnf(f_538_4,plain,
    ( U_1435 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1435),bot_bot_fun_a_bool))
    | ~ is_fun_a_bool(U_1435) ),
    inference(clausify,[status(thm)],[f_538_3]) ).

fof(f_539_1,plain,
    ! [A_9] :
      ( A_9 = bot_bot_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),bot_bot_nat)) ),
    inference(fof_nnf,[status(thm)],[fact_435_le__bot]) ).

fof(f_539_2,plain,
    ! [U_1436] :
      ( U_1436 = bot_bot_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1436),bot_bot_nat)) ),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

fof(f_539_3,plain,
    ! [U_1436] :
      ( U_1436 = bot_bot_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1436),bot_bot_nat)) ),
    inference(definitional_conversion,[status(esa)],[f_539_2]) ).

cnf(f_539_4,plain,
    ( U_1436 = bot_bot_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1436),bot_bot_nat)) ),
    inference(clausify,[status(thm)],[f_539_3]) ).

fof(f_540_1,plain,
    ! [A_3] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),bot_bo844097828e_bool))
          | A_3 != bot_bo844097828e_bool )
        & ( A_3 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),bot_bo844097828e_bool)) ) )
      | ~ is_fun_pname_bool(A_3) ),
    inference(fof_nnf,[status(thm)],[fact_436_bot__unique]) ).

fof(f_540_2,plain,
    ! [U_1437] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1437),bot_bo844097828e_bool))
          | U_1437 != bot_bo844097828e_bool )
        & ( U_1437 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1437),bot_bo844097828e_bool)) ) )
      | ~ is_fun_pname_bool(U_1437) ),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

fof(f_540_3,plain,
    ( ! [U_1437] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1437),bot_bo844097828e_bool))
        | U_1437 != bot_bo844097828e_bool
        | ~ sP148(U_1437) )
    & ! [U_1437] :
        ( U_1437 = bot_bo844097828e_bool
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1437),bot_bo844097828e_bool))
        | ~ sP148(U_1437) )
    & ! [U_1437] :
        ( sP148(U_1437)
        | ~ is_fun_pname_bool(U_1437) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP148])],[f_540_2]) ).

cnf(f_540_4,plain,
    ( sP148(U_1437)
    | ~ is_fun_pname_bool(U_1437) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

cnf(f_540_5,plain,
    ( U_1437 = bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1437),bot_bo844097828e_bool))
    | ~ sP148(U_1437) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

cnf(f_540_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1437),bot_bo844097828e_bool))
    | U_1437 != bot_bo844097828e_bool
    | ~ sP148(U_1437) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

fof(f_541_1,plain,
    ! [A_3] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),bot_bot_bool))
        | ( ~ hBOOL(A_3)
          & hBOOL(bot_bot_bool) )
        | ( ~ hBOOL(bot_bot_bool)
          & hBOOL(A_3) ) )
      & ( ( ( hBOOL(A_3)
            | ~ hBOOL(bot_bot_bool) )
          & ( hBOOL(bot_bot_bool)
            | ~ hBOOL(A_3) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),bot_bot_bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_437_bot__unique]) ).

fof(f_541_2,plain,
    ! [U_1438] :
      ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1438),bot_bot_bool))
        | ( ~ hBOOL(U_1438)
          & hBOOL(bot_bot_bool) )
        | ( ~ hBOOL(bot_bot_bool)
          & hBOOL(U_1438) ) )
      & ( ( ( hBOOL(U_1438)
            | ~ hBOOL(bot_bot_bool) )
          & ( hBOOL(bot_bot_bool)
            | ~ hBOOL(U_1438) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1438),bot_bot_bool)) ) ),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

fof(f_541_3,plain,
    ( ! [U_1440] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1440),bot_bot_bool))
        | ( ~ hBOOL(U_1440)
          & hBOOL(bot_bot_bool) )
        | ( ~ hBOOL(bot_bot_bool)
          & hBOOL(U_1440) ) )
    & ! [U_1439] :
        ( ( ( hBOOL(U_1439)
            | ~ hBOOL(bot_bot_bool) )
          & ( hBOOL(bot_bot_bool)
            | ~ hBOOL(U_1439) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1439),bot_bot_bool)) ) ),
    inference(miniscope,[status(thm)],[f_541_2]) ).

fof(f_541_4,plain,
    ( ! [U_1440] :
        ( ~ hBOOL(U_1440)
        | ~ sP151(U_1440) )
    & ! [U_1440] :
        ( hBOOL(bot_bot_bool)
        | ~ sP151(U_1440) )
    & ! [U_1440] :
        ( ~ hBOOL(bot_bot_bool)
        | ~ sP150(U_1440) )
    & ! [U_1440] :
        ( hBOOL(U_1440)
        | ~ sP150(U_1440) )
    & ! [U_1439] :
        ( hBOOL(U_1439)
        | ~ hBOOL(bot_bot_bool)
        | ~ sP149(U_1439) )
    & ! [U_1439] :
        ( hBOOL(bot_bot_bool)
        | ~ hBOOL(U_1439)
        | ~ sP149(U_1439) )
    & ! [U_1440] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1440),bot_bot_bool))
        | sP151(U_1440)
        | sP150(U_1440) )
    & ! [U_1439] :
        ( sP149(U_1439)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1439),bot_bot_bool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP149,sP150,sP151])],[f_541_3]) ).

cnf(f_541_5,plain,
    ( sP149(U_1439)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1439),bot_bot_bool)) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

cnf(f_541_6,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1440),bot_bot_bool))
    | sP151(U_1440)
    | sP150(U_1440) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

cnf(f_541_7,plain,
    ( hBOOL(bot_bot_bool)
    | ~ hBOOL(U_1439)
    | ~ sP149(U_1439) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

cnf(f_541_8,plain,
    ( hBOOL(U_1439)
    | ~ hBOOL(bot_bot_bool)
    | ~ sP149(U_1439) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

cnf(f_541_9,plain,
    ( hBOOL(U_1440)
    | ~ sP150(U_1440) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

cnf(f_541_10,plain,
    ( ~ hBOOL(bot_bot_bool)
    | ~ sP150(U_1440) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

cnf(f_541_11,plain,
    ( hBOOL(bot_bot_bool)
    | ~ sP151(U_1440) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

cnf(f_541_12,plain,
    ( ~ hBOOL(U_1440)
    | ~ sP151(U_1440) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

fof(f_542_1,plain,
    ! [A_3] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),bot_bot_fun_nat_bool))
        | A_3 != bot_bot_fun_nat_bool )
      & ( A_3 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),bot_bot_fun_nat_bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_438_bot__unique]) ).

fof(f_542_2,plain,
    ! [U_1441] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1441),bot_bot_fun_nat_bool))
        | U_1441 != bot_bot_fun_nat_bool )
      & ( U_1441 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1441),bot_bot_fun_nat_bool)) ) ),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

fof(f_542_3,plain,
    ( ! [U_1443] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1443),bot_bot_fun_nat_bool))
        | U_1443 != bot_bot_fun_nat_bool )
    & ! [U_1442] :
        ( U_1442 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1442),bot_bot_fun_nat_bool)) ) ),
    inference(miniscope,[status(thm)],[f_542_2]) ).

fof(f_542_4,plain,
    ( ! [U_1443] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1443),bot_bot_fun_nat_bool))
        | U_1443 != bot_bot_fun_nat_bool )
    & ! [U_1442] :
        ( U_1442 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1442),bot_bot_fun_nat_bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_542_3]) ).

cnf(f_542_5,plain,
    ( U_1442 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1442),bot_bot_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_542_4]) ).

cnf(f_542_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1443),bot_bot_fun_nat_bool))
    | U_1443 != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_542_4]) ).

fof(f_543_1,plain,
    ! [A_3] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),bot_bot_fun_a_bool))
          | A_3 != bot_bot_fun_a_bool )
        & ( A_3 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),bot_bot_fun_a_bool)) ) )
      | ~ is_fun_a_bool(A_3) ),
    inference(fof_nnf,[status(thm)],[fact_439_bot__unique]) ).

fof(f_543_2,plain,
    ! [U_1444] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1444),bot_bot_fun_a_bool))
          | U_1444 != bot_bot_fun_a_bool )
        & ( U_1444 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1444),bot_bot_fun_a_bool)) ) )
      | ~ is_fun_a_bool(U_1444) ),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

fof(f_543_3,plain,
    ( ! [U_1444] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1444),bot_bot_fun_a_bool))
        | U_1444 != bot_bot_fun_a_bool
        | ~ sP152(U_1444) )
    & ! [U_1444] :
        ( U_1444 = bot_bot_fun_a_bool
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1444),bot_bot_fun_a_bool))
        | ~ sP152(U_1444) )
    & ! [U_1444] :
        ( sP152(U_1444)
        | ~ is_fun_a_bool(U_1444) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152])],[f_543_2]) ).

cnf(f_543_4,plain,
    ( sP152(U_1444)
    | ~ is_fun_a_bool(U_1444) ),
    inference(clausify,[status(thm)],[f_543_3]) ).

cnf(f_543_5,plain,
    ( U_1444 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1444),bot_bot_fun_a_bool))
    | ~ sP152(U_1444) ),
    inference(clausify,[status(thm)],[f_543_3]) ).

cnf(f_543_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1444),bot_bot_fun_a_bool))
    | U_1444 != bot_bot_fun_a_bool
    | ~ sP152(U_1444) ),
    inference(clausify,[status(thm)],[f_543_3]) ).

fof(f_544_1,plain,
    ! [A_3] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_3),bot_bot_nat))
        | A_3 != bot_bot_nat )
      & ( A_3 = bot_bot_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_3),bot_bot_nat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_440_bot__unique]) ).

fof(f_544_2,plain,
    ! [U_1445] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1445),bot_bot_nat))
        | U_1445 != bot_bot_nat )
      & ( U_1445 = bot_bot_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1445),bot_bot_nat)) ) ),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

fof(f_544_3,plain,
    ( ! [U_1447] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1447),bot_bot_nat))
        | U_1447 != bot_bot_nat )
    & ! [U_1446] :
        ( U_1446 = bot_bot_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1446),bot_bot_nat)) ) ),
    inference(miniscope,[status(thm)],[f_544_2]) ).

fof(f_544_4,plain,
    ( ! [U_1447] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1447),bot_bot_nat))
        | U_1447 != bot_bot_nat )
    & ! [U_1446] :
        ( U_1446 = bot_bot_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1446),bot_bot_nat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_544_3]) ).

cnf(f_544_5,plain,
    ( U_1446 = bot_bot_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1446),bot_bot_nat)) ),
    inference(clausify,[status(thm)],[f_544_4]) ).

cnf(f_544_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1447),bot_bot_nat))
    | U_1447 != bot_bot_nat ),
    inference(clausify,[status(thm)],[f_544_4]) ).

fof(f_545_1,plain,
    ! [A_3] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A_3)),
    inference(fof_nnf,[status(thm)],[fact_441_bot__least]) ).

fof(f_545_2,plain,
    ! [U_1448] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),U_1448)),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

fof(f_545_3,plain,
    ! [U_1448] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),U_1448)),
    inference(definitional_conversion,[status(esa)],[f_545_2]) ).

cnf(f_545_4,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),U_1448)),
    inference(clausify,[status(thm)],[f_545_3]) ).

fof(f_546_1,plain,
    ! [A_3] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A_3)),
    inference(fof_nnf,[status(thm)],[fact_442_bot__least]) ).

fof(f_546_2,plain,
    ! [U_1449] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),U_1449)),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

fof(f_546_3,plain,
    ! [U_1449] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),U_1449)),
    inference(definitional_conversion,[status(esa)],[f_546_2]) ).

cnf(f_546_4,plain,
    hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),U_1449)),
    inference(clausify,[status(thm)],[f_546_3]) ).

fof(f_547_1,plain,
    ! [A_3] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_3)),
    inference(fof_nnf,[status(thm)],[fact_443_bot__least]) ).

fof(f_547_2,plain,
    ! [U_1450] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),U_1450)),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

fof(f_547_3,plain,
    ! [U_1450] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),U_1450)),
    inference(definitional_conversion,[status(esa)],[f_547_2]) ).

cnf(f_547_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),U_1450)),
    inference(clausify,[status(thm)],[f_547_3]) ).

fof(f_548_1,plain,
    ! [A_3] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A_3)),
    inference(fof_nnf,[status(thm)],[fact_444_bot__least]) ).

fof(f_548_2,plain,
    ! [U_1451] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),U_1451)),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

fof(f_548_3,plain,
    ! [U_1451] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),U_1451)),
    inference(definitional_conversion,[status(esa)],[f_548_2]) ).

cnf(f_548_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),U_1451)),
    inference(clausify,[status(thm)],[f_548_3]) ).

fof(f_549_1,plain,
    ! [A_8] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),A_8)),
    inference(fof_nnf,[status(thm)],[fact_445_bot__least]) ).

fof(f_549_2,plain,
    ! [U_1452] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),U_1452)),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

fof(f_549_3,plain,
    ! [U_1452] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),U_1452)),
    inference(definitional_conversion,[status(esa)],[f_549_2]) ).

cnf(f_549_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),U_1452)),
    inference(clausify,[status(thm)],[f_549_3]) ).

fof(f_550_1,plain,
    ! [A_3,B_1] :
      ( A_3 = B_1
      | insert_pname(A_3,bot_bo844097828e_bool) != insert_pname(B_1,bot_bo844097828e_bool)
      | ~ is_pname(B_1)
      | ~ is_pname(A_3) ),
    inference(fof_nnf,[status(thm)],[fact_446_singleton__inject]) ).

fof(f_550_2,plain,
    ! [U_1454,U_1453] :
      ( U_1454 = U_1453
      | insert_pname(U_1454,bot_bo844097828e_bool) != insert_pname(U_1453,bot_bo844097828e_bool)
      | ~ is_pname(U_1453)
      | ~ is_pname(U_1454) ),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

fof(f_550_3,plain,
    ! [U_1454,U_1453] :
      ( U_1454 = U_1453
      | insert_pname(U_1454,bot_bo844097828e_bool) != insert_pname(U_1453,bot_bo844097828e_bool)
      | ~ is_pname(U_1453)
      | ~ is_pname(U_1454) ),
    inference(definitional_conversion,[status(esa)],[f_550_2]) ).

cnf(f_550_4,plain,
    ( U_1454 = U_1453
    | insert_pname(U_1454,bot_bo844097828e_bool) != insert_pname(U_1453,bot_bo844097828e_bool)
    | ~ is_pname(U_1453)
    | ~ is_pname(U_1454) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

fof(f_551_1,plain,
    ! [A_3,B_1] :
      ( A_3 = B_1
      | insert_nat(A_3,bot_bot_fun_nat_bool) != insert_nat(B_1,bot_bot_fun_nat_bool) ),
    inference(fof_nnf,[status(thm)],[fact_447_singleton__inject]) ).

fof(f_551_2,plain,
    ! [U_1456,U_1455] :
      ( U_1456 = U_1455
      | insert_nat(U_1456,bot_bot_fun_nat_bool) != insert_nat(U_1455,bot_bot_fun_nat_bool) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

fof(f_551_3,plain,
    ! [U_1456,U_1455] :
      ( U_1456 = U_1455
      | insert_nat(U_1456,bot_bot_fun_nat_bool) != insert_nat(U_1455,bot_bot_fun_nat_bool) ),
    inference(definitional_conversion,[status(esa)],[f_551_2]) ).

cnf(f_551_4,plain,
    ( U_1456 = U_1455
    | insert_nat(U_1456,bot_bot_fun_nat_bool) != insert_nat(U_1455,bot_bot_fun_nat_bool) ),
    inference(clausify,[status(thm)],[f_551_3]) ).

fof(f_552_1,plain,
    ! [A_3,B_1] :
      ( A_3 = B_1
      | insert_a(A_3,bot_bot_fun_a_bool) != insert_a(B_1,bot_bot_fun_a_bool)
      | ~ is_a(B_1)
      | ~ is_a(A_3) ),
    inference(fof_nnf,[status(thm)],[fact_448_singleton__inject]) ).

fof(f_552_2,plain,
    ! [U_1458,U_1457] :
      ( U_1458 = U_1457
      | insert_a(U_1458,bot_bot_fun_a_bool) != insert_a(U_1457,bot_bot_fun_a_bool)
      | ~ is_a(U_1457)
      | ~ is_a(U_1458) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

fof(f_552_3,plain,
    ! [U_1458,U_1457] :
      ( U_1458 = U_1457
      | insert_a(U_1458,bot_bot_fun_a_bool) != insert_a(U_1457,bot_bot_fun_a_bool)
      | ~ is_a(U_1457)
      | ~ is_a(U_1458) ),
    inference(definitional_conversion,[status(esa)],[f_552_2]) ).

cnf(f_552_4,plain,
    ( U_1458 = U_1457
    | insert_a(U_1458,bot_bot_fun_a_bool) != insert_a(U_1457,bot_bot_fun_a_bool)
    | ~ is_a(U_1457)
    | ~ is_a(U_1458) ),
    inference(clausify,[status(thm)],[f_552_3]) ).

fof(f_553_1,plain,
    ! [B_1,A_3] :
      ( B_1 = A_3
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),insert_nat(A_3,bot_bot_fun_nat_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_449_singletonE]) ).

fof(f_553_2,plain,
    ! [U_1460,U_1459] :
      ( U_1460 = U_1459
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1460),insert_nat(U_1459,bot_bot_fun_nat_bool))) ),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

fof(f_553_3,plain,
    ! [U_1460,U_1459] :
      ( U_1460 = U_1459
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1460),insert_nat(U_1459,bot_bot_fun_nat_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_553_2]) ).

cnf(f_553_4,plain,
    ( U_1460 = U_1459
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1460),insert_nat(U_1459,bot_bot_fun_nat_bool))) ),
    inference(clausify,[status(thm)],[f_553_3]) ).

fof(f_554_1,plain,
    ! [B_1,A_3] :
      ( B_1 = A_3
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_3,bot_bo844097828e_bool)))
      | ~ is_pname(A_3)
      | ~ is_pname(B_1) ),
    inference(fof_nnf,[status(thm)],[fact_450_singletonE]) ).

fof(f_554_2,plain,
    ! [U_1462,U_1461] :
      ( U_1462 = U_1461
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1462),insert_pname(U_1461,bot_bo844097828e_bool)))
      | ~ is_pname(U_1461)
      | ~ is_pname(U_1462) ),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

fof(f_554_3,plain,
    ! [U_1461,U_1462] :
      ( U_1462 = U_1461
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1462),insert_pname(U_1461,bot_bo844097828e_bool)))
      | ~ is_pname(U_1461)
      | ~ is_pname(U_1462) ),
    inference(definitional_conversion,[status(esa)],[f_554_2]) ).

cnf(f_554_4,plain,
    ( U_1462 = U_1461
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1462),insert_pname(U_1461,bot_bo844097828e_bool)))
    | ~ is_pname(U_1461)
    | ~ is_pname(U_1462) ),
    inference(clausify,[status(thm)],[f_554_3]) ).

fof(f_555_1,plain,
    ! [B_1,A_3] :
      ( B_1 = A_3
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),insert_a(A_3,bot_bot_fun_a_bool)))
      | ~ is_a(A_3)
      | ~ is_a(B_1) ),
    inference(fof_nnf,[status(thm)],[fact_451_singletonE]) ).

fof(f_555_2,plain,
    ! [U_1464,U_1463] :
      ( U_1464 = U_1463
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1464),insert_a(U_1463,bot_bot_fun_a_bool)))
      | ~ is_a(U_1463)
      | ~ is_a(U_1464) ),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

fof(f_555_3,plain,
    ! [U_1464,U_1463] :
      ( U_1464 = U_1463
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1464),insert_a(U_1463,bot_bot_fun_a_bool)))
      | ~ is_a(U_1463)
      | ~ is_a(U_1464) ),
    inference(definitional_conversion,[status(esa)],[f_555_2]) ).

cnf(f_555_4,plain,
    ( U_1464 = U_1463
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1464),insert_a(U_1463,bot_bot_fun_a_bool)))
    | ~ is_a(U_1463)
    | ~ is_a(U_1464) ),
    inference(clausify,[status(thm)],[f_555_3]) ).

fof(f_556_1,plain,
    ! [A_3,B_1,C_1,D] :
      ( ( ( insert_pname(A_3,insert_pname(B_1,bot_bo844097828e_bool)) = insert_pname(C_1,insert_pname(D,bot_bo844097828e_bool))
          | ( ( B_1 != C_1
              | A_3 != D )
            & ( B_1 != D
              | A_3 != C_1 ) ) )
        & ( ( B_1 = C_1
            & A_3 = D )
          | ( B_1 = D
            & A_3 = C_1 )
          | insert_pname(A_3,insert_pname(B_1,bot_bo844097828e_bool)) != insert_pname(C_1,insert_pname(D,bot_bo844097828e_bool)) ) )
      | ~ is_pname(D)
      | ~ is_pname(C_1)
      | ~ is_pname(B_1)
      | ~ is_pname(A_3) ),
    inference(fof_nnf,[status(thm)],[fact_452_doubleton__eq__iff]) ).

fof(f_556_2,plain,
    ! [U_1468,U_1467,U_1466,U_1465] :
      ( ( ( insert_pname(U_1468,insert_pname(U_1467,bot_bo844097828e_bool)) = insert_pname(U_1466,insert_pname(U_1465,bot_bo844097828e_bool))
          | ( ( U_1467 != U_1466
              | U_1468 != U_1465 )
            & ( U_1467 != U_1465
              | U_1468 != U_1466 ) ) )
        & ( ( U_1467 = U_1466
            & U_1468 = U_1465 )
          | ( U_1467 = U_1465
            & U_1468 = U_1466 )
          | insert_pname(U_1468,insert_pname(U_1467,bot_bo844097828e_bool)) != insert_pname(U_1466,insert_pname(U_1465,bot_bo844097828e_bool)) ) )
      | ~ is_pname(U_1465)
      | ~ is_pname(U_1466)
      | ~ is_pname(U_1467)
      | ~ is_pname(U_1468) ),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

fof(f_556_3,plain,
    ( ! [U_1466,U_1465,U_1467,U_1468] :
        ( U_1467 != U_1466
        | U_1468 != U_1465
        | ~ sP155(U_1466,U_1465,U_1467,U_1468) )
    & ! [U_1466,U_1465,U_1467,U_1468] :
        ( U_1467 != U_1465
        | U_1468 != U_1466
        | ~ sP155(U_1466,U_1465,U_1467,U_1468) )
    & ! [U_1466,U_1465,U_1467,U_1468] :
        ( U_1467 = U_1466
        | ~ sP154(U_1466,U_1465,U_1467,U_1468) )
    & ! [U_1466,U_1465,U_1467,U_1468] :
        ( U_1468 = U_1465
        | ~ sP154(U_1466,U_1465,U_1467,U_1468) )
    & ! [U_1466,U_1465,U_1467,U_1468] :
        ( U_1467 = U_1465
        | ~ sP153(U_1466,U_1465,U_1467,U_1468) )
    & ! [U_1466,U_1465,U_1467,U_1468] :
        ( U_1468 = U_1466
        | ~ sP153(U_1466,U_1465,U_1467,U_1468) )
    & ! [U_1466,U_1465,U_1467,U_1468] :
        ( insert_pname(U_1468,insert_pname(U_1467,bot_bo844097828e_bool)) = insert_pname(U_1466,insert_pname(U_1465,bot_bo844097828e_bool))
        | sP155(U_1466,U_1465,U_1467,U_1468)
        | ~ sP156(U_1466,U_1465,U_1467,U_1468) )
    & ! [U_1466,U_1465,U_1467,U_1468] :
        ( sP154(U_1466,U_1465,U_1467,U_1468)
        | sP153(U_1466,U_1465,U_1467,U_1468)
        | insert_pname(U_1468,insert_pname(U_1467,bot_bo844097828e_bool)) != insert_pname(U_1466,insert_pname(U_1465,bot_bo844097828e_bool))
        | ~ sP156(U_1466,U_1465,U_1467,U_1468) )
    & ! [U_1466,U_1465,U_1467,U_1468] :
        ( sP156(U_1466,U_1465,U_1467,U_1468)
        | ~ is_pname(U_1465)
        | ~ is_pname(U_1466)
        | ~ is_pname(U_1467)
        | ~ is_pname(U_1468) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153,sP154,sP155,sP156])],[f_556_2]) ).

cnf(f_556_4,plain,
    ( sP156(U_1466,U_1465,U_1467,U_1468)
    | ~ is_pname(U_1465)
    | ~ is_pname(U_1466)
    | ~ is_pname(U_1467)
    | ~ is_pname(U_1468) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

cnf(f_556_5,plain,
    ( sP154(U_1466,U_1465,U_1467,U_1468)
    | sP153(U_1466,U_1465,U_1467,U_1468)
    | insert_pname(U_1468,insert_pname(U_1467,bot_bo844097828e_bool)) != insert_pname(U_1466,insert_pname(U_1465,bot_bo844097828e_bool))
    | ~ sP156(U_1466,U_1465,U_1467,U_1468) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

cnf(f_556_6,plain,
    ( insert_pname(U_1468,insert_pname(U_1467,bot_bo844097828e_bool)) = insert_pname(U_1466,insert_pname(U_1465,bot_bo844097828e_bool))
    | sP155(U_1466,U_1465,U_1467,U_1468)
    | ~ sP156(U_1466,U_1465,U_1467,U_1468) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

cnf(f_556_7,plain,
    ( U_1468 = U_1466
    | ~ sP153(U_1466,U_1465,U_1467,U_1468) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

cnf(f_556_8,plain,
    ( U_1467 = U_1465
    | ~ sP153(U_1466,U_1465,U_1467,U_1468) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

cnf(f_556_9,plain,
    ( U_1468 = U_1465
    | ~ sP154(U_1466,U_1465,U_1467,U_1468) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

cnf(f_556_10,plain,
    ( U_1467 = U_1466
    | ~ sP154(U_1466,U_1465,U_1467,U_1468) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

cnf(f_556_11,plain,
    ( U_1467 != U_1465
    | U_1468 != U_1466
    | ~ sP155(U_1466,U_1465,U_1467,U_1468) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

cnf(f_556_12,plain,
    ( U_1467 != U_1466
    | U_1468 != U_1465
    | ~ sP155(U_1466,U_1465,U_1467,U_1468) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

fof(f_557_1,plain,
    ! [A_3,B_1,C_1,D] :
      ( ( insert_nat(A_3,insert_nat(B_1,bot_bot_fun_nat_bool)) = insert_nat(C_1,insert_nat(D,bot_bot_fun_nat_bool))
        | ( ( B_1 != C_1
            | A_3 != D )
          & ( B_1 != D
            | A_3 != C_1 ) ) )
      & ( ( B_1 = C_1
          & A_3 = D )
        | ( B_1 = D
          & A_3 = C_1 )
        | insert_nat(A_3,insert_nat(B_1,bot_bot_fun_nat_bool)) != insert_nat(C_1,insert_nat(D,bot_bot_fun_nat_bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_453_doubleton__eq__iff]) ).

fof(f_557_2,plain,
    ! [U_1472,U_1471,U_1470,U_1469] :
      ( ( insert_nat(U_1472,insert_nat(U_1471,bot_bot_fun_nat_bool)) = insert_nat(U_1470,insert_nat(U_1469,bot_bot_fun_nat_bool))
        | ( ( U_1471 != U_1470
            | U_1472 != U_1469 )
          & ( U_1471 != U_1469
            | U_1472 != U_1470 ) ) )
      & ( ( U_1471 = U_1470
          & U_1472 = U_1469 )
        | ( U_1471 = U_1469
          & U_1472 = U_1470 )
        | insert_nat(U_1472,insert_nat(U_1471,bot_bot_fun_nat_bool)) != insert_nat(U_1470,insert_nat(U_1469,bot_bot_fun_nat_bool)) ) ),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

fof(f_557_3,plain,
    ( ! [U_1480,U_1478,U_1476,U_1474] :
        ( insert_nat(U_1480,insert_nat(U_1478,bot_bot_fun_nat_bool)) = insert_nat(U_1476,insert_nat(U_1474,bot_bot_fun_nat_bool))
        | ( ( U_1478 != U_1476
            | U_1480 != U_1474 )
          & ( U_1478 != U_1474
            | U_1480 != U_1476 ) ) )
    & ! [U_1479,U_1477,U_1475,U_1473] :
        ( ( U_1477 = U_1475
          & U_1479 = U_1473 )
        | ( U_1477 = U_1473
          & U_1479 = U_1475 )
        | insert_nat(U_1479,insert_nat(U_1477,bot_bot_fun_nat_bool)) != insert_nat(U_1475,insert_nat(U_1473,bot_bot_fun_nat_bool)) ) ),
    inference(miniscope,[status(thm)],[f_557_2]) ).

fof(f_557_4,plain,
    ( ! [U_1478,U_1474,U_1476,U_1480] :
        ( U_1478 != U_1476
        | U_1480 != U_1474
        | ~ sP159(U_1478,U_1474,U_1476,U_1480) )
    & ! [U_1478,U_1474,U_1476,U_1480] :
        ( U_1478 != U_1474
        | U_1480 != U_1476
        | ~ sP159(U_1478,U_1474,U_1476,U_1480) )
    & ! [U_1477,U_1473,U_1479,U_1475] :
        ( U_1477 = U_1475
        | ~ sP158(U_1477,U_1473,U_1479,U_1475) )
    & ! [U_1477,U_1473,U_1479,U_1475] :
        ( U_1479 = U_1473
        | ~ sP158(U_1477,U_1473,U_1479,U_1475) )
    & ! [U_1477,U_1473,U_1479,U_1475] :
        ( U_1477 = U_1473
        | ~ sP157(U_1477,U_1473,U_1479,U_1475) )
    & ! [U_1477,U_1473,U_1479,U_1475] :
        ( U_1479 = U_1475
        | ~ sP157(U_1477,U_1473,U_1479,U_1475) )
    & ! [U_1478,U_1474,U_1476,U_1480] :
        ( insert_nat(U_1480,insert_nat(U_1478,bot_bot_fun_nat_bool)) = insert_nat(U_1476,insert_nat(U_1474,bot_bot_fun_nat_bool))
        | sP159(U_1478,U_1474,U_1476,U_1480) )
    & ! [U_1477,U_1473,U_1479,U_1475] :
        ( sP158(U_1477,U_1473,U_1479,U_1475)
        | sP157(U_1477,U_1473,U_1479,U_1475)
        | insert_nat(U_1479,insert_nat(U_1477,bot_bot_fun_nat_bool)) != insert_nat(U_1475,insert_nat(U_1473,bot_bot_fun_nat_bool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP157,sP158,sP159])],[f_557_3]) ).

cnf(f_557_5,plain,
    ( sP158(U_1477,U_1473,U_1479,U_1475)
    | sP157(U_1477,U_1473,U_1479,U_1475)
    | insert_nat(U_1479,insert_nat(U_1477,bot_bot_fun_nat_bool)) != insert_nat(U_1475,insert_nat(U_1473,bot_bot_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

cnf(f_557_6,plain,
    ( insert_nat(U_1480,insert_nat(U_1478,bot_bot_fun_nat_bool)) = insert_nat(U_1476,insert_nat(U_1474,bot_bot_fun_nat_bool))
    | sP159(U_1478,U_1474,U_1476,U_1480) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

cnf(f_557_7,plain,
    ( U_1479 = U_1475
    | ~ sP157(U_1477,U_1473,U_1479,U_1475) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

cnf(f_557_8,plain,
    ( U_1477 = U_1473
    | ~ sP157(U_1477,U_1473,U_1479,U_1475) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

cnf(f_557_9,plain,
    ( U_1479 = U_1473
    | ~ sP158(U_1477,U_1473,U_1479,U_1475) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

cnf(f_557_10,plain,
    ( U_1477 = U_1475
    | ~ sP158(U_1477,U_1473,U_1479,U_1475) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

cnf(f_557_11,plain,
    ( U_1478 != U_1474
    | U_1480 != U_1476
    | ~ sP159(U_1478,U_1474,U_1476,U_1480) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

cnf(f_557_12,plain,
    ( U_1478 != U_1476
    | U_1480 != U_1474
    | ~ sP159(U_1478,U_1474,U_1476,U_1480) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

fof(f_558_1,plain,
    ! [A_3,B_1,C_1,D] :
      ( ( ( insert_a(A_3,insert_a(B_1,bot_bot_fun_a_bool)) = insert_a(C_1,insert_a(D,bot_bot_fun_a_bool))
          | ( ( B_1 != C_1
              | A_3 != D )
            & ( B_1 != D
              | A_3 != C_1 ) ) )
        & ( ( B_1 = C_1
            & A_3 = D )
          | ( B_1 = D
            & A_3 = C_1 )
          | insert_a(A_3,insert_a(B_1,bot_bot_fun_a_bool)) != insert_a(C_1,insert_a(D,bot_bot_fun_a_bool)) ) )
      | ~ is_a(D)
      | ~ is_a(C_1)
      | ~ is_a(B_1)
      | ~ is_a(A_3) ),
    inference(fof_nnf,[status(thm)],[fact_454_doubleton__eq__iff]) ).

fof(f_558_2,plain,
    ! [U_1484,U_1483,U_1482,U_1481] :
      ( ( ( insert_a(U_1484,insert_a(U_1483,bot_bot_fun_a_bool)) = insert_a(U_1482,insert_a(U_1481,bot_bot_fun_a_bool))
          | ( ( U_1483 != U_1482
              | U_1484 != U_1481 )
            & ( U_1483 != U_1481
              | U_1484 != U_1482 ) ) )
        & ( ( U_1483 = U_1482
            & U_1484 = U_1481 )
          | ( U_1483 = U_1481
            & U_1484 = U_1482 )
          | insert_a(U_1484,insert_a(U_1483,bot_bot_fun_a_bool)) != insert_a(U_1482,insert_a(U_1481,bot_bot_fun_a_bool)) ) )
      | ~ is_a(U_1481)
      | ~ is_a(U_1482)
      | ~ is_a(U_1483)
      | ~ is_a(U_1484) ),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

fof(f_558_3,plain,
    ( ! [U_1483,U_1481,U_1484,U_1482] :
        ( U_1483 != U_1482
        | U_1484 != U_1481
        | ~ sP162(U_1483,U_1481,U_1484,U_1482) )
    & ! [U_1483,U_1481,U_1484,U_1482] :
        ( U_1483 != U_1481
        | U_1484 != U_1482
        | ~ sP162(U_1483,U_1481,U_1484,U_1482) )
    & ! [U_1483,U_1481,U_1484,U_1482] :
        ( U_1483 = U_1482
        | ~ sP161(U_1483,U_1481,U_1484,U_1482) )
    & ! [U_1483,U_1481,U_1484,U_1482] :
        ( U_1484 = U_1481
        | ~ sP161(U_1483,U_1481,U_1484,U_1482) )
    & ! [U_1483,U_1481,U_1484,U_1482] :
        ( U_1483 = U_1481
        | ~ sP160(U_1483,U_1481,U_1484,U_1482) )
    & ! [U_1483,U_1481,U_1484,U_1482] :
        ( U_1484 = U_1482
        | ~ sP160(U_1483,U_1481,U_1484,U_1482) )
    & ! [U_1483,U_1481,U_1484,U_1482] :
        ( insert_a(U_1484,insert_a(U_1483,bot_bot_fun_a_bool)) = insert_a(U_1482,insert_a(U_1481,bot_bot_fun_a_bool))
        | sP162(U_1483,U_1481,U_1484,U_1482)
        | ~ sP163(U_1483,U_1481,U_1484,U_1482) )
    & ! [U_1483,U_1481,U_1484,U_1482] :
        ( sP161(U_1483,U_1481,U_1484,U_1482)
        | sP160(U_1483,U_1481,U_1484,U_1482)
        | insert_a(U_1484,insert_a(U_1483,bot_bot_fun_a_bool)) != insert_a(U_1482,insert_a(U_1481,bot_bot_fun_a_bool))
        | ~ sP163(U_1483,U_1481,U_1484,U_1482) )
    & ! [U_1483,U_1481,U_1484,U_1482] :
        ( sP163(U_1483,U_1481,U_1484,U_1482)
        | ~ is_a(U_1481)
        | ~ is_a(U_1482)
        | ~ is_a(U_1483)
        | ~ is_a(U_1484) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP160,sP161,sP162,sP163])],[f_558_2]) ).

cnf(f_558_4,plain,
    ( sP163(U_1483,U_1481,U_1484,U_1482)
    | ~ is_a(U_1481)
    | ~ is_a(U_1482)
    | ~ is_a(U_1483)
    | ~ is_a(U_1484) ),
    inference(clausify,[status(thm)],[f_558_3]) ).

cnf(f_558_5,plain,
    ( sP161(U_1483,U_1481,U_1484,U_1482)
    | sP160(U_1483,U_1481,U_1484,U_1482)
    | insert_a(U_1484,insert_a(U_1483,bot_bot_fun_a_bool)) != insert_a(U_1482,insert_a(U_1481,bot_bot_fun_a_bool))
    | ~ sP163(U_1483,U_1481,U_1484,U_1482) ),
    inference(clausify,[status(thm)],[f_558_3]) ).

cnf(f_558_6,plain,
    ( insert_a(U_1484,insert_a(U_1483,bot_bot_fun_a_bool)) = insert_a(U_1482,insert_a(U_1481,bot_bot_fun_a_bool))
    | sP162(U_1483,U_1481,U_1484,U_1482)
    | ~ sP163(U_1483,U_1481,U_1484,U_1482) ),
    inference(clausify,[status(thm)],[f_558_3]) ).

cnf(f_558_7,plain,
    ( U_1484 = U_1482
    | ~ sP160(U_1483,U_1481,U_1484,U_1482) ),
    inference(clausify,[status(thm)],[f_558_3]) ).

cnf(f_558_8,plain,
    ( U_1483 = U_1481
    | ~ sP160(U_1483,U_1481,U_1484,U_1482) ),
    inference(clausify,[status(thm)],[f_558_3]) ).

cnf(f_558_9,plain,
    ( U_1484 = U_1481
    | ~ sP161(U_1483,U_1481,U_1484,U_1482) ),
    inference(clausify,[status(thm)],[f_558_3]) ).

cnf(f_558_10,plain,
    ( U_1483 = U_1482
    | ~ sP161(U_1483,U_1481,U_1484,U_1482) ),
    inference(clausify,[status(thm)],[f_558_3]) ).

cnf(f_558_11,plain,
    ( U_1483 != U_1481
    | U_1484 != U_1482
    | ~ sP162(U_1483,U_1481,U_1484,U_1482) ),
    inference(clausify,[status(thm)],[f_558_3]) ).

cnf(f_558_12,plain,
    ( U_1483 != U_1482
    | U_1484 != U_1481
    | ~ sP162(U_1483,U_1481,U_1484,U_1482) ),
    inference(clausify,[status(thm)],[f_558_3]) ).

fof(f_559_1,plain,
    ! [B_1,A_3] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),insert_nat(A_3,bot_bot_fun_nat_bool)))
        | B_1 != A_3 )
      & ( B_1 = A_3
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),insert_nat(A_3,bot_bot_fun_nat_bool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_455_singleton__iff]) ).

fof(f_559_2,plain,
    ! [U_1486,U_1485] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1486),insert_nat(U_1485,bot_bot_fun_nat_bool)))
        | U_1486 != U_1485 )
      & ( U_1486 = U_1485
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1486),insert_nat(U_1485,bot_bot_fun_nat_bool))) ) ),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

fof(f_559_3,plain,
    ( ! [U_1490,U_1488] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1490),insert_nat(U_1488,bot_bot_fun_nat_bool)))
        | U_1490 != U_1488 )
    & ! [U_1489,U_1487] :
        ( U_1489 = U_1487
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1489),insert_nat(U_1487,bot_bot_fun_nat_bool))) ) ),
    inference(miniscope,[status(thm)],[f_559_2]) ).

fof(f_559_4,plain,
    ( ! [U_1488,U_1490] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1490),insert_nat(U_1488,bot_bot_fun_nat_bool)))
        | U_1490 != U_1488 )
    & ! [U_1487,U_1489] :
        ( U_1489 = U_1487
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1489),insert_nat(U_1487,bot_bot_fun_nat_bool))) ) ),
    inference(definitional_conversion,[status(esa)],[f_559_3]) ).

cnf(f_559_5,plain,
    ( U_1489 = U_1487
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1489),insert_nat(U_1487,bot_bot_fun_nat_bool))) ),
    inference(clausify,[status(thm)],[f_559_4]) ).

cnf(f_559_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1490),insert_nat(U_1488,bot_bot_fun_nat_bool)))
    | U_1490 != U_1488 ),
    inference(clausify,[status(thm)],[f_559_4]) ).

fof(f_560_1,plain,
    ! [B_1,A_3] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_3,bot_bo844097828e_bool)))
          | B_1 != A_3 )
        & ( B_1 = A_3
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_3,bot_bo844097828e_bool))) ) )
      | ~ is_pname(A_3)
      | ~ is_pname(B_1) ),
    inference(fof_nnf,[status(thm)],[fact_456_singleton__iff]) ).

fof(f_560_2,plain,
    ! [U_1492,U_1491] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1492),insert_pname(U_1491,bot_bo844097828e_bool)))
          | U_1492 != U_1491 )
        & ( U_1492 = U_1491
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1492),insert_pname(U_1491,bot_bo844097828e_bool))) ) )
      | ~ is_pname(U_1491)
      | ~ is_pname(U_1492) ),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

fof(f_560_3,plain,
    ( ! [U_1491,U_1492] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1492),insert_pname(U_1491,bot_bo844097828e_bool)))
        | U_1492 != U_1491
        | ~ sP164(U_1491,U_1492) )
    & ! [U_1491,U_1492] :
        ( U_1492 = U_1491
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1492),insert_pname(U_1491,bot_bo844097828e_bool)))
        | ~ sP164(U_1491,U_1492) )
    & ! [U_1491,U_1492] :
        ( sP164(U_1491,U_1492)
        | ~ is_pname(U_1491)
        | ~ is_pname(U_1492) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164])],[f_560_2]) ).

cnf(f_560_4,plain,
    ( sP164(U_1491,U_1492)
    | ~ is_pname(U_1491)
    | ~ is_pname(U_1492) ),
    inference(clausify,[status(thm)],[f_560_3]) ).

cnf(f_560_5,plain,
    ( U_1492 = U_1491
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1492),insert_pname(U_1491,bot_bo844097828e_bool)))
    | ~ sP164(U_1491,U_1492) ),
    inference(clausify,[status(thm)],[f_560_3]) ).

cnf(f_560_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1492),insert_pname(U_1491,bot_bo844097828e_bool)))
    | U_1492 != U_1491
    | ~ sP164(U_1491,U_1492) ),
    inference(clausify,[status(thm)],[f_560_3]) ).

fof(f_561_1,plain,
    ! [B_1,A_3] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),insert_a(A_3,bot_bot_fun_a_bool)))
          | B_1 != A_3 )
        & ( B_1 = A_3
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),insert_a(A_3,bot_bot_fun_a_bool))) ) )
      | ~ is_a(A_3)
      | ~ is_a(B_1) ),
    inference(fof_nnf,[status(thm)],[fact_457_singleton__iff]) ).

fof(f_561_2,plain,
    ! [U_1494,U_1493] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1494),insert_a(U_1493,bot_bot_fun_a_bool)))
          | U_1494 != U_1493 )
        & ( U_1494 = U_1493
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1494),insert_a(U_1493,bot_bot_fun_a_bool))) ) )
      | ~ is_a(U_1493)
      | ~ is_a(U_1494) ),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

fof(f_561_3,plain,
    ( ! [U_1494,U_1493] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1494),insert_a(U_1493,bot_bot_fun_a_bool)))
        | U_1494 != U_1493
        | ~ sP165(U_1494,U_1493) )
    & ! [U_1494,U_1493] :
        ( U_1494 = U_1493
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1494),insert_a(U_1493,bot_bot_fun_a_bool)))
        | ~ sP165(U_1494,U_1493) )
    & ! [U_1494,U_1493] :
        ( sP165(U_1494,U_1493)
        | ~ is_a(U_1493)
        | ~ is_a(U_1494) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP165])],[f_561_2]) ).

cnf(f_561_4,plain,
    ( sP165(U_1494,U_1493)
    | ~ is_a(U_1493)
    | ~ is_a(U_1494) ),
    inference(clausify,[status(thm)],[f_561_3]) ).

cnf(f_561_5,plain,
    ( U_1494 = U_1493
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1494),insert_a(U_1493,bot_bot_fun_a_bool)))
    | ~ sP165(U_1494,U_1493) ),
    inference(clausify,[status(thm)],[f_561_3]) ).

cnf(f_561_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1494),insert_a(U_1493,bot_bot_fun_a_bool)))
    | U_1494 != U_1493
    | ~ sP165(U_1494,U_1493) ),
    inference(clausify,[status(thm)],[f_561_3]) ).

fof(f_562_1,plain,
    ! [A_3,A_1] : insert_pname(A_3,A_1) != bot_bo844097828e_bool,
    inference(fof_nnf,[status(thm)],[fact_458_insert__not__empty]) ).

fof(f_562_2,plain,
    ! [U_1496,U_1495] : insert_pname(U_1496,U_1495) != bot_bo844097828e_bool,
    inference(variable_rename,[status(thm)],[f_562_1]) ).

fof(f_562_3,plain,
    ! [U_1496,U_1495] : insert_pname(U_1496,U_1495) != bot_bo844097828e_bool,
    inference(definitional_conversion,[status(esa)],[f_562_2]) ).

cnf(f_562_4,plain,
    insert_pname(U_1496,U_1495) != bot_bo844097828e_bool,
    inference(clausify,[status(thm)],[f_562_3]) ).

fof(f_563_1,plain,
    ! [A_3,A_1] : insert_nat(A_3,A_1) != bot_bot_fun_nat_bool,
    inference(fof_nnf,[status(thm)],[fact_459_insert__not__empty]) ).

fof(f_563_2,plain,
    ! [U_1498,U_1497] : insert_nat(U_1498,U_1497) != bot_bot_fun_nat_bool,
    inference(variable_rename,[status(thm)],[f_563_1]) ).

fof(f_563_3,plain,
    ! [U_1497,U_1498] : insert_nat(U_1498,U_1497) != bot_bot_fun_nat_bool,
    inference(definitional_conversion,[status(esa)],[f_563_2]) ).

cnf(f_563_4,plain,
    insert_nat(U_1498,U_1497) != bot_bot_fun_nat_bool,
    inference(clausify,[status(thm)],[f_563_3]) ).

fof(f_564_1,plain,
    ! [A_3,A_1] : insert_a(A_3,A_1) != bot_bot_fun_a_bool,
    inference(fof_nnf,[status(thm)],[fact_460_insert__not__empty]) ).

fof(f_564_2,plain,
    ! [U_1500,U_1499] : insert_a(U_1500,U_1499) != bot_bot_fun_a_bool,
    inference(variable_rename,[status(thm)],[f_564_1]) ).

fof(f_564_3,plain,
    ! [U_1500,U_1499] : insert_a(U_1500,U_1499) != bot_bot_fun_a_bool,
    inference(definitional_conversion,[status(esa)],[f_564_2]) ).

cnf(f_564_4,plain,
    insert_a(U_1500,U_1499) != bot_bot_fun_a_bool,
    inference(clausify,[status(thm)],[f_564_3]) ).

fof(f_565_1,plain,
    ! [A_3,A_1] : bot_bo844097828e_bool != insert_pname(A_3,A_1),
    inference(fof_nnf,[status(thm)],[fact_461_empty__not__insert]) ).

fof(f_565_2,plain,
    ! [U_1502,U_1501] : bot_bo844097828e_bool != insert_pname(U_1502,U_1501),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

fof(f_565_3,plain,
    ! [U_1502,U_1501] : bot_bo844097828e_bool != insert_pname(U_1502,U_1501),
    inference(definitional_conversion,[status(esa)],[f_565_2]) ).

cnf(f_565_4,plain,
    bot_bo844097828e_bool != insert_pname(U_1502,U_1501),
    inference(clausify,[status(thm)],[f_565_3]) ).

fof(f_566_1,plain,
    ! [A_3,A_1] : bot_bot_fun_nat_bool != insert_nat(A_3,A_1),
    inference(fof_nnf,[status(thm)],[fact_462_empty__not__insert]) ).

fof(f_566_2,plain,
    ! [U_1504,U_1503] : bot_bot_fun_nat_bool != insert_nat(U_1504,U_1503),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

fof(f_566_3,plain,
    ! [U_1504,U_1503] : bot_bot_fun_nat_bool != insert_nat(U_1504,U_1503),
    inference(definitional_conversion,[status(esa)],[f_566_2]) ).

cnf(f_566_4,plain,
    bot_bot_fun_nat_bool != insert_nat(U_1504,U_1503),
    inference(clausify,[status(thm)],[f_566_3]) ).

fof(f_567_1,plain,
    ! [A_3,A_1] : bot_bot_fun_a_bool != insert_a(A_3,A_1),
    inference(fof_nnf,[status(thm)],[fact_463_empty__not__insert]) ).

fof(f_567_2,plain,
    ! [U_1506,U_1505] : bot_bot_fun_a_bool != insert_a(U_1506,U_1505),
    inference(variable_rename,[status(thm)],[f_567_1]) ).

fof(f_567_3,plain,
    ! [U_1506,U_1505] : bot_bot_fun_a_bool != insert_a(U_1506,U_1505),
    inference(definitional_conversion,[status(esa)],[f_567_2]) ).

cnf(f_567_4,plain,
    bot_bot_fun_a_bool != insert_a(U_1506,U_1505),
    inference(clausify,[status(thm)],[f_567_3]) ).

fof(f_568_1,plain,
    ! [A_1] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),bot_bot_fun_nat_bool))
        | A_1 != bot_bot_fun_nat_bool )
      & ( A_1 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),bot_bot_fun_nat_bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_464_subset__empty]) ).

fof(f_568_2,plain,
    ! [U_1507] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1507),bot_bot_fun_nat_bool))
        | U_1507 != bot_bot_fun_nat_bool )
      & ( U_1507 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1507),bot_bot_fun_nat_bool)) ) ),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

fof(f_568_3,plain,
    ( ! [U_1509] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1509),bot_bot_fun_nat_bool))
        | U_1509 != bot_bot_fun_nat_bool )
    & ! [U_1508] :
        ( U_1508 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1508),bot_bot_fun_nat_bool)) ) ),
    inference(miniscope,[status(thm)],[f_568_2]) ).

fof(f_568_4,plain,
    ( ! [U_1509] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1509),bot_bot_fun_nat_bool))
        | U_1509 != bot_bot_fun_nat_bool )
    & ! [U_1508] :
        ( U_1508 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1508),bot_bot_fun_nat_bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_568_3]) ).

cnf(f_568_5,plain,
    ( U_1508 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1508),bot_bot_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_568_4]) ).

cnf(f_568_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1509),bot_bot_fun_nat_bool))
    | U_1509 != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_568_4]) ).

fof(f_569_1,plain,
    ! [A_1] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),bot_bo844097828e_bool))
          | A_1 != bot_bo844097828e_bool )
        & ( A_1 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),bot_bo844097828e_bool)) ) )
      | ~ is_fun_pname_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_465_subset__empty]) ).

fof(f_569_2,plain,
    ! [U_1510] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1510),bot_bo844097828e_bool))
          | U_1510 != bot_bo844097828e_bool )
        & ( U_1510 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1510),bot_bo844097828e_bool)) ) )
      | ~ is_fun_pname_bool(U_1510) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

fof(f_569_3,plain,
    ( ! [U_1510] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1510),bot_bo844097828e_bool))
        | U_1510 != bot_bo844097828e_bool
        | ~ sP166(U_1510) )
    & ! [U_1510] :
        ( U_1510 = bot_bo844097828e_bool
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1510),bot_bo844097828e_bool))
        | ~ sP166(U_1510) )
    & ! [U_1510] :
        ( sP166(U_1510)
        | ~ is_fun_pname_bool(U_1510) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166])],[f_569_2]) ).

cnf(f_569_4,plain,
    ( sP166(U_1510)
    | ~ is_fun_pname_bool(U_1510) ),
    inference(clausify,[status(thm)],[f_569_3]) ).

cnf(f_569_5,plain,
    ( U_1510 = bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1510),bot_bo844097828e_bool))
    | ~ sP166(U_1510) ),
    inference(clausify,[status(thm)],[f_569_3]) ).

cnf(f_569_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1510),bot_bo844097828e_bool))
    | U_1510 != bot_bo844097828e_bool
    | ~ sP166(U_1510) ),
    inference(clausify,[status(thm)],[f_569_3]) ).

fof(f_570_1,plain,
    ! [A_1] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),bot_bot_fun_a_bool))
          | A_1 != bot_bot_fun_a_bool )
        & ( A_1 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),bot_bot_fun_a_bool)) ) )
      | ~ is_fun_a_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_466_subset__empty]) ).

fof(f_570_2,plain,
    ! [U_1511] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1511),bot_bot_fun_a_bool))
          | U_1511 != bot_bot_fun_a_bool )
        & ( U_1511 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1511),bot_bot_fun_a_bool)) ) )
      | ~ is_fun_a_bool(U_1511) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

fof(f_570_3,plain,
    ( ! [U_1511] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1511),bot_bot_fun_a_bool))
        | U_1511 != bot_bot_fun_a_bool
        | ~ sP167(U_1511) )
    & ! [U_1511] :
        ( U_1511 = bot_bot_fun_a_bool
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1511),bot_bot_fun_a_bool))
        | ~ sP167(U_1511) )
    & ! [U_1511] :
        ( sP167(U_1511)
        | ~ is_fun_a_bool(U_1511) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP167])],[f_570_2]) ).

cnf(f_570_4,plain,
    ( sP167(U_1511)
    | ~ is_fun_a_bool(U_1511) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

cnf(f_570_5,plain,
    ( U_1511 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1511),bot_bot_fun_a_bool))
    | ~ sP167(U_1511) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

cnf(f_570_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1511),bot_bot_fun_a_bool))
    | U_1511 != bot_bot_fun_a_bool
    | ~ sP167(U_1511) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

fof(f_571_1,plain,
    ! [F,A_1] :
      ( ( ( image_pname_a(F,A_1) = bot_bot_fun_a_bool
          | A_1 != bot_bo844097828e_bool )
        & ( A_1 = bot_bo844097828e_bool
          | image_pname_a(F,A_1) != bot_bot_fun_a_bool ) )
      | ~ is_fun_pname_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_467_image__is__empty]) ).

fof(f_571_2,plain,
    ! [U_1513,U_1512] :
      ( ( ( image_pname_a(U_1513,U_1512) = bot_bot_fun_a_bool
          | U_1512 != bot_bo844097828e_bool )
        & ( U_1512 = bot_bo844097828e_bool
          | image_pname_a(U_1513,U_1512) != bot_bot_fun_a_bool ) )
      | ~ is_fun_pname_bool(U_1512) ),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

fof(f_571_3,plain,
    ( ! [U_1513,U_1512] :
        ( image_pname_a(U_1513,U_1512) = bot_bot_fun_a_bool
        | U_1512 != bot_bo844097828e_bool
        | ~ sP168(U_1513,U_1512) )
    & ! [U_1513,U_1512] :
        ( U_1512 = bot_bo844097828e_bool
        | image_pname_a(U_1513,U_1512) != bot_bot_fun_a_bool
        | ~ sP168(U_1513,U_1512) )
    & ! [U_1513,U_1512] :
        ( sP168(U_1513,U_1512)
        | ~ is_fun_pname_bool(U_1512) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168])],[f_571_2]) ).

cnf(f_571_4,plain,
    ( sP168(U_1513,U_1512)
    | ~ is_fun_pname_bool(U_1512) ),
    inference(clausify,[status(thm)],[f_571_3]) ).

cnf(f_571_5,plain,
    ( U_1512 = bot_bo844097828e_bool
    | image_pname_a(U_1513,U_1512) != bot_bot_fun_a_bool
    | ~ sP168(U_1513,U_1512) ),
    inference(clausify,[status(thm)],[f_571_3]) ).

cnf(f_571_6,plain,
    ( image_pname_a(U_1513,U_1512) = bot_bot_fun_a_bool
    | U_1512 != bot_bo844097828e_bool
    | ~ sP168(U_1513,U_1512) ),
    inference(clausify,[status(thm)],[f_571_3]) ).

fof(f_572_1,plain,
    ! [F] : image_pname_a(F,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    inference(fof_nnf,[status(thm)],[fact_468_image__empty]) ).

fof(f_572_2,plain,
    ! [U_1514] : image_pname_a(U_1514,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    inference(variable_rename,[status(thm)],[f_572_1]) ).

fof(f_572_3,plain,
    ! [U_1514] : image_pname_a(U_1514,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    inference(definitional_conversion,[status(esa)],[f_572_2]) ).

cnf(f_572_4,plain,
    image_pname_a(U_1514,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    inference(clausify,[status(thm)],[f_572_3]) ).

fof(f_573_1,plain,
    ! [F,A_1] :
      ( ( ( bot_bot_fun_a_bool = image_pname_a(F,A_1)
          | A_1 != bot_bo844097828e_bool )
        & ( A_1 = bot_bo844097828e_bool
          | bot_bot_fun_a_bool != image_pname_a(F,A_1) ) )
      | ~ is_fun_pname_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_469_empty__is__image]) ).

fof(f_573_2,plain,
    ! [U_1516,U_1515] :
      ( ( ( bot_bot_fun_a_bool = image_pname_a(U_1516,U_1515)
          | U_1515 != bot_bo844097828e_bool )
        & ( U_1515 = bot_bo844097828e_bool
          | bot_bot_fun_a_bool != image_pname_a(U_1516,U_1515) ) )
      | ~ is_fun_pname_bool(U_1515) ),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

fof(f_573_3,plain,
    ( ! [U_1515,U_1516] :
        ( bot_bot_fun_a_bool = image_pname_a(U_1516,U_1515)
        | U_1515 != bot_bo844097828e_bool
        | ~ sP169(U_1515,U_1516) )
    & ! [U_1515,U_1516] :
        ( U_1515 = bot_bo844097828e_bool
        | bot_bot_fun_a_bool != image_pname_a(U_1516,U_1515)
        | ~ sP169(U_1515,U_1516) )
    & ! [U_1515,U_1516] :
        ( sP169(U_1515,U_1516)
        | ~ is_fun_pname_bool(U_1515) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP169])],[f_573_2]) ).

cnf(f_573_4,plain,
    ( sP169(U_1515,U_1516)
    | ~ is_fun_pname_bool(U_1515) ),
    inference(clausify,[status(thm)],[f_573_3]) ).

cnf(f_573_5,plain,
    ( U_1515 = bot_bo844097828e_bool
    | bot_bot_fun_a_bool != image_pname_a(U_1516,U_1515)
    | ~ sP169(U_1515,U_1516) ),
    inference(clausify,[status(thm)],[f_573_3]) ).

cnf(f_573_6,plain,
    ( bot_bot_fun_a_bool = image_pname_a(U_1516,U_1515)
    | U_1515 != bot_bo844097828e_bool
    | ~ sP169(U_1515,U_1516) ),
    inference(clausify,[status(thm)],[f_573_3]) ).

fof(f_574_1,plain,
    ! [Pa,A_3] :
      ( ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)),Pa)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(Pa,A_3)) )
      & ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)),Pa)) = insert_nat(A_3,bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(Pa,A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_470_Collect__conv__if]) ).

fof(f_574_2,plain,
    ! [U_1518,U_1517] :
      ( ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1517)),U_1518)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_1518,U_1517)) )
      & ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1517)),U_1518)) = insert_nat(U_1517,bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(U_1518,U_1517)) ) ),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

fof(f_574_3,plain,
    ( ! [U_1522,U_1520] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1520)),U_1522)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_1522,U_1520)) )
    & ! [U_1521,U_1519] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1519)),U_1521)) = insert_nat(U_1519,bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(U_1521,U_1519)) ) ),
    inference(miniscope,[status(thm)],[f_574_2]) ).

fof(f_574_4,plain,
    ( ! [U_1520,U_1522] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1520)),U_1522)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_1522,U_1520)) )
    & ! [U_1519,U_1521] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1519)),U_1521)) = insert_nat(U_1519,bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(U_1521,U_1519)) ) ),
    inference(definitional_conversion,[status(esa)],[f_574_3]) ).

cnf(f_574_5,plain,
    ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1519)),U_1521)) = insert_nat(U_1519,bot_bot_fun_nat_bool)
    | ~ hBOOL(hAPP_nat_bool(U_1521,U_1519)) ),
    inference(clausify,[status(thm)],[f_574_4]) ).

cnf(f_574_6,plain,
    ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1520)),U_1522)) = bot_bot_fun_nat_bool
    | hBOOL(hAPP_nat_bool(U_1522,U_1520)) ),
    inference(clausify,[status(thm)],[f_574_4]) ).

fof(f_575_1,plain,
    ! [Pa,A_3] :
      ( ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)),Pa)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(Pa,A_3)) )
      & ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)),Pa)) = insert_pname(A_3,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(Pa,A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_471_Collect__conv__if]) ).

fof(f_575_2,plain,
    ! [U_1524,U_1523] :
      ( ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1523)),U_1524)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(U_1524,U_1523)) )
      & ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1523)),U_1524)) = insert_pname(U_1523,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(U_1524,U_1523)) ) ),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

fof(f_575_3,plain,
    ( ! [U_1528,U_1526] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1526)),U_1528)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(U_1528,U_1526)) )
    & ! [U_1527,U_1525] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1525)),U_1527)) = insert_pname(U_1525,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(U_1527,U_1525)) ) ),
    inference(miniscope,[status(thm)],[f_575_2]) ).

fof(f_575_4,plain,
    ( ! [U_1526,U_1528] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1526)),U_1528)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(U_1528,U_1526)) )
    & ! [U_1527,U_1525] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1525)),U_1527)) = insert_pname(U_1525,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(U_1527,U_1525)) ) ),
    inference(definitional_conversion,[status(esa)],[f_575_3]) ).

cnf(f_575_5,plain,
    ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1525)),U_1527)) = insert_pname(U_1525,bot_bo844097828e_bool)
    | ~ hBOOL(hAPP_pname_bool(U_1527,U_1525)) ),
    inference(clausify,[status(thm)],[f_575_4]) ).

cnf(f_575_6,plain,
    ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1526)),U_1528)) = bot_bo844097828e_bool
    | hBOOL(hAPP_pname_bool(U_1528,U_1526)) ),
    inference(clausify,[status(thm)],[f_575_4]) ).

fof(f_576_1,plain,
    ! [Pa,A_3] :
      ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)),Pa)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(Pa,A_3)) )
      & ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)),Pa)) = insert_a(A_3,bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(Pa,A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_472_Collect__conv__if]) ).

fof(f_576_2,plain,
    ! [U_1530,U_1529] :
      ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1529)),U_1530)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(U_1530,U_1529)) )
      & ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1529)),U_1530)) = insert_a(U_1529,bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(U_1530,U_1529)) ) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

fof(f_576_3,plain,
    ( ! [U_1534,U_1532] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1532)),U_1534)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(U_1534,U_1532)) )
    & ! [U_1533,U_1531] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1531)),U_1533)) = insert_a(U_1531,bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(U_1533,U_1531)) ) ),
    inference(miniscope,[status(thm)],[f_576_2]) ).

fof(f_576_4,plain,
    ( ! [U_1532,U_1534] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1532)),U_1534)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(U_1534,U_1532)) )
    & ! [U_1533,U_1531] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1531)),U_1533)) = insert_a(U_1531,bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(U_1533,U_1531)) ) ),
    inference(definitional_conversion,[status(esa)],[f_576_3]) ).

cnf(f_576_5,plain,
    ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1531)),U_1533)) = insert_a(U_1531,bot_bot_fun_a_bool)
    | ~ hBOOL(hAPP_a_bool(U_1533,U_1531)) ),
    inference(clausify,[status(thm)],[f_576_4]) ).

cnf(f_576_6,plain,
    ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1532)),U_1534)) = bot_bot_fun_a_bool
    | hBOOL(hAPP_a_bool(U_1534,U_1532)) ),
    inference(clausify,[status(thm)],[f_576_4]) ).

fof(f_577_1,plain,
    ! [Pa,A_3] :
      ( ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)),Pa)) = bot_bo1701429464l_bool
        | hBOOL(hAPP_f54304608l_bool(Pa,A_3)) )
      & ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)),Pa)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool)
        | ~ hBOOL(hAPP_f54304608l_bool(Pa,A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_473_Collect__conv__if]) ).

fof(f_577_2,plain,
    ! [U_1536,U_1535] :
      ( ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1535)),U_1536)) = bot_bo1701429464l_bool
        | hBOOL(hAPP_f54304608l_bool(U_1536,U_1535)) )
      & ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1535)),U_1536)) = insert_fun_nat_bool(U_1535,bot_bo1701429464l_bool)
        | ~ hBOOL(hAPP_f54304608l_bool(U_1536,U_1535)) ) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

fof(f_577_3,plain,
    ( ! [U_1540,U_1538] :
        ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1538)),U_1540)) = bot_bo1701429464l_bool
        | hBOOL(hAPP_f54304608l_bool(U_1540,U_1538)) )
    & ! [U_1539,U_1537] :
        ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1537)),U_1539)) = insert_fun_nat_bool(U_1537,bot_bo1701429464l_bool)
        | ~ hBOOL(hAPP_f54304608l_bool(U_1539,U_1537)) ) ),
    inference(miniscope,[status(thm)],[f_577_2]) ).

fof(f_577_4,plain,
    ( ! [U_1538,U_1540] :
        ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1538)),U_1540)) = bot_bo1701429464l_bool
        | hBOOL(hAPP_f54304608l_bool(U_1540,U_1538)) )
    & ! [U_1539,U_1537] :
        ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1537)),U_1539)) = insert_fun_nat_bool(U_1537,bot_bo1701429464l_bool)
        | ~ hBOOL(hAPP_f54304608l_bool(U_1539,U_1537)) ) ),
    inference(definitional_conversion,[status(esa)],[f_577_3]) ).

cnf(f_577_5,plain,
    ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1537)),U_1539)) = insert_fun_nat_bool(U_1537,bot_bo1701429464l_bool)
    | ~ hBOOL(hAPP_f54304608l_bool(U_1539,U_1537)) ),
    inference(clausify,[status(thm)],[f_577_4]) ).

cnf(f_577_6,plain,
    ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1538)),U_1540)) = bot_bo1701429464l_bool
    | hBOOL(hAPP_f54304608l_bool(U_1540,U_1538)) ),
    inference(clausify,[status(thm)],[f_577_4]) ).

fof(f_578_1,plain,
    ! [Pa,A_3] :
      ( ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)),Pa)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(Pa,A_3)) )
      & ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)),Pa)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(Pa,A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_474_Collect__conv__if]) ).

fof(f_578_2,plain,
    ! [U_1542,U_1541] :
      ( ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1541)),U_1542)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(U_1542,U_1541)) )
      & ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1541)),U_1542)) = insert1325755072e_bool(U_1541,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_1542,U_1541)) ) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

fof(f_578_3,plain,
    ( ! [U_1546,U_1544] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1544)),U_1546)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(U_1546,U_1544)) )
    & ! [U_1545,U_1543] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1543)),U_1545)) = insert1325755072e_bool(U_1543,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_1545,U_1543)) ) ),
    inference(miniscope,[status(thm)],[f_578_2]) ).

fof(f_578_4,plain,
    ( ! [U_1544,U_1546] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1544)),U_1546)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(U_1546,U_1544)) )
    & ! [U_1545,U_1543] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1543)),U_1545)) = insert1325755072e_bool(U_1543,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_1545,U_1543)) ) ),
    inference(definitional_conversion,[status(esa)],[f_578_3]) ).

cnf(f_578_5,plain,
    ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1543)),U_1545)) = insert1325755072e_bool(U_1543,bot_bo1649642514l_bool)
    | ~ hBOOL(hAPP_f1664156314l_bool(U_1545,U_1543)) ),
    inference(clausify,[status(thm)],[f_578_4]) ).

cnf(f_578_6,plain,
    ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1544)),U_1546)) = bot_bo1649642514l_bool
    | hBOOL(hAPP_f1664156314l_bool(U_1546,U_1544)) ),
    inference(clausify,[status(thm)],[f_578_4]) ).

fof(f_579_1,plain,
    ! [Pa,A_3] :
      ( ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)),Pa)) = bot_bo1389914601l_bool
        | hBOOL(hAPP_fun_a_bool_bool(Pa,A_3)) )
      & ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)),Pa)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool)
        | ~ hBOOL(hAPP_fun_a_bool_bool(Pa,A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_475_Collect__conv__if]) ).

fof(f_579_2,plain,
    ! [U_1548,U_1547] :
      ( ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1547)),U_1548)) = bot_bo1389914601l_bool
        | hBOOL(hAPP_fun_a_bool_bool(U_1548,U_1547)) )
      & ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1547)),U_1548)) = insert_fun_a_bool(U_1547,bot_bo1389914601l_bool)
        | ~ hBOOL(hAPP_fun_a_bool_bool(U_1548,U_1547)) ) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

fof(f_579_3,plain,
    ( ! [U_1552,U_1550] :
        ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1550)),U_1552)) = bot_bo1389914601l_bool
        | hBOOL(hAPP_fun_a_bool_bool(U_1552,U_1550)) )
    & ! [U_1551,U_1549] :
        ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1549)),U_1551)) = insert_fun_a_bool(U_1549,bot_bo1389914601l_bool)
        | ~ hBOOL(hAPP_fun_a_bool_bool(U_1551,U_1549)) ) ),
    inference(miniscope,[status(thm)],[f_579_2]) ).

fof(f_579_4,plain,
    ( ! [U_1550,U_1552] :
        ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1550)),U_1552)) = bot_bo1389914601l_bool
        | hBOOL(hAPP_fun_a_bool_bool(U_1552,U_1550)) )
    & ! [U_1551,U_1549] :
        ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1549)),U_1551)) = insert_fun_a_bool(U_1549,bot_bo1389914601l_bool)
        | ~ hBOOL(hAPP_fun_a_bool_bool(U_1551,U_1549)) ) ),
    inference(definitional_conversion,[status(esa)],[f_579_3]) ).

cnf(f_579_5,plain,
    ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1549)),U_1551)) = insert_fun_a_bool(U_1549,bot_bo1389914601l_bool)
    | ~ hBOOL(hAPP_fun_a_bool_bool(U_1551,U_1549)) ),
    inference(clausify,[status(thm)],[f_579_4]) ).

cnf(f_579_6,plain,
    ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1550)),U_1552)) = bot_bo1389914601l_bool
    | hBOOL(hAPP_fun_a_bool_bool(U_1552,U_1550)) ),
    inference(clausify,[status(thm)],[f_579_4]) ).

fof(f_580_1,plain,
    ! [Pa,A_3] :
      ( ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_3)),Pa)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(Pa,A_3)) )
      & ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_3)),Pa)) = insert_nat(A_3,bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(Pa,A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_476_Collect__conv__if2]) ).

fof(f_580_2,plain,
    ! [U_1554,U_1553] :
      ( ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_1553)),U_1554)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_1554,U_1553)) )
      & ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_1553)),U_1554)) = insert_nat(U_1553,bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(U_1554,U_1553)) ) ),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

fof(f_580_3,plain,
    ( ! [U_1558,U_1556] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_1556)),U_1558)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_1558,U_1556)) )
    & ! [U_1557,U_1555] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_1555)),U_1557)) = insert_nat(U_1555,bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(U_1557,U_1555)) ) ),
    inference(miniscope,[status(thm)],[f_580_2]) ).

fof(f_580_4,plain,
    ( ! [U_1556,U_1558] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_1556)),U_1558)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_1558,U_1556)) )
    & ! [U_1557,U_1555] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_1555)),U_1557)) = insert_nat(U_1555,bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(U_1557,U_1555)) ) ),
    inference(definitional_conversion,[status(esa)],[f_580_3]) ).

cnf(f_580_5,plain,
    ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_1555)),U_1557)) = insert_nat(U_1555,bot_bot_fun_nat_bool)
    | ~ hBOOL(hAPP_nat_bool(U_1557,U_1555)) ),
    inference(clausify,[status(thm)],[f_580_4]) ).

cnf(f_580_6,plain,
    ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_1556)),U_1558)) = bot_bot_fun_nat_bool
    | hBOOL(hAPP_nat_bool(U_1558,U_1556)) ),
    inference(clausify,[status(thm)],[f_580_4]) ).

fof(f_581_1,plain,
    ! [Pa,A_3] :
      ( ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_3)),Pa)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(Pa,A_3)) )
      & ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_3)),Pa)) = insert_pname(A_3,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(Pa,A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_477_Collect__conv__if2]) ).

fof(f_581_2,plain,
    ! [U_1560,U_1559] :
      ( ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_1559)),U_1560)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(U_1560,U_1559)) )
      & ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_1559)),U_1560)) = insert_pname(U_1559,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(U_1560,U_1559)) ) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

fof(f_581_3,plain,
    ( ! [U_1564,U_1562] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_1562)),U_1564)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(U_1564,U_1562)) )
    & ! [U_1563,U_1561] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_1561)),U_1563)) = insert_pname(U_1561,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(U_1563,U_1561)) ) ),
    inference(miniscope,[status(thm)],[f_581_2]) ).

fof(f_581_4,plain,
    ( ! [U_1562,U_1564] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_1562)),U_1564)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(U_1564,U_1562)) )
    & ! [U_1563,U_1561] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_1561)),U_1563)) = insert_pname(U_1561,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(U_1563,U_1561)) ) ),
    inference(definitional_conversion,[status(esa)],[f_581_3]) ).

cnf(f_581_5,plain,
    ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_1561)),U_1563)) = insert_pname(U_1561,bot_bo844097828e_bool)
    | ~ hBOOL(hAPP_pname_bool(U_1563,U_1561)) ),
    inference(clausify,[status(thm)],[f_581_4]) ).

cnf(f_581_6,plain,
    ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_1562)),U_1564)) = bot_bo844097828e_bool
    | hBOOL(hAPP_pname_bool(U_1564,U_1562)) ),
    inference(clausify,[status(thm)],[f_581_4]) ).

fof(f_582_1,plain,
    ! [Pa,A_3] :
      ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_3)),Pa)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(Pa,A_3)) )
      & ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_3)),Pa)) = insert_a(A_3,bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(Pa,A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_478_Collect__conv__if2]) ).

fof(f_582_2,plain,
    ! [U_1566,U_1565] :
      ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_1565)),U_1566)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(U_1566,U_1565)) )
      & ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_1565)),U_1566)) = insert_a(U_1565,bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(U_1566,U_1565)) ) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

fof(f_582_3,plain,
    ( ! [U_1570,U_1568] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_1568)),U_1570)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(U_1570,U_1568)) )
    & ! [U_1569,U_1567] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_1567)),U_1569)) = insert_a(U_1567,bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(U_1569,U_1567)) ) ),
    inference(miniscope,[status(thm)],[f_582_2]) ).

fof(f_582_4,plain,
    ( ! [U_1568,U_1570] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_1568)),U_1570)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(U_1570,U_1568)) )
    & ! [U_1569,U_1567] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_1567)),U_1569)) = insert_a(U_1567,bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(U_1569,U_1567)) ) ),
    inference(definitional_conversion,[status(esa)],[f_582_3]) ).

cnf(f_582_5,plain,
    ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_1567)),U_1569)) = insert_a(U_1567,bot_bot_fun_a_bool)
    | ~ hBOOL(hAPP_a_bool(U_1569,U_1567)) ),
    inference(clausify,[status(thm)],[f_582_4]) ).

cnf(f_582_6,plain,
    ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_1568)),U_1570)) = bot_bot_fun_a_bool
    | hBOOL(hAPP_a_bool(U_1570,U_1568)) ),
    inference(clausify,[status(thm)],[f_582_4]) ).

fof(f_583_1,plain,
    ! [Pa,A_3] :
      ( ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,A_3)),Pa)) = bot_bo1701429464l_bool
        | hBOOL(hAPP_f54304608l_bool(Pa,A_3)) )
      & ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,A_3)),Pa)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool)
        | ~ hBOOL(hAPP_f54304608l_bool(Pa,A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_479_Collect__conv__if2]) ).

fof(f_583_2,plain,
    ! [U_1572,U_1571] :
      ( ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,U_1571)),U_1572)) = bot_bo1701429464l_bool
        | hBOOL(hAPP_f54304608l_bool(U_1572,U_1571)) )
      & ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,U_1571)),U_1572)) = insert_fun_nat_bool(U_1571,bot_bo1701429464l_bool)
        | ~ hBOOL(hAPP_f54304608l_bool(U_1572,U_1571)) ) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

fof(f_583_3,plain,
    ( ! [U_1576,U_1574] :
        ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,U_1574)),U_1576)) = bot_bo1701429464l_bool
        | hBOOL(hAPP_f54304608l_bool(U_1576,U_1574)) )
    & ! [U_1575,U_1573] :
        ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,U_1573)),U_1575)) = insert_fun_nat_bool(U_1573,bot_bo1701429464l_bool)
        | ~ hBOOL(hAPP_f54304608l_bool(U_1575,U_1573)) ) ),
    inference(miniscope,[status(thm)],[f_583_2]) ).

fof(f_583_4,plain,
    ( ! [U_1574,U_1576] :
        ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,U_1574)),U_1576)) = bot_bo1701429464l_bool
        | hBOOL(hAPP_f54304608l_bool(U_1576,U_1574)) )
    & ! [U_1575,U_1573] :
        ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,U_1573)),U_1575)) = insert_fun_nat_bool(U_1573,bot_bo1701429464l_bool)
        | ~ hBOOL(hAPP_f54304608l_bool(U_1575,U_1573)) ) ),
    inference(definitional_conversion,[status(esa)],[f_583_3]) ).

cnf(f_583_5,plain,
    ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,U_1573)),U_1575)) = insert_fun_nat_bool(U_1573,bot_bo1701429464l_bool)
    | ~ hBOOL(hAPP_f54304608l_bool(U_1575,U_1573)) ),
    inference(clausify,[status(thm)],[f_583_4]) ).

cnf(f_583_6,plain,
    ( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,U_1574)),U_1576)) = bot_bo1701429464l_bool
    | hBOOL(hAPP_f54304608l_bool(U_1576,U_1574)) ),
    inference(clausify,[status(thm)],[f_583_4]) ).

fof(f_584_1,plain,
    ! [Pa,A_3] :
      ( ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_3)),Pa)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(Pa,A_3)) )
      & ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_3)),Pa)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(Pa,A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_480_Collect__conv__if2]) ).

fof(f_584_2,plain,
    ! [U_1578,U_1577] :
      ( ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_1577)),U_1578)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(U_1578,U_1577)) )
      & ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_1577)),U_1578)) = insert1325755072e_bool(U_1577,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_1578,U_1577)) ) ),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

fof(f_584_3,plain,
    ( ! [U_1582,U_1580] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_1580)),U_1582)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(U_1582,U_1580)) )
    & ! [U_1581,U_1579] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_1579)),U_1581)) = insert1325755072e_bool(U_1579,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_1581,U_1579)) ) ),
    inference(miniscope,[status(thm)],[f_584_2]) ).

fof(f_584_4,plain,
    ( ! [U_1580,U_1582] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_1580)),U_1582)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(U_1582,U_1580)) )
    & ! [U_1581,U_1579] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_1579)),U_1581)) = insert1325755072e_bool(U_1579,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_1581,U_1579)) ) ),
    inference(definitional_conversion,[status(esa)],[f_584_3]) ).

cnf(f_584_5,plain,
    ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_1579)),U_1581)) = insert1325755072e_bool(U_1579,bot_bo1649642514l_bool)
    | ~ hBOOL(hAPP_f1664156314l_bool(U_1581,U_1579)) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

cnf(f_584_6,plain,
    ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_1580)),U_1582)) = bot_bo1649642514l_bool
    | hBOOL(hAPP_f1664156314l_bool(U_1582,U_1580)) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

fof(f_585_1,plain,
    ! [Pa,A_3] :
      ( ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,A_3)),Pa)) = bot_bo1389914601l_bool
        | hBOOL(hAPP_fun_a_bool_bool(Pa,A_3)) )
      & ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,A_3)),Pa)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool)
        | ~ hBOOL(hAPP_fun_a_bool_bool(Pa,A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_481_Collect__conv__if2]) ).

fof(f_585_2,plain,
    ! [U_1584,U_1583] :
      ( ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,U_1583)),U_1584)) = bot_bo1389914601l_bool
        | hBOOL(hAPP_fun_a_bool_bool(U_1584,U_1583)) )
      & ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,U_1583)),U_1584)) = insert_fun_a_bool(U_1583,bot_bo1389914601l_bool)
        | ~ hBOOL(hAPP_fun_a_bool_bool(U_1584,U_1583)) ) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

fof(f_585_3,plain,
    ( ! [U_1588,U_1586] :
        ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,U_1586)),U_1588)) = bot_bo1389914601l_bool
        | hBOOL(hAPP_fun_a_bool_bool(U_1588,U_1586)) )
    & ! [U_1587,U_1585] :
        ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,U_1585)),U_1587)) = insert_fun_a_bool(U_1585,bot_bo1389914601l_bool)
        | ~ hBOOL(hAPP_fun_a_bool_bool(U_1587,U_1585)) ) ),
    inference(miniscope,[status(thm)],[f_585_2]) ).

fof(f_585_4,plain,
    ( ! [U_1586,U_1588] :
        ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,U_1586)),U_1588)) = bot_bo1389914601l_bool
        | hBOOL(hAPP_fun_a_bool_bool(U_1588,U_1586)) )
    & ! [U_1587,U_1585] :
        ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,U_1585)),U_1587)) = insert_fun_a_bool(U_1585,bot_bo1389914601l_bool)
        | ~ hBOOL(hAPP_fun_a_bool_bool(U_1587,U_1585)) ) ),
    inference(definitional_conversion,[status(esa)],[f_585_3]) ).

cnf(f_585_5,plain,
    ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,U_1585)),U_1587)) = insert_fun_a_bool(U_1585,bot_bo1389914601l_bool)
    | ~ hBOOL(hAPP_fun_a_bool_bool(U_1587,U_1585)) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

cnf(f_585_6,plain,
    ( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,U_1586)),U_1588)) = bot_bo1389914601l_bool
    | hBOOL(hAPP_fun_a_bool_bool(U_1588,U_1586)) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

fof(f_586_1,plain,
    ! [A_3] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_3)) = insert_nat(A_3,bot_bot_fun_nat_bool),
    inference(fof_nnf,[status(thm)],[fact_482_singleton__conv]) ).

fof(f_586_2,plain,
    ! [U_1589] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1589)) = insert_nat(U_1589,bot_bot_fun_nat_bool),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

fof(f_586_3,plain,
    ! [U_1589] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1589)) = insert_nat(U_1589,bot_bot_fun_nat_bool),
    inference(definitional_conversion,[status(esa)],[f_586_2]) ).

cnf(f_586_4,plain,
    collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1589)) = insert_nat(U_1589,bot_bot_fun_nat_bool),
    inference(clausify,[status(thm)],[f_586_3]) ).

fof(f_587_1,plain,
    ! [A_3] : collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_3)) = insert_pname(A_3,bot_bo844097828e_bool),
    inference(fof_nnf,[status(thm)],[fact_483_singleton__conv]) ).

fof(f_587_2,plain,
    ! [U_1590] : collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1590)) = insert_pname(U_1590,bot_bo844097828e_bool),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

fof(f_587_3,plain,
    ! [U_1590] : collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1590)) = insert_pname(U_1590,bot_bo844097828e_bool),
    inference(definitional_conversion,[status(esa)],[f_587_2]) ).

cnf(f_587_4,plain,
    collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1590)) = insert_pname(U_1590,bot_bo844097828e_bool),
    inference(clausify,[status(thm)],[f_587_3]) ).

fof(f_588_1,plain,
    ! [A_3] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_3)) = insert_a(A_3,bot_bot_fun_a_bool),
    inference(fof_nnf,[status(thm)],[fact_484_singleton__conv]) ).

fof(f_588_2,plain,
    ! [U_1591] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1591)) = insert_a(U_1591,bot_bot_fun_a_bool),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

fof(f_588_3,plain,
    ! [U_1591] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1591)) = insert_a(U_1591,bot_bot_fun_a_bool),
    inference(definitional_conversion,[status(esa)],[f_588_2]) ).

cnf(f_588_4,plain,
    collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1591)) = insert_a(U_1591,bot_bot_fun_a_bool),
    inference(clausify,[status(thm)],[f_588_3]) ).

fof(f_589_1,plain,
    ! [A_3] : collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_3)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool),
    inference(fof_nnf,[status(thm)],[fact_485_singleton__conv]) ).

fof(f_589_2,plain,
    ! [U_1592] : collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1592)) = insert_fun_nat_bool(U_1592,bot_bo1701429464l_bool),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

fof(f_589_3,plain,
    ! [U_1592] : collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1592)) = insert_fun_nat_bool(U_1592,bot_bo1701429464l_bool),
    inference(definitional_conversion,[status(esa)],[f_589_2]) ).

cnf(f_589_4,plain,
    collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_1592)) = insert_fun_nat_bool(U_1592,bot_bo1701429464l_bool),
    inference(clausify,[status(thm)],[f_589_3]) ).

fof(f_590_1,plain,
    ! [A_3] : collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_3)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool),
    inference(fof_nnf,[status(thm)],[fact_486_singleton__conv]) ).

fof(f_590_2,plain,
    ! [U_1593] : collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1593)) = insert1325755072e_bool(U_1593,bot_bo1649642514l_bool),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

fof(f_590_3,plain,
    ! [U_1593] : collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1593)) = insert1325755072e_bool(U_1593,bot_bo1649642514l_bool),
    inference(definitional_conversion,[status(esa)],[f_590_2]) ).

cnf(f_590_4,plain,
    collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_1593)) = insert1325755072e_bool(U_1593,bot_bo1649642514l_bool),
    inference(clausify,[status(thm)],[f_590_3]) ).

fof(f_591_1,plain,
    ! [A_3] : collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_3)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool),
    inference(fof_nnf,[status(thm)],[fact_487_singleton__conv]) ).

fof(f_591_2,plain,
    ! [U_1594] : collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1594)) = insert_fun_a_bool(U_1594,bot_bo1389914601l_bool),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

fof(f_591_3,plain,
    ! [U_1594] : collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1594)) = insert_fun_a_bool(U_1594,bot_bo1389914601l_bool),
    inference(definitional_conversion,[status(esa)],[f_591_2]) ).

cnf(f_591_4,plain,
    collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_1594)) = insert_fun_a_bool(U_1594,bot_bo1389914601l_bool),
    inference(clausify,[status(thm)],[f_591_3]) ).

fof(f_592_1,plain,
    ! [A_3] : collect_nat(hAPP_n1699378549t_bool(fequal_nat,A_3)) = insert_nat(A_3,bot_bot_fun_nat_bool),
    inference(fof_nnf,[status(thm)],[fact_488_singleton__conv2]) ).

fof(f_592_2,plain,
    ! [U_1595] : collect_nat(hAPP_n1699378549t_bool(fequal_nat,U_1595)) = insert_nat(U_1595,bot_bot_fun_nat_bool),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

fof(f_592_3,plain,
    ! [U_1595] : collect_nat(hAPP_n1699378549t_bool(fequal_nat,U_1595)) = insert_nat(U_1595,bot_bot_fun_nat_bool),
    inference(definitional_conversion,[status(esa)],[f_592_2]) ).

cnf(f_592_4,plain,
    collect_nat(hAPP_n1699378549t_bool(fequal_nat,U_1595)) = insert_nat(U_1595,bot_bot_fun_nat_bool),
    inference(clausify,[status(thm)],[f_592_3]) ).

fof(f_593_1,plain,
    ! [A_3] : collect_pname(hAPP_p61793385e_bool(fequal_pname,A_3)) = insert_pname(A_3,bot_bo844097828e_bool),
    inference(fof_nnf,[status(thm)],[fact_489_singleton__conv2]) ).

fof(f_593_2,plain,
    ! [U_1596] : collect_pname(hAPP_p61793385e_bool(fequal_pname,U_1596)) = insert_pname(U_1596,bot_bo844097828e_bool),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

fof(f_593_3,plain,
    ! [U_1596] : collect_pname(hAPP_p61793385e_bool(fequal_pname,U_1596)) = insert_pname(U_1596,bot_bo844097828e_bool),
    inference(definitional_conversion,[status(esa)],[f_593_2]) ).

cnf(f_593_4,plain,
    collect_pname(hAPP_p61793385e_bool(fequal_pname,U_1596)) = insert_pname(U_1596,bot_bo844097828e_bool),
    inference(clausify,[status(thm)],[f_593_3]) ).

fof(f_594_1,plain,
    ! [A_3] : collect_a(hAPP_a_fun_a_bool(fequal_a,A_3)) = insert_a(A_3,bot_bot_fun_a_bool),
    inference(fof_nnf,[status(thm)],[fact_490_singleton__conv2]) ).

fof(f_594_2,plain,
    ! [U_1597] : collect_a(hAPP_a_fun_a_bool(fequal_a,U_1597)) = insert_a(U_1597,bot_bot_fun_a_bool),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

fof(f_594_3,plain,
    ! [U_1597] : collect_a(hAPP_a_fun_a_bool(fequal_a,U_1597)) = insert_a(U_1597,bot_bot_fun_a_bool),
    inference(definitional_conversion,[status(esa)],[f_594_2]) ).

cnf(f_594_4,plain,
    collect_a(hAPP_a_fun_a_bool(fequal_a,U_1597)) = insert_a(U_1597,bot_bot_fun_a_bool),
    inference(clausify,[status(thm)],[f_594_3]) ).

fof(f_595_1,plain,
    ! [A_3] : collect_fun_nat_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,A_3)) = insert_fun_nat_bool(A_3,bot_bo1701429464l_bool),
    inference(fof_nnf,[status(thm)],[fact_491_singleton__conv2]) ).

fof(f_595_2,plain,
    ! [U_1598] : collect_fun_nat_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_1598)) = insert_fun_nat_bool(U_1598,bot_bo1701429464l_bool),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

fof(f_595_3,plain,
    ! [U_1598] : collect_fun_nat_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_1598)) = insert_fun_nat_bool(U_1598,bot_bo1701429464l_bool),
    inference(definitional_conversion,[status(esa)],[f_595_2]) ).

cnf(f_595_4,plain,
    collect_fun_nat_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_1598)) = insert_fun_nat_bool(U_1598,bot_bo1701429464l_bool),
    inference(clausify,[status(thm)],[f_595_3]) ).

fof(f_596_1,plain,
    ! [A_3] : collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,A_3)) = insert1325755072e_bool(A_3,bot_bo1649642514l_bool),
    inference(fof_nnf,[status(thm)],[fact_492_singleton__conv2]) ).

fof(f_596_2,plain,
    ! [U_1599] : collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_1599)) = insert1325755072e_bool(U_1599,bot_bo1649642514l_bool),
    inference(variable_rename,[status(thm)],[f_596_1]) ).

fof(f_596_3,plain,
    ! [U_1599] : collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_1599)) = insert1325755072e_bool(U_1599,bot_bo1649642514l_bool),
    inference(definitional_conversion,[status(esa)],[f_596_2]) ).

cnf(f_596_4,plain,
    collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_1599)) = insert1325755072e_bool(U_1599,bot_bo1649642514l_bool),
    inference(clausify,[status(thm)],[f_596_3]) ).

fof(f_597_1,plain,
    ! [A_3] : collect_fun_a_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,A_3)) = insert_fun_a_bool(A_3,bot_bo1389914601l_bool),
    inference(fof_nnf,[status(thm)],[fact_493_singleton__conv2]) ).

fof(f_597_2,plain,
    ! [U_1600] : collect_fun_a_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_1600)) = insert_fun_a_bool(U_1600,bot_bo1389914601l_bool),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

fof(f_597_3,plain,
    ! [U_1600] : collect_fun_a_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_1600)) = insert_fun_a_bool(U_1600,bot_bo1389914601l_bool),
    inference(definitional_conversion,[status(esa)],[f_597_2]) ).

cnf(f_597_4,plain,
    collect_fun_a_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_1600)) = insert_fun_a_bool(U_1600,bot_bo1389914601l_bool),
    inference(clausify,[status(thm)],[f_597_3]) ).

fof(f_598_1,plain,
    ! [A_1,X_3] :
      ( A_1 = insert_nat(X_3,bot_bot_fun_nat_bool)
      | A_1 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_1),insert_nat(X_3,bot_bot_fun_nat_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_494_subset__singletonD]) ).

fof(f_598_2,plain,
    ! [U_1602,U_1601] :
      ( U_1602 = insert_nat(U_1601,bot_bot_fun_nat_bool)
      | U_1602 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1602),insert_nat(U_1601,bot_bot_fun_nat_bool))) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

fof(f_598_3,plain,
    ! [U_1601,U_1602] :
      ( U_1602 = insert_nat(U_1601,bot_bot_fun_nat_bool)
      | U_1602 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1602),insert_nat(U_1601,bot_bot_fun_nat_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_598_2]) ).

cnf(f_598_4,plain,
    ( U_1602 = insert_nat(U_1601,bot_bot_fun_nat_bool)
    | U_1602 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1602),insert_nat(U_1601,bot_bot_fun_nat_bool))) ),
    inference(clausify,[status(thm)],[f_598_3]) ).

fof(f_599_1,plain,
    ! [A_1,X_3] :
      ( A_1 = insert_pname(X_3,bot_bo844097828e_bool)
      | A_1 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_1),insert_pname(X_3,bot_bo844097828e_bool)))
      | ~ is_fun_pname_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_495_subset__singletonD]) ).

fof(f_599_2,plain,
    ! [U_1604,U_1603] :
      ( U_1604 = insert_pname(U_1603,bot_bo844097828e_bool)
      | U_1604 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1604),insert_pname(U_1603,bot_bo844097828e_bool)))
      | ~ is_fun_pname_bool(U_1604) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

fof(f_599_3,plain,
    ! [U_1604] :
      ( ! [U_1603] :
          ( U_1604 = insert_pname(U_1603,bot_bo844097828e_bool)
          | U_1604 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1604),insert_pname(U_1603,bot_bo844097828e_bool))) )
      | ~ is_fun_pname_bool(U_1604) ),
    inference(miniscope,[status(thm)],[f_599_2]) ).

fof(f_599_4,plain,
    ! [U_1604,U_1603] :
      ( U_1604 = insert_pname(U_1603,bot_bo844097828e_bool)
      | U_1604 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1604),insert_pname(U_1603,bot_bo844097828e_bool)))
      | ~ is_fun_pname_bool(U_1604) ),
    inference(definitional_conversion,[status(esa)],[f_599_3]) ).

cnf(f_599_5,plain,
    ( U_1604 = insert_pname(U_1603,bot_bo844097828e_bool)
    | U_1604 = bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1604),insert_pname(U_1603,bot_bo844097828e_bool)))
    | ~ is_fun_pname_bool(U_1604) ),
    inference(clausify,[status(thm)],[f_599_4]) ).

fof(f_600_1,plain,
    ! [A_1,X_3] :
      ( A_1 = insert_a(X_3,bot_bot_fun_a_bool)
      | A_1 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_1),insert_a(X_3,bot_bot_fun_a_bool)))
      | ~ is_fun_a_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_496_subset__singletonD]) ).

fof(f_600_2,plain,
    ! [U_1606,U_1605] :
      ( U_1606 = insert_a(U_1605,bot_bot_fun_a_bool)
      | U_1606 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1606),insert_a(U_1605,bot_bot_fun_a_bool)))
      | ~ is_fun_a_bool(U_1606) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

fof(f_600_3,plain,
    ! [U_1606] :
      ( ! [U_1605] :
          ( U_1606 = insert_a(U_1605,bot_bot_fun_a_bool)
          | U_1606 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1606),insert_a(U_1605,bot_bot_fun_a_bool))) )
      | ~ is_fun_a_bool(U_1606) ),
    inference(miniscope,[status(thm)],[f_600_2]) ).

fof(f_600_4,plain,
    ! [U_1605,U_1606] :
      ( U_1606 = insert_a(U_1605,bot_bot_fun_a_bool)
      | U_1606 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1606),insert_a(U_1605,bot_bot_fun_a_bool)))
      | ~ is_fun_a_bool(U_1606) ),
    inference(definitional_conversion,[status(esa)],[f_600_3]) ).

cnf(f_600_5,plain,
    ( U_1606 = insert_a(U_1605,bot_bot_fun_a_bool)
    | U_1606 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1606),insert_a(U_1605,bot_bot_fun_a_bool)))
    | ~ is_fun_a_bool(U_1606) ),
    inference(clausify,[status(thm)],[f_600_4]) ).

fof(f_601_1,plain,
    ! [C_1,X_3,A_1] :
      ( image_pname_a(cOMBK_a_pname(C_1),A_1) = insert_a(C_1,bot_bot_fun_a_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_3),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_497_image__constant]) ).

fof(f_601_2,plain,
    ! [U_1609,U_1608,U_1607] :
      ( image_pname_a(cOMBK_a_pname(U_1609),U_1607) = insert_a(U_1609,bot_bot_fun_a_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1608),U_1607)) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

fof(f_601_3,plain,
    ! [U_1608,U_1609,U_1607] :
      ( image_pname_a(cOMBK_a_pname(U_1609),U_1607) = insert_a(U_1609,bot_bot_fun_a_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1608),U_1607)) ),
    inference(definitional_conversion,[status(esa)],[f_601_2]) ).

cnf(f_601_4,plain,
    ( image_pname_a(cOMBK_a_pname(U_1609),U_1607) = insert_a(U_1609,bot_bot_fun_a_bool)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1608),U_1607)) ),
    inference(clausify,[status(thm)],[f_601_3]) ).

fof(f_602_1,plain,
    ! [C_1,A_1] :
      ( ( ( image_pname_a(cOMBK_a_pname(C_1),A_1) = insert_a(C_1,bot_bot_fun_a_bool)
          | A_1 = bot_bo844097828e_bool )
        & ( image_pname_a(cOMBK_a_pname(C_1),A_1) = bot_bot_fun_a_bool
          | A_1 != bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_498_image__constant__conv]) ).

fof(f_602_2,plain,
    ! [U_1611,U_1610] :
      ( ( ( image_pname_a(cOMBK_a_pname(U_1611),U_1610) = insert_a(U_1611,bot_bot_fun_a_bool)
          | U_1610 = bot_bo844097828e_bool )
        & ( image_pname_a(cOMBK_a_pname(U_1611),U_1610) = bot_bot_fun_a_bool
          | U_1610 != bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(U_1610) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

fof(f_602_3,plain,
    ( ! [U_1610,U_1611] :
        ( image_pname_a(cOMBK_a_pname(U_1611),U_1610) = insert_a(U_1611,bot_bot_fun_a_bool)
        | U_1610 = bot_bo844097828e_bool
        | ~ sP170(U_1610,U_1611) )
    & ! [U_1610,U_1611] :
        ( image_pname_a(cOMBK_a_pname(U_1611),U_1610) = bot_bot_fun_a_bool
        | U_1610 != bot_bo844097828e_bool
        | ~ sP170(U_1610,U_1611) )
    & ! [U_1610,U_1611] :
        ( sP170(U_1610,U_1611)
        | ~ is_fun_pname_bool(U_1610) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170])],[f_602_2]) ).

cnf(f_602_4,plain,
    ( sP170(U_1610,U_1611)
    | ~ is_fun_pname_bool(U_1610) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

cnf(f_602_5,plain,
    ( image_pname_a(cOMBK_a_pname(U_1611),U_1610) = bot_bot_fun_a_bool
    | U_1610 != bot_bo844097828e_bool
    | ~ sP170(U_1610,U_1611) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

cnf(f_602_6,plain,
    ( image_pname_a(cOMBK_a_pname(U_1611),U_1610) = insert_a(U_1611,bot_bot_fun_a_bool)
    | U_1610 = bot_bo844097828e_bool
    | ~ sP170(U_1610,U_1611) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

fof(f_603_1,plain,
    ! [X_9,Y_8] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_8),X_9))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_9),Y_8)) ),
    inference(fof_nnf,[status(thm)],[fact_499_linorder__le__cases]) ).

fof(f_603_2,plain,
    ! [U_1613,U_1612] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1612),U_1613))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1613),U_1612)) ),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

fof(f_603_3,plain,
    ! [U_1613,U_1612] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1612),U_1613))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1613),U_1612)) ),
    inference(definitional_conversion,[status(esa)],[f_603_2]) ).

cnf(f_603_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1612),U_1613))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1613),U_1612)) ),
    inference(clausify,[status(thm)],[f_603_3]) ).

fof(f_604_1,plain,
    ! [Z_1,Y_2,X_3] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),X_3))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)) ),
    inference(fof_nnf,[status(thm)],[fact_500_xt1_I6_J]) ).

fof(f_604_2,plain,
    ! [U_1616,U_1615,U_1614] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1616),U_1614))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1616),U_1615))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1615),U_1614)) ),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

fof(f_604_3,plain,
    ! [U_1614,U_1615,U_1616] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1616),U_1614))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1616),U_1615))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1615),U_1614)) ),
    inference(definitional_conversion,[status(esa)],[f_604_2]) ).

cnf(f_604_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1616),U_1614))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1616),U_1615))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1615),U_1614)) ),
    inference(clausify,[status(thm)],[f_604_3]) ).

fof(f_605_1,plain,
    ! [Z_1,Y_2,X_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),X_3))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)) ),
    inference(fof_nnf,[status(thm)],[fact_501_xt1_I6_J]) ).

fof(f_605_2,plain,
    ! [U_1619,U_1618,U_1617] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1619),U_1617))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1619),U_1618))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1618),U_1617)) ),
    inference(variable_rename,[status(thm)],[f_605_1]) ).

fof(f_605_3,plain,
    ! [U_1618,U_1617,U_1619] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1619),U_1617))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1619),U_1618))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1618),U_1617)) ),
    inference(definitional_conversion,[status(esa)],[f_605_2]) ).

cnf(f_605_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1619),U_1617))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1619),U_1618))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1618),U_1617)) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

fof(f_606_1,plain,
    ! [Z_1,Y_2,X_3] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z_1),X_3))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3)) ),
    inference(fof_nnf,[status(thm)],[fact_502_xt1_I6_J]) ).

fof(f_606_2,plain,
    ! [U_1622,U_1621,U_1620] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1622),U_1620))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1622),U_1621))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1621),U_1620)) ),
    inference(variable_rename,[status(thm)],[f_606_1]) ).

fof(f_606_3,plain,
    ! [U_1620,U_1621,U_1622] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1622),U_1620))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1622),U_1621))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1621),U_1620)) ),
    inference(definitional_conversion,[status(esa)],[f_606_2]) ).

cnf(f_606_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1622),U_1620))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1622),U_1621))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1621),U_1620)) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

fof(f_607_1,plain,
    ! [Z_3,Y_7,X_8] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_3),X_8))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_3),Y_7))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_7),X_8)) ),
    inference(fof_nnf,[status(thm)],[fact_503_xt1_I6_J]) ).

fof(f_607_2,plain,
    ! [U_1625,U_1624,U_1623] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1625),U_1623))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1625),U_1624))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1624),U_1623)) ),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

fof(f_607_3,plain,
    ! [U_1623,U_1624,U_1625] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1625),U_1623))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1625),U_1624))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1624),U_1623)) ),
    inference(definitional_conversion,[status(esa)],[f_607_2]) ).

cnf(f_607_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1625),U_1623))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1625),U_1624))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1624),U_1623)) ),
    inference(clausify,[status(thm)],[f_607_3]) ).

fof(f_608_1,plain,
    ! [Z_1,Y_2,X_3] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_1),X_3))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_1),Y_2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3)) ),
    inference(fof_nnf,[status(thm)],[fact_504_xt1_I6_J]) ).

fof(f_608_2,plain,
    ! [U_1628,U_1627,U_1626] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1628),U_1626))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1628),U_1627))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1627),U_1626)) ),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

fof(f_608_3,plain,
    ! [U_1626,U_1627,U_1628] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1628),U_1626))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1628),U_1627))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1627),U_1626)) ),
    inference(definitional_conversion,[status(esa)],[f_608_2]) ).

cnf(f_608_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1628),U_1626))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1628),U_1627))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1627),U_1626)) ),
    inference(clausify,[status(thm)],[f_608_3]) ).

fof(f_609_1,plain,
    ! [Y_2,X_3] :
      ( ( ( hBOOL(X_3)
          | ~ hBOOL(Y_2) )
        & ( hBOOL(Y_2)
          | ~ hBOOL(X_3) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)) ),
    inference(fof_nnf,[status(thm)],[fact_505_xt1_I5_J]) ).

fof(f_609_2,plain,
    ! [U_1630,U_1629] :
      ( ( ( hBOOL(U_1629)
          | ~ hBOOL(U_1630) )
        & ( hBOOL(U_1630)
          | ~ hBOOL(U_1629) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1629),U_1630))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1630),U_1629)) ),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

fof(f_609_3,plain,
    ( ! [U_1629,U_1630] :
        ( hBOOL(U_1629)
        | ~ hBOOL(U_1630)
        | ~ sP171(U_1629,U_1630) )
    & ! [U_1629,U_1630] :
        ( hBOOL(U_1630)
        | ~ hBOOL(U_1629)
        | ~ sP171(U_1629,U_1630) )
    & ! [U_1629,U_1630] :
        ( sP171(U_1629,U_1630)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1629),U_1630))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1630),U_1629)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP171])],[f_609_2]) ).

cnf(f_609_4,plain,
    ( sP171(U_1629,U_1630)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1629),U_1630))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1630),U_1629)) ),
    inference(clausify,[status(thm)],[f_609_3]) ).

cnf(f_609_5,plain,
    ( hBOOL(U_1630)
    | ~ hBOOL(U_1629)
    | ~ sP171(U_1629,U_1630) ),
    inference(clausify,[status(thm)],[f_609_3]) ).

cnf(f_609_6,plain,
    ( hBOOL(U_1629)
    | ~ hBOOL(U_1630)
    | ~ sP171(U_1629,U_1630) ),
    inference(clausify,[status(thm)],[f_609_3]) ).

fof(f_610_1,plain,
    ! [Y_2,X_3] :
      ( X_3 = Y_2
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)) ),
    inference(fof_nnf,[status(thm)],[fact_506_xt1_I5_J]) ).

fof(f_610_2,plain,
    ! [U_1632,U_1631] :
      ( U_1631 = U_1632
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1631),U_1632))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1632),U_1631)) ),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

fof(f_610_3,plain,
    ! [U_1632,U_1631] :
      ( U_1631 = U_1632
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1631),U_1632))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1632),U_1631)) ),
    inference(definitional_conversion,[status(esa)],[f_610_2]) ).

cnf(f_610_4,plain,
    ( U_1631 = U_1632
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1631),U_1632))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1632),U_1631)) ),
    inference(clausify,[status(thm)],[f_610_3]) ).

fof(f_611_1,plain,
    ! [Y_2,X_3] :
      ( X_3 = Y_2
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3))
      | ~ is_fun_pname_bool(X_3)
      | ~ is_fun_pname_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_507_xt1_I5_J]) ).

fof(f_611_2,plain,
    ! [U_1634,U_1633] :
      ( U_1633 = U_1634
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1633),U_1634))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1634),U_1633))
      | ~ is_fun_pname_bool(U_1633)
      | ~ is_fun_pname_bool(U_1634) ),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

fof(f_611_3,plain,
    ! [U_1634,U_1633] :
      ( U_1633 = U_1634
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1633),U_1634))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1634),U_1633))
      | ~ is_fun_pname_bool(U_1633)
      | ~ is_fun_pname_bool(U_1634) ),
    inference(definitional_conversion,[status(esa)],[f_611_2]) ).

cnf(f_611_4,plain,
    ( U_1633 = U_1634
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1633),U_1634))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1634),U_1633))
    | ~ is_fun_pname_bool(U_1633)
    | ~ is_fun_pname_bool(U_1634) ),
    inference(clausify,[status(thm)],[f_611_3]) ).

fof(f_612_1,plain,
    ! [Y_6,X_7] :
      ( 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),X_7)) ),
    inference(fof_nnf,[status(thm)],[fact_508_xt1_I5_J]) ).

fof(f_612_2,plain,
    ! [U_1636,U_1635] :
      ( U_1635 = U_1636
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1635),U_1636))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1636),U_1635)) ),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

fof(f_612_3,plain,
    ! [U_1635,U_1636] :
      ( U_1635 = U_1636
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1635),U_1636))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1636),U_1635)) ),
    inference(definitional_conversion,[status(esa)],[f_612_2]) ).

cnf(f_612_4,plain,
    ( U_1635 = U_1636
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1635),U_1636))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1636),U_1635)) ),
    inference(clausify,[status(thm)],[f_612_3]) ).

fof(f_613_1,plain,
    ! [Y_2,X_3] :
      ( X_3 = Y_2
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3))
      | ~ is_fun_a_bool(X_3)
      | ~ is_fun_a_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_509_xt1_I5_J]) ).

fof(f_613_2,plain,
    ! [U_1638,U_1637] :
      ( U_1637 = U_1638
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1637),U_1638))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1638),U_1637))
      | ~ is_fun_a_bool(U_1637)
      | ~ is_fun_a_bool(U_1638) ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

fof(f_613_3,plain,
    ! [U_1637,U_1638] :
      ( U_1637 = U_1638
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1637),U_1638))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1638),U_1637))
      | ~ is_fun_a_bool(U_1637)
      | ~ is_fun_a_bool(U_1638) ),
    inference(definitional_conversion,[status(esa)],[f_613_2]) ).

cnf(f_613_4,plain,
    ( U_1637 = U_1638
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1637),U_1638))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1638),U_1637))
    | ~ is_fun_a_bool(U_1637)
    | ~ is_fun_a_bool(U_1638) ),
    inference(clausify,[status(thm)],[f_613_3]) ).

fof(f_614_1,plain,
    ! [Z_1,X_3,Y_2] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Z_1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_510_order__trans]) ).

fof(f_614_2,plain,
    ! [U_1641,U_1640,U_1639] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1640),U_1641))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1639),U_1641))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1640),U_1639)) ),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

fof(f_614_3,plain,
    ! [U_1641,U_1640,U_1639] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1640),U_1641))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1639),U_1641))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1640),U_1639)) ),
    inference(definitional_conversion,[status(esa)],[f_614_2]) ).

cnf(f_614_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1640),U_1641))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1639),U_1641))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1640),U_1639)) ),
    inference(clausify,[status(thm)],[f_614_3]) ).

fof(f_615_1,plain,
    ! [Z_1,X_3,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Z_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_511_order__trans]) ).

fof(f_615_2,plain,
    ! [U_1644,U_1643,U_1642] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1643),U_1644))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1642),U_1644))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1643),U_1642)) ),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

fof(f_615_3,plain,
    ! [U_1643,U_1642,U_1644] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1643),U_1644))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1642),U_1644))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1643),U_1642)) ),
    inference(definitional_conversion,[status(esa)],[f_615_2]) ).

cnf(f_615_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1643),U_1644))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1642),U_1644))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1643),U_1642)) ),
    inference(clausify,[status(thm)],[f_615_3]) ).

fof(f_616_1,plain,
    ! [Z_1,X_3,Y_2] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Z_1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_512_order__trans]) ).

fof(f_616_2,plain,
    ! [U_1647,U_1646,U_1645] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1646),U_1647))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1645),U_1647))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1646),U_1645)) ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

fof(f_616_3,plain,
    ! [U_1645,U_1646,U_1647] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1646),U_1647))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1645),U_1647))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1646),U_1645)) ),
    inference(definitional_conversion,[status(esa)],[f_616_2]) ).

cnf(f_616_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1646),U_1647))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1645),U_1647))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1646),U_1645)) ),
    inference(clausify,[status(thm)],[f_616_3]) ).

fof(f_617_1,plain,
    ! [Z_2,X_6,Y_5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Z_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),Z_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Y_5)) ),
    inference(fof_nnf,[status(thm)],[fact_513_order__trans]) ).

fof(f_617_2,plain,
    ! [U_1650,U_1649,U_1648] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1649),U_1650))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1648),U_1650))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1649),U_1648)) ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

fof(f_617_3,plain,
    ! [U_1648,U_1649,U_1650] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1649),U_1650))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1648),U_1650))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1649),U_1648)) ),
    inference(definitional_conversion,[status(esa)],[f_617_2]) ).

cnf(f_617_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1649),U_1650))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1648),U_1650))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1649),U_1648)) ),
    inference(clausify,[status(thm)],[f_617_3]) ).

fof(f_618_1,plain,
    ! [Z_1,X_3,Y_2] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Z_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),Z_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_514_order__trans]) ).

fof(f_618_2,plain,
    ! [U_1653,U_1652,U_1651] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1652),U_1653))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1651),U_1653))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1652),U_1651)) ),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

fof(f_618_3,plain,
    ! [U_1652,U_1651,U_1653] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1652),U_1653))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1651),U_1653))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1652),U_1651)) ),
    inference(definitional_conversion,[status(esa)],[f_618_2]) ).

cnf(f_618_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1652),U_1653))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1651),U_1653))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1652),U_1651)) ),
    inference(clausify,[status(thm)],[f_618_3]) ).

fof(f_619_1,plain,
    ! [X_3,Y_2] :
      ( ( ( hBOOL(X_3)
          | ~ hBOOL(Y_2) )
        & ( hBOOL(Y_2)
          | ~ hBOOL(X_3) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_515_order__antisym]) ).

fof(f_619_2,plain,
    ! [U_1655,U_1654] :
      ( ( ( hBOOL(U_1655)
          | ~ hBOOL(U_1654) )
        & ( hBOOL(U_1654)
          | ~ hBOOL(U_1655) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1654),U_1655))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1655),U_1654)) ),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

fof(f_619_3,plain,
    ( ! [U_1654,U_1655] :
        ( hBOOL(U_1655)
        | ~ hBOOL(U_1654)
        | ~ sP172(U_1654,U_1655) )
    & ! [U_1654,U_1655] :
        ( hBOOL(U_1654)
        | ~ hBOOL(U_1655)
        | ~ sP172(U_1654,U_1655) )
    & ! [U_1654,U_1655] :
        ( sP172(U_1654,U_1655)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1654),U_1655))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1655),U_1654)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172])],[f_619_2]) ).

cnf(f_619_4,plain,
    ( sP172(U_1654,U_1655)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1654),U_1655))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1655),U_1654)) ),
    inference(clausify,[status(thm)],[f_619_3]) ).

cnf(f_619_5,plain,
    ( hBOOL(U_1654)
    | ~ hBOOL(U_1655)
    | ~ sP172(U_1654,U_1655) ),
    inference(clausify,[status(thm)],[f_619_3]) ).

cnf(f_619_6,plain,
    ( hBOOL(U_1655)
    | ~ hBOOL(U_1654)
    | ~ sP172(U_1654,U_1655) ),
    inference(clausify,[status(thm)],[f_619_3]) ).

fof(f_620_1,plain,
    ! [X_3,Y_2] :
      ( X_3 = Y_2
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_516_order__antisym]) ).

fof(f_620_2,plain,
    ! [U_1657,U_1656] :
      ( U_1657 = U_1656
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1656),U_1657))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1657),U_1656)) ),
    inference(variable_rename,[status(thm)],[f_620_1]) ).

fof(f_620_3,plain,
    ! [U_1657,U_1656] :
      ( U_1657 = U_1656
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1656),U_1657))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1657),U_1656)) ),
    inference(definitional_conversion,[status(esa)],[f_620_2]) ).

cnf(f_620_4,plain,
    ( U_1657 = U_1656
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1656),U_1657))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1657),U_1656)) ),
    inference(clausify,[status(thm)],[f_620_3]) ).

fof(f_621_1,plain,
    ! [X_3,Y_2] :
      ( X_3 = Y_2
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2))
      | ~ is_fun_pname_bool(Y_2)
      | ~ is_fun_pname_bool(X_3) ),
    inference(fof_nnf,[status(thm)],[fact_517_order__antisym]) ).

fof(f_621_2,plain,
    ! [U_1659,U_1658] :
      ( U_1659 = U_1658
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1658),U_1659))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1659),U_1658))
      | ~ is_fun_pname_bool(U_1658)
      | ~ is_fun_pname_bool(U_1659) ),
    inference(variable_rename,[status(thm)],[f_621_1]) ).

fof(f_621_3,plain,
    ! [U_1659,U_1658] :
      ( U_1659 = U_1658
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1658),U_1659))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1659),U_1658))
      | ~ is_fun_pname_bool(U_1658)
      | ~ is_fun_pname_bool(U_1659) ),
    inference(definitional_conversion,[status(esa)],[f_621_2]) ).

cnf(f_621_4,plain,
    ( U_1659 = U_1658
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1658),U_1659))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1659),U_1658))
    | ~ is_fun_pname_bool(U_1658)
    | ~ is_fun_pname_bool(U_1659) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

fof(f_622_1,plain,
    ! [X_5,Y_4] :
      ( X_5 = Y_4
      | ~ 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,X_5),Y_4)) ),
    inference(fof_nnf,[status(thm)],[fact_518_order__antisym]) ).

fof(f_622_2,plain,
    ! [U_1661,U_1660] :
      ( U_1661 = U_1660
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1660),U_1661))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1661),U_1660)) ),
    inference(variable_rename,[status(thm)],[f_622_1]) ).

fof(f_622_3,plain,
    ! [U_1660,U_1661] :
      ( U_1661 = U_1660
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1660),U_1661))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1661),U_1660)) ),
    inference(definitional_conversion,[status(esa)],[f_622_2]) ).

cnf(f_622_4,plain,
    ( U_1661 = U_1660
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1660),U_1661))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1661),U_1660)) ),
    inference(clausify,[status(thm)],[f_622_3]) ).

fof(f_623_1,plain,
    ! [X_3,Y_2] :
      ( X_3 = Y_2
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2))
      | ~ is_fun_a_bool(Y_2)
      | ~ is_fun_a_bool(X_3) ),
    inference(fof_nnf,[status(thm)],[fact_519_order__antisym]) ).

fof(f_623_2,plain,
    ! [U_1663,U_1662] :
      ( U_1663 = U_1662
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1662),U_1663))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1663),U_1662))
      | ~ is_fun_a_bool(U_1662)
      | ~ is_fun_a_bool(U_1663) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

fof(f_623_3,plain,
    ! [U_1662,U_1663] :
      ( U_1663 = U_1662
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1662),U_1663))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1663),U_1662))
      | ~ is_fun_a_bool(U_1662)
      | ~ is_fun_a_bool(U_1663) ),
    inference(definitional_conversion,[status(esa)],[f_623_2]) ).

cnf(f_623_4,plain,
    ( U_1663 = U_1662
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1662),U_1663))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1663),U_1662))
    | ~ is_fun_a_bool(U_1662)
    | ~ is_fun_a_bool(U_1663) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

fof(f_624_1,plain,
    ! [C_1,B_1,A_3] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C_1),A_3))
      | ( ~ hBOOL(B_1)
        & hBOOL(C_1) )
      | ( ~ hBOOL(C_1)
        & hBOOL(B_1) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_520_xt1_I4_J]) ).

fof(f_624_2,plain,
    ! [U_1666,U_1665,U_1664] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1666),U_1664))
      | ( ~ hBOOL(U_1665)
        & hBOOL(U_1666) )
      | ( ~ hBOOL(U_1666)
        & hBOOL(U_1665) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1665),U_1664)) ),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

fof(f_624_3,plain,
    ( ! [U_1665,U_1666] :
        ( ~ hBOOL(U_1665)
        | ~ sP174(U_1665,U_1666) )
    & ! [U_1665,U_1666] :
        ( hBOOL(U_1666)
        | ~ sP174(U_1665,U_1666) )
    & ! [U_1665,U_1666] :
        ( ~ hBOOL(U_1666)
        | ~ sP173(U_1665,U_1666) )
    & ! [U_1665,U_1666] :
        ( hBOOL(U_1665)
        | ~ sP173(U_1665,U_1666) )
    & ! [U_1664,U_1665,U_1666] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1666),U_1664))
        | sP174(U_1665,U_1666)
        | sP173(U_1665,U_1666)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1665),U_1664)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173,sP174])],[f_624_2]) ).

cnf(f_624_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1666),U_1664))
    | sP174(U_1665,U_1666)
    | sP173(U_1665,U_1666)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1665),U_1664)) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

cnf(f_624_5,plain,
    ( hBOOL(U_1665)
    | ~ sP173(U_1665,U_1666) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

cnf(f_624_6,plain,
    ( ~ hBOOL(U_1666)
    | ~ sP173(U_1665,U_1666) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

cnf(f_624_7,plain,
    ( hBOOL(U_1666)
    | ~ sP174(U_1665,U_1666) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

cnf(f_624_8,plain,
    ( ~ hBOOL(U_1665)
    | ~ sP174(U_1665,U_1666) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

fof(f_625_1,plain,
    ! [C_1,B_1,A_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_1),A_3))
      | B_1 != C_1
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_521_xt1_I4_J]) ).

fof(f_625_2,plain,
    ! [U_1669,U_1668,U_1667] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1669),U_1667))
      | U_1668 != U_1669
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1668),U_1667)) ),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

fof(f_625_3,plain,
    ! [U_1668,U_1669,U_1667] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1669),U_1667))
      | U_1668 != U_1669
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1668),U_1667)) ),
    inference(definitional_conversion,[status(esa)],[f_625_2]) ).

cnf(f_625_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1669),U_1667))
    | U_1668 != U_1669
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1668),U_1667)) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

fof(f_626_1,plain,
    ! [C_1,B_1,A_3] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_3))
      | B_1 != C_1
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_522_xt1_I4_J]) ).

fof(f_626_2,plain,
    ! [U_1672,U_1671,U_1670] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1672),U_1670))
      | U_1671 != U_1672
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1671),U_1670)) ),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

fof(f_626_3,plain,
    ! [U_1670,U_1671,U_1672] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1672),U_1670))
      | U_1671 != U_1672
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1671),U_1670)) ),
    inference(definitional_conversion,[status(esa)],[f_626_2]) ).

cnf(f_626_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1672),U_1670))
    | U_1671 != U_1672
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1671),U_1670)) ),
    inference(clausify,[status(thm)],[f_626_3]) ).

fof(f_627_1,plain,
    ! [C_5,B_5,A_7] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_5),A_7))
      | B_5 != C_5
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_5),A_7)) ),
    inference(fof_nnf,[status(thm)],[fact_523_xt1_I4_J]) ).

fof(f_627_2,plain,
    ! [U_1675,U_1674,U_1673] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1675),U_1673))
      | U_1674 != U_1675
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1674),U_1673)) ),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

fof(f_627_3,plain,
    ! [U_1674,U_1673,U_1675] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1675),U_1673))
      | U_1674 != U_1675
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1674),U_1673)) ),
    inference(definitional_conversion,[status(esa)],[f_627_2]) ).

cnf(f_627_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1675),U_1673))
    | U_1674 != U_1675
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1674),U_1673)) ),
    inference(clausify,[status(thm)],[f_627_3]) ).

fof(f_628_1,plain,
    ! [C_1,B_1,A_3] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_1),A_3))
      | B_1 != C_1
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_524_xt1_I4_J]) ).

fof(f_628_2,plain,
    ! [U_1678,U_1677,U_1676] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1678),U_1676))
      | U_1677 != U_1678
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1677),U_1676)) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

fof(f_628_3,plain,
    ! [U_1677,U_1676,U_1678] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1678),U_1676))
      | U_1677 != U_1678
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1677),U_1676)) ),
    inference(definitional_conversion,[status(esa)],[f_628_2]) ).

cnf(f_628_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1678),U_1676))
    | U_1677 != U_1678
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1677),U_1676)) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

fof(f_629_1,plain,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),C_1))
      | ( ~ hBOOL(B_1)
        & hBOOL(C_1) )
      | ( ~ hBOOL(C_1)
        & hBOOL(B_1) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_525_ord__le__eq__trans]) ).

fof(f_629_2,plain,
    ! [U_1681,U_1680,U_1679] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1680),U_1681))
      | ( ~ hBOOL(U_1679)
        & hBOOL(U_1681) )
      | ( ~ hBOOL(U_1681)
        & hBOOL(U_1679) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1680),U_1679)) ),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

fof(f_629_3,plain,
    ( ! [U_1679,U_1681] :
        ( ~ hBOOL(U_1679)
        | ~ sP176(U_1679,U_1681) )
    & ! [U_1679,U_1681] :
        ( hBOOL(U_1681)
        | ~ sP176(U_1679,U_1681) )
    & ! [U_1679,U_1681] :
        ( ~ hBOOL(U_1681)
        | ~ sP175(U_1679,U_1681) )
    & ! [U_1679,U_1681] :
        ( hBOOL(U_1679)
        | ~ sP175(U_1679,U_1681) )
    & ! [U_1679,U_1680,U_1681] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1680),U_1681))
        | sP176(U_1679,U_1681)
        | sP175(U_1679,U_1681)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1680),U_1679)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP175,sP176])],[f_629_2]) ).

cnf(f_629_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1680),U_1681))
    | sP176(U_1679,U_1681)
    | sP175(U_1679,U_1681)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1680),U_1679)) ),
    inference(clausify,[status(thm)],[f_629_3]) ).

cnf(f_629_5,plain,
    ( hBOOL(U_1679)
    | ~ sP175(U_1679,U_1681) ),
    inference(clausify,[status(thm)],[f_629_3]) ).

cnf(f_629_6,plain,
    ( ~ hBOOL(U_1681)
    | ~ sP175(U_1679,U_1681) ),
    inference(clausify,[status(thm)],[f_629_3]) ).

cnf(f_629_7,plain,
    ( hBOOL(U_1681)
    | ~ sP176(U_1679,U_1681) ),
    inference(clausify,[status(thm)],[f_629_3]) ).

cnf(f_629_8,plain,
    ( ~ hBOOL(U_1679)
    | ~ sP176(U_1679,U_1681) ),
    inference(clausify,[status(thm)],[f_629_3]) ).

fof(f_630_1,plain,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),C_1))
      | B_1 != C_1
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_526_ord__le__eq__trans]) ).

fof(f_630_2,plain,
    ! [U_1684,U_1683,U_1682] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1683),U_1684))
      | U_1682 != U_1684
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1683),U_1682)) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

fof(f_630_3,plain,
    ! [U_1682,U_1683,U_1684] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1683),U_1684))
      | U_1682 != U_1684
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1683),U_1682)) ),
    inference(definitional_conversion,[status(esa)],[f_630_2]) ).

cnf(f_630_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1683),U_1684))
    | U_1682 != U_1684
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1683),U_1682)) ),
    inference(clausify,[status(thm)],[f_630_3]) ).

fof(f_631_1,plain,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),C_1))
      | B_1 != C_1
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_527_ord__le__eq__trans]) ).

fof(f_631_2,plain,
    ! [U_1687,U_1686,U_1685] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1686),U_1687))
      | U_1685 != U_1687
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1686),U_1685)) ),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

fof(f_631_3,plain,
    ! [U_1685,U_1686,U_1687] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1686),U_1687))
      | U_1685 != U_1687
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1686),U_1685)) ),
    inference(definitional_conversion,[status(esa)],[f_631_2]) ).

cnf(f_631_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1686),U_1687))
    | U_1685 != U_1687
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1686),U_1685)) ),
    inference(clausify,[status(thm)],[f_631_3]) ).

fof(f_632_1,plain,
    ! [C_4,A_6,B_4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),C_4))
      | B_4 != C_4
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),B_4)) ),
    inference(fof_nnf,[status(thm)],[fact_528_ord__le__eq__trans]) ).

fof(f_632_2,plain,
    ! [U_1690,U_1689,U_1688] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1689),U_1690))
      | U_1688 != U_1690
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1689),U_1688)) ),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

fof(f_632_3,plain,
    ! [U_1689,U_1688,U_1690] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1689),U_1690))
      | U_1688 != U_1690
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1689),U_1688)) ),
    inference(definitional_conversion,[status(esa)],[f_632_2]) ).

cnf(f_632_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1689),U_1690))
    | U_1688 != U_1690
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1689),U_1688)) ),
    inference(clausify,[status(thm)],[f_632_3]) ).

fof(f_633_1,plain,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),C_1))
      | B_1 != C_1
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_529_ord__le__eq__trans]) ).

fof(f_633_2,plain,
    ! [U_1693,U_1692,U_1691] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1692),U_1693))
      | U_1691 != U_1693
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1692),U_1691)) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

fof(f_633_3,plain,
    ! [U_1693,U_1692,U_1691] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1692),U_1693))
      | U_1691 != U_1693
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1692),U_1691)) ),
    inference(definitional_conversion,[status(esa)],[f_633_2]) ).

cnf(f_633_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1692),U_1693))
    | U_1691 != U_1693
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1692),U_1691)) ),
    inference(clausify,[status(thm)],[f_633_3]) ).

fof(f_634_1,plain,
    ! [C_1,B_1,A_3] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C_1),A_3))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,C_1),B_1))
      | ( ~ hBOOL(A_3)
        & hBOOL(B_1) )
      | ( ~ hBOOL(B_1)
        & hBOOL(A_3) ) ),
    inference(fof_nnf,[status(thm)],[fact_530_xt1_I3_J]) ).

fof(f_634_2,plain,
    ! [U_1696,U_1695,U_1694] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1696),U_1694))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1696),U_1695))
      | ( ~ hBOOL(U_1694)
        & hBOOL(U_1695) )
      | ( ~ hBOOL(U_1695)
        & hBOOL(U_1694) ) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

fof(f_634_3,plain,
    ( ! [U_1694,U_1695] :
        ( ~ hBOOL(U_1694)
        | ~ sP178(U_1694,U_1695) )
    & ! [U_1694,U_1695] :
        ( hBOOL(U_1695)
        | ~ sP178(U_1694,U_1695) )
    & ! [U_1694,U_1695] :
        ( ~ hBOOL(U_1695)
        | ~ sP177(U_1694,U_1695) )
    & ! [U_1694,U_1695] :
        ( hBOOL(U_1694)
        | ~ sP177(U_1694,U_1695) )
    & ! [U_1694,U_1696,U_1695] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1696),U_1694))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1696),U_1695))
        | sP178(U_1694,U_1695)
        | sP177(U_1694,U_1695) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177,sP178])],[f_634_2]) ).

cnf(f_634_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1696),U_1694))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1696),U_1695))
    | sP178(U_1694,U_1695)
    | sP177(U_1694,U_1695) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

cnf(f_634_5,plain,
    ( hBOOL(U_1694)
    | ~ sP177(U_1694,U_1695) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

cnf(f_634_6,plain,
    ( ~ hBOOL(U_1695)
    | ~ sP177(U_1694,U_1695) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

cnf(f_634_7,plain,
    ( hBOOL(U_1695)
    | ~ sP178(U_1694,U_1695) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

cnf(f_634_8,plain,
    ( ~ hBOOL(U_1694)
    | ~ sP178(U_1694,U_1695) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

fof(f_635_1,plain,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_1),A_3))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_1),B_1))
      | A_3 != B_1 ),
    inference(fof_nnf,[status(thm)],[fact_531_xt1_I3_J]) ).

fof(f_635_2,plain,
    ! [U_1699,U_1698,U_1697] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1699),U_1698))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1699),U_1697))
      | U_1698 != U_1697 ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

fof(f_635_3,plain,
    ! [U_1697,U_1699,U_1698] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1699),U_1698))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1699),U_1697))
      | U_1698 != U_1697 ),
    inference(definitional_conversion,[status(esa)],[f_635_2]) ).

cnf(f_635_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1699),U_1698))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1699),U_1697))
    | U_1698 != U_1697 ),
    inference(clausify,[status(thm)],[f_635_3]) ).

fof(f_636_1,plain,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),A_3))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_1),B_1))
      | A_3 != B_1 ),
    inference(fof_nnf,[status(thm)],[fact_532_xt1_I3_J]) ).

fof(f_636_2,plain,
    ! [U_1702,U_1701,U_1700] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1702),U_1701))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1702),U_1700))
      | U_1701 != U_1700 ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

fof(f_636_3,plain,
    ! [U_1701,U_1702,U_1700] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1702),U_1701))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1702),U_1700))
      | U_1701 != U_1700 ),
    inference(definitional_conversion,[status(esa)],[f_636_2]) ).

cnf(f_636_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1702),U_1701))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1702),U_1700))
    | U_1701 != U_1700 ),
    inference(clausify,[status(thm)],[f_636_3]) ).

fof(f_637_1,plain,
    ! [C_3,A_5,B_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_3),A_5))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_3),B_3))
      | A_5 != B_3 ),
    inference(fof_nnf,[status(thm)],[fact_533_xt1_I3_J]) ).

fof(f_637_2,plain,
    ! [U_1705,U_1704,U_1703] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1705),U_1704))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1705),U_1703))
      | U_1704 != U_1703 ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

fof(f_637_3,plain,
    ! [U_1703,U_1704,U_1705] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1705),U_1704))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1705),U_1703))
      | U_1704 != U_1703 ),
    inference(definitional_conversion,[status(esa)],[f_637_2]) ).

cnf(f_637_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1705),U_1704))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1705),U_1703))
    | U_1704 != U_1703 ),
    inference(clausify,[status(thm)],[f_637_3]) ).

fof(f_638_1,plain,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_1),A_3))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_1),B_1))
      | A_3 != B_1 ),
    inference(fof_nnf,[status(thm)],[fact_534_xt1_I3_J]) ).

fof(f_638_2,plain,
    ! [U_1708,U_1707,U_1706] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1708),U_1707))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1708),U_1706))
      | U_1707 != U_1706 ),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

fof(f_638_3,plain,
    ! [U_1707,U_1706,U_1708] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1708),U_1707))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1708),U_1706))
      | U_1707 != U_1706 ),
    inference(definitional_conversion,[status(esa)],[f_638_2]) ).

cnf(f_638_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1708),U_1707))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1708),U_1706))
    | U_1707 != U_1706 ),
    inference(clausify,[status(thm)],[f_638_3]) ).

fof(f_639_1,plain,
    ! [C_1,B_1,A_3] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A_3),C_1))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B_1),C_1))
      | ( ~ hBOOL(A_3)
        & hBOOL(B_1) )
      | ( ~ hBOOL(B_1)
        & hBOOL(A_3) ) ),
    inference(fof_nnf,[status(thm)],[fact_535_ord__eq__le__trans]) ).

fof(f_639_2,plain,
    ! [U_1711,U_1710,U_1709] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1709),U_1711))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1710),U_1711))
      | ( ~ hBOOL(U_1709)
        & hBOOL(U_1710) )
      | ( ~ hBOOL(U_1710)
        & hBOOL(U_1709) ) ),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

fof(f_639_3,plain,
    ( ! [U_1709,U_1710] :
        ( ~ hBOOL(U_1709)
        | ~ sP180(U_1709,U_1710) )
    & ! [U_1709,U_1710] :
        ( hBOOL(U_1710)
        | ~ sP180(U_1709,U_1710) )
    & ! [U_1709,U_1710] :
        ( ~ hBOOL(U_1710)
        | ~ sP179(U_1709,U_1710) )
    & ! [U_1709,U_1710] :
        ( hBOOL(U_1709)
        | ~ sP179(U_1709,U_1710) )
    & ! [U_1709,U_1710,U_1711] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1709),U_1711))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1710),U_1711))
        | sP180(U_1709,U_1710)
        | sP179(U_1709,U_1710) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179,sP180])],[f_639_2]) ).

cnf(f_639_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1709),U_1711))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1710),U_1711))
    | sP180(U_1709,U_1710)
    | sP179(U_1709,U_1710) ),
    inference(clausify,[status(thm)],[f_639_3]) ).

cnf(f_639_5,plain,
    ( hBOOL(U_1709)
    | ~ sP179(U_1709,U_1710) ),
    inference(clausify,[status(thm)],[f_639_3]) ).

cnf(f_639_6,plain,
    ( ~ hBOOL(U_1710)
    | ~ sP179(U_1709,U_1710) ),
    inference(clausify,[status(thm)],[f_639_3]) ).

cnf(f_639_7,plain,
    ( hBOOL(U_1710)
    | ~ sP180(U_1709,U_1710) ),
    inference(clausify,[status(thm)],[f_639_3]) ).

cnf(f_639_8,plain,
    ( ~ hBOOL(U_1709)
    | ~ sP180(U_1709,U_1710) ),
    inference(clausify,[status(thm)],[f_639_3]) ).

fof(f_640_1,plain,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_3),C_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_1),C_1))
      | A_3 != B_1 ),
    inference(fof_nnf,[status(thm)],[fact_536_ord__eq__le__trans]) ).

fof(f_640_2,plain,
    ! [U_1714,U_1713,U_1712] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1713),U_1714))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1712),U_1714))
      | U_1713 != U_1712 ),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

fof(f_640_3,plain,
    ! [U_1714,U_1712,U_1713] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1713),U_1714))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1712),U_1714))
      | U_1713 != U_1712 ),
    inference(definitional_conversion,[status(esa)],[f_640_2]) ).

cnf(f_640_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1713),U_1714))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1712),U_1714))
    | U_1713 != U_1712 ),
    inference(clausify,[status(thm)],[f_640_3]) ).

fof(f_641_1,plain,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A_3),C_1))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B_1),C_1))
      | A_3 != B_1 ),
    inference(fof_nnf,[status(thm)],[fact_537_ord__eq__le__trans]) ).

fof(f_641_2,plain,
    ! [U_1717,U_1716,U_1715] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1716),U_1717))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1715),U_1717))
      | U_1716 != U_1715 ),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

fof(f_641_3,plain,
    ! [U_1715,U_1716,U_1717] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1716),U_1717))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1715),U_1717))
      | U_1716 != U_1715 ),
    inference(definitional_conversion,[status(esa)],[f_641_2]) ).

cnf(f_641_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1716),U_1717))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1715),U_1717))
    | U_1716 != U_1715 ),
    inference(clausify,[status(thm)],[f_641_3]) ).

fof(f_642_1,plain,
    ! [C_2,A_4,B_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_4),C_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_2),C_2))
      | A_4 != B_2 ),
    inference(fof_nnf,[status(thm)],[fact_538_ord__eq__le__trans]) ).

fof(f_642_2,plain,
    ! [U_1720,U_1719,U_1718] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1719),U_1720))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1718),U_1720))
      | U_1719 != U_1718 ),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

fof(f_642_3,plain,
    ! [U_1719,U_1718,U_1720] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1719),U_1720))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1718),U_1720))
      | U_1719 != U_1718 ),
    inference(definitional_conversion,[status(esa)],[f_642_2]) ).

cnf(f_642_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1719),U_1720))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1718),U_1720))
    | U_1719 != U_1718 ),
    inference(clausify,[status(thm)],[f_642_3]) ).

fof(f_643_1,plain,
    ! [C_1,A_3,B_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_3),C_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_1),C_1))
      | A_3 != B_1 ),
    inference(fof_nnf,[status(thm)],[fact_539_ord__eq__le__trans]) ).

fof(f_643_2,plain,
    ! [U_1723,U_1722,U_1721] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1722),U_1723))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1721),U_1723))
      | U_1722 != U_1721 ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

fof(f_643_3,plain,
    ! [U_1721,U_1722,U_1723] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1722),U_1723))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1721),U_1723))
      | U_1722 != U_1721 ),
    inference(definitional_conversion,[status(esa)],[f_643_2]) ).

cnf(f_643_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1722),U_1723))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1721),U_1723))
    | U_1722 != U_1721 ),
    inference(clausify,[status(thm)],[f_643_3]) ).

fof(f_644_1,plain,
    ! [Y_2,X_3] :
      ( ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2))
          | ( ~ hBOOL(X_3)
            & hBOOL(Y_2) )
          | ( ~ hBOOL(Y_2)
            & hBOOL(X_3) ) )
        & ( ( ( hBOOL(X_3)
              | ~ hBOOL(Y_2) )
            & ( hBOOL(Y_2)
              | ~ hBOOL(X_3) ) )
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3)) ),
    inference(fof_nnf,[status(thm)],[fact_540_order__antisym__conv]) ).

fof(f_644_2,plain,
    ! [U_1725,U_1724] :
      ( ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1724),U_1725))
          | ( ~ hBOOL(U_1724)
            & hBOOL(U_1725) )
          | ( ~ hBOOL(U_1725)
            & hBOOL(U_1724) ) )
        & ( ( ( hBOOL(U_1724)
              | ~ hBOOL(U_1725) )
            & ( hBOOL(U_1725)
              | ~ hBOOL(U_1724) ) )
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1724),U_1725)) ) )
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1725),U_1724)) ),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

fof(f_644_3,plain,
    ( ! [U_1724,U_1725] :
        ( ~ hBOOL(U_1724)
        | ~ sP183(U_1724,U_1725) )
    & ! [U_1724,U_1725] :
        ( hBOOL(U_1725)
        | ~ sP183(U_1724,U_1725) )
    & ! [U_1724,U_1725] :
        ( ~ hBOOL(U_1725)
        | ~ sP182(U_1724,U_1725) )
    & ! [U_1724,U_1725] :
        ( hBOOL(U_1724)
        | ~ sP182(U_1724,U_1725) )
    & ! [U_1724,U_1725] :
        ( hBOOL(U_1724)
        | ~ hBOOL(U_1725)
        | ~ sP181(U_1724,U_1725) )
    & ! [U_1724,U_1725] :
        ( hBOOL(U_1725)
        | ~ hBOOL(U_1724)
        | ~ sP181(U_1724,U_1725) )
    & ! [U_1724,U_1725] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1724),U_1725))
        | sP183(U_1724,U_1725)
        | sP182(U_1724,U_1725)
        | ~ sP184(U_1724,U_1725) )
    & ! [U_1724,U_1725] :
        ( sP181(U_1724,U_1725)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1724),U_1725))
        | ~ sP184(U_1724,U_1725) )
    & ! [U_1724,U_1725] :
        ( sP184(U_1724,U_1725)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1725),U_1724)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181,sP182,sP183,sP184])],[f_644_2]) ).

cnf(f_644_4,plain,
    ( sP184(U_1724,U_1725)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1725),U_1724)) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_5,plain,
    ( sP181(U_1724,U_1725)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1724),U_1725))
    | ~ sP184(U_1724,U_1725) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_6,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1724),U_1725))
    | sP183(U_1724,U_1725)
    | sP182(U_1724,U_1725)
    | ~ sP184(U_1724,U_1725) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_7,plain,
    ( hBOOL(U_1725)
    | ~ hBOOL(U_1724)
    | ~ sP181(U_1724,U_1725) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_8,plain,
    ( hBOOL(U_1724)
    | ~ hBOOL(U_1725)
    | ~ sP181(U_1724,U_1725) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_9,plain,
    ( hBOOL(U_1724)
    | ~ sP182(U_1724,U_1725) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_10,plain,
    ( ~ hBOOL(U_1725)
    | ~ sP182(U_1724,U_1725) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_11,plain,
    ( hBOOL(U_1725)
    | ~ sP183(U_1724,U_1725) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

cnf(f_644_12,plain,
    ( ~ hBOOL(U_1724)
    | ~ sP183(U_1724,U_1725) ),
    inference(clausify,[status(thm)],[f_644_3]) ).

fof(f_645_1,plain,
    ! [Y_2,X_3] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2))
          | X_3 != Y_2 )
        & ( X_3 = Y_2
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3)) ),
    inference(fof_nnf,[status(thm)],[fact_541_order__antisym__conv]) ).

fof(f_645_2,plain,
    ! [U_1727,U_1726] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1726),U_1727))
          | U_1726 != U_1727 )
        & ( U_1726 = U_1727
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1726),U_1727)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1727),U_1726)) ),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

fof(f_645_3,plain,
    ( ! [U_1726,U_1727] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1726),U_1727))
        | U_1726 != U_1727
        | ~ sP185(U_1726,U_1727) )
    & ! [U_1726,U_1727] :
        ( U_1726 = U_1727
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1726),U_1727))
        | ~ sP185(U_1726,U_1727) )
    & ! [U_1726,U_1727] :
        ( sP185(U_1726,U_1727)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1727),U_1726)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_645_2]) ).

cnf(f_645_4,plain,
    ( sP185(U_1726,U_1727)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1727),U_1726)) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

cnf(f_645_5,plain,
    ( U_1726 = U_1727
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1726),U_1727))
    | ~ sP185(U_1726,U_1727) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

cnf(f_645_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1726),U_1727))
    | U_1726 != U_1727
    | ~ sP185(U_1726,U_1727) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

fof(f_646_1,plain,
    ! [Y_2,X_3] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2))
          | X_3 != Y_2 )
        & ( X_3 = Y_2
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3))
      | ~ is_fun_pname_bool(X_3)
      | ~ is_fun_pname_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_542_order__antisym__conv]) ).

fof(f_646_2,plain,
    ! [U_1729,U_1728] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1728),U_1729))
          | U_1728 != U_1729 )
        & ( U_1728 = U_1729
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1728),U_1729)) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1729),U_1728))
      | ~ is_fun_pname_bool(U_1728)
      | ~ is_fun_pname_bool(U_1729) ),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

fof(f_646_3,plain,
    ( ! [U_1728,U_1729] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1728),U_1729))
        | U_1728 != U_1729
        | ~ sP186(U_1728,U_1729) )
    & ! [U_1728,U_1729] :
        ( U_1728 = U_1729
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1728),U_1729))
        | ~ sP186(U_1728,U_1729) )
    & ! [U_1728,U_1729] :
        ( sP186(U_1728,U_1729)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1729),U_1728))
        | ~ is_fun_pname_bool(U_1728)
        | ~ is_fun_pname_bool(U_1729) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_646_2]) ).

cnf(f_646_4,plain,
    ( sP186(U_1728,U_1729)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1729),U_1728))
    | ~ is_fun_pname_bool(U_1728)
    | ~ is_fun_pname_bool(U_1729) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

cnf(f_646_5,plain,
    ( U_1728 = U_1729
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1728),U_1729))
    | ~ sP186(U_1728,U_1729) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

cnf(f_646_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1728),U_1729))
    | U_1728 != U_1729
    | ~ sP186(U_1728,U_1729) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

fof(f_647_1,plain,
    ! [Y_2,X_3] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),Y_2))
          | X_3 != Y_2 )
        & ( X_3 = Y_2
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),Y_2)) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_3)) ),
    inference(fof_nnf,[status(thm)],[fact_543_order__antisym__conv]) ).

fof(f_647_2,plain,
    ! [U_1731,U_1730] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1730),U_1731))
          | U_1730 != U_1731 )
        & ( U_1730 = U_1731
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1730),U_1731)) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1731),U_1730)) ),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

fof(f_647_3,plain,
    ( ! [U_1731,U_1730] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1730),U_1731))
        | U_1730 != U_1731
        | ~ sP187(U_1731,U_1730) )
    & ! [U_1731,U_1730] :
        ( U_1730 = U_1731
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1730),U_1731))
        | ~ sP187(U_1731,U_1730) )
    & ! [U_1731,U_1730] :
        ( sP187(U_1731,U_1730)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1731),U_1730)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187])],[f_647_2]) ).

cnf(f_647_4,plain,
    ( sP187(U_1731,U_1730)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1731),U_1730)) ),
    inference(clausify,[status(thm)],[f_647_3]) ).

cnf(f_647_5,plain,
    ( U_1730 = U_1731
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1730),U_1731))
    | ~ sP187(U_1731,U_1730) ),
    inference(clausify,[status(thm)],[f_647_3]) ).

cnf(f_647_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1730),U_1731))
    | U_1730 != U_1731
    | ~ sP187(U_1731,U_1730) ),
    inference(clausify,[status(thm)],[f_647_3]) ).

fof(f_648_1,plain,
    ! [Y_2,X_3] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2))
          | X_3 != Y_2 )
        & ( X_3 = Y_2
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3))
      | ~ is_fun_a_bool(X_3)
      | ~ is_fun_a_bool(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_544_order__antisym__conv]) ).

fof(f_648_2,plain,
    ! [U_1733,U_1732] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1732),U_1733))
          | U_1732 != U_1733 )
        & ( U_1732 = U_1733
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1732),U_1733)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1733),U_1732))
      | ~ is_fun_a_bool(U_1732)
      | ~ is_fun_a_bool(U_1733) ),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

fof(f_648_3,plain,
    ( ! [U_1733,U_1732] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1732),U_1733))
        | U_1732 != U_1733
        | ~ sP188(U_1733,U_1732) )
    & ! [U_1733,U_1732] :
        ( U_1732 = U_1733
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1732),U_1733))
        | ~ sP188(U_1733,U_1732) )
    & ! [U_1733,U_1732] :
        ( sP188(U_1733,U_1732)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1733),U_1732))
        | ~ is_fun_a_bool(U_1732)
        | ~ is_fun_a_bool(U_1733) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188])],[f_648_2]) ).

cnf(f_648_4,plain,
    ( sP188(U_1733,U_1732)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1733),U_1732))
    | ~ is_fun_a_bool(U_1732)
    | ~ is_fun_a_bool(U_1733) ),
    inference(clausify,[status(thm)],[f_648_3]) ).

cnf(f_648_5,plain,
    ( U_1732 = U_1733
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1732),U_1733))
    | ~ sP188(U_1733,U_1732) ),
    inference(clausify,[status(thm)],[f_648_3]) ).

cnf(f_648_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1732),U_1733))
    | U_1732 != U_1733
    | ~ sP188(U_1733,U_1732) ),
    inference(clausify,[status(thm)],[f_648_3]) ).

fof(f_649_1,plain,
    ! [Y_2,X_3] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2))
      | ( ~ hBOOL(X_3)
        & hBOOL(Y_2) )
      | ( ~ hBOOL(Y_2)
        & hBOOL(X_3) ) ),
    inference(fof_nnf,[status(thm)],[fact_545_order__eq__refl]) ).

fof(f_649_2,plain,
    ! [U_1735,U_1734] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1734),U_1735))
      | ( ~ hBOOL(U_1734)
        & hBOOL(U_1735) )
      | ( ~ hBOOL(U_1735)
        & hBOOL(U_1734) ) ),
    inference(variable_rename,[status(thm)],[f_649_1]) ).

fof(f_649_3,plain,
    ( ! [U_1735,U_1734] :
        ( ~ hBOOL(U_1734)
        | ~ sP190(U_1735,U_1734) )
    & ! [U_1735,U_1734] :
        ( hBOOL(U_1735)
        | ~ sP190(U_1735,U_1734) )
    & ! [U_1735,U_1734] :
        ( ~ hBOOL(U_1735)
        | ~ sP189(U_1735,U_1734) )
    & ! [U_1735,U_1734] :
        ( hBOOL(U_1734)
        | ~ sP189(U_1735,U_1734) )
    & ! [U_1735,U_1734] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1734),U_1735))
        | sP190(U_1735,U_1734)
        | sP189(U_1735,U_1734) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189,sP190])],[f_649_2]) ).

cnf(f_649_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1734),U_1735))
    | sP190(U_1735,U_1734)
    | sP189(U_1735,U_1734) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

cnf(f_649_5,plain,
    ( hBOOL(U_1734)
    | ~ sP189(U_1735,U_1734) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

cnf(f_649_6,plain,
    ( ~ hBOOL(U_1735)
    | ~ sP189(U_1735,U_1734) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

cnf(f_649_7,plain,
    ( hBOOL(U_1735)
    | ~ sP190(U_1735,U_1734) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

cnf(f_649_8,plain,
    ( ~ hBOOL(U_1734)
    | ~ sP190(U_1735,U_1734) ),
    inference(clausify,[status(thm)],[f_649_3]) ).

fof(f_650_1,plain,
    ! [X_3,Y_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2))
      | X_3 != Y_2 ),
    inference(fof_nnf,[status(thm)],[fact_546_order__eq__refl]) ).

fof(f_650_2,plain,
    ! [U_1737,U_1736] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1737),U_1736))
      | U_1737 != U_1736 ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

fof(f_650_3,plain,
    ! [U_1737,U_1736] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1737),U_1736))
      | U_1737 != U_1736 ),
    inference(definitional_conversion,[status(esa)],[f_650_2]) ).

cnf(f_650_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1737),U_1736))
    | U_1737 != U_1736 ),
    inference(clausify,[status(thm)],[f_650_3]) ).

fof(f_651_1,plain,
    ! [X_3,Y_2] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2))
      | X_3 != Y_2 ),
    inference(fof_nnf,[status(thm)],[fact_547_order__eq__refl]) ).

fof(f_651_2,plain,
    ! [U_1739,U_1738] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1739),U_1738))
      | U_1739 != U_1738 ),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

fof(f_651_3,plain,
    ! [U_1739,U_1738] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1739),U_1738))
      | U_1739 != U_1738 ),
    inference(definitional_conversion,[status(esa)],[f_651_2]) ).

cnf(f_651_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1739),U_1738))
    | U_1739 != U_1738 ),
    inference(clausify,[status(thm)],[f_651_3]) ).

fof(f_652_1,plain,
    ! [X_4,Y_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_3))
      | X_4 != Y_3 ),
    inference(fof_nnf,[status(thm)],[fact_548_order__eq__refl]) ).

fof(f_652_2,plain,
    ! [U_1741,U_1740] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1741),U_1740))
      | U_1741 != U_1740 ),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

fof(f_652_3,plain,
    ! [U_1741,U_1740] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1741),U_1740))
      | U_1741 != U_1740 ),
    inference(definitional_conversion,[status(esa)],[f_652_2]) ).

cnf(f_652_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1741),U_1740))
    | U_1741 != U_1740 ),
    inference(clausify,[status(thm)],[f_652_3]) ).

fof(f_653_1,plain,
    ! [X_3,Y_2] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2))
      | X_3 != Y_2 ),
    inference(fof_nnf,[status(thm)],[fact_549_order__eq__refl]) ).

fof(f_653_2,plain,
    ! [U_1743,U_1742] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1743),U_1742))
      | U_1743 != U_1742 ),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

fof(f_653_3,plain,
    ! [U_1743,U_1742] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1743),U_1742))
      | U_1743 != U_1742 ),
    inference(definitional_conversion,[status(esa)],[f_653_2]) ).

cnf(f_653_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1743),U_1742))
    | U_1743 != U_1742 ),
    inference(clausify,[status(thm)],[f_653_3]) ).

fof(f_654_1,plain,
    ! [Y_2,X_3] :
      ( ( ( ( hBOOL(X_3)
            | ~ hBOOL(Y_2) )
          & ( hBOOL(Y_2)
            | ~ hBOOL(X_3) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) )
      & ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_3))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_3),Y_2)) )
        | ( ~ hBOOL(X_3)
          & hBOOL(Y_2) )
        | ( ~ hBOOL(Y_2)
          & hBOOL(X_3) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_550_order__eq__iff]) ).

fof(f_654_2,plain,
    ! [U_1745,U_1744] :
      ( ( ( ( hBOOL(U_1744)
            | ~ hBOOL(U_1745) )
          & ( hBOOL(U_1745)
            | ~ hBOOL(U_1744) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1745),U_1744))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1744),U_1745)) )
      & ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1745),U_1744))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1744),U_1745)) )
        | ( ~ hBOOL(U_1744)
          & hBOOL(U_1745) )
        | ( ~ hBOOL(U_1745)
          & hBOOL(U_1744) ) ) ),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

fof(f_654_3,plain,
    ( ! [U_1749,U_1747] :
        ( ( ( hBOOL(U_1747)
            | ~ hBOOL(U_1749) )
          & ( hBOOL(U_1749)
            | ~ hBOOL(U_1747) ) )
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1749),U_1747))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1747),U_1749)) )
    & ! [U_1748,U_1746] :
        ( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1748),U_1746))
          & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1746),U_1748)) )
        | ( ~ hBOOL(U_1746)
          & hBOOL(U_1748) )
        | ( ~ hBOOL(U_1748)
          & hBOOL(U_1746) ) ) ),
    inference(miniscope,[status(thm)],[f_654_2]) ).

fof(f_654_4,plain,
    ( ! [U_1747,U_1749] :
        ( hBOOL(U_1747)
        | ~ hBOOL(U_1749)
        | ~ sP194(U_1747,U_1749) )
    & ! [U_1747,U_1749] :
        ( hBOOL(U_1749)
        | ~ hBOOL(U_1747)
        | ~ sP194(U_1747,U_1749) )
    & ! [U_1748,U_1746] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1748),U_1746))
        | ~ sP193(U_1748,U_1746) )
    & ! [U_1748,U_1746] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1746),U_1748))
        | ~ sP193(U_1748,U_1746) )
    & ! [U_1748,U_1746] :
        ( ~ hBOOL(U_1746)
        | ~ sP192(U_1748,U_1746) )
    & ! [U_1748,U_1746] :
        ( hBOOL(U_1748)
        | ~ sP192(U_1748,U_1746) )
    & ! [U_1748,U_1746] :
        ( ~ hBOOL(U_1748)
        | ~ sP191(U_1748,U_1746) )
    & ! [U_1748,U_1746] :
        ( hBOOL(U_1746)
        | ~ sP191(U_1748,U_1746) )
    & ! [U_1747,U_1749] :
        ( sP194(U_1747,U_1749)
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1749),U_1747))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1747),U_1749)) )
    & ! [U_1748,U_1746] :
        ( sP193(U_1748,U_1746)
        | sP192(U_1748,U_1746)
        | sP191(U_1748,U_1746) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP191,sP192,sP193,sP194])],[f_654_3]) ).

cnf(f_654_5,plain,
    ( sP193(U_1748,U_1746)
    | sP192(U_1748,U_1746)
    | sP191(U_1748,U_1746) ),
    inference(clausify,[status(thm)],[f_654_4]) ).

cnf(f_654_6,plain,
    ( sP194(U_1747,U_1749)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1749),U_1747))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1747),U_1749)) ),
    inference(clausify,[status(thm)],[f_654_4]) ).

cnf(f_654_7,plain,
    ( hBOOL(U_1746)
    | ~ sP191(U_1748,U_1746) ),
    inference(clausify,[status(thm)],[f_654_4]) ).

cnf(f_654_8,plain,
    ( ~ hBOOL(U_1748)
    | ~ sP191(U_1748,U_1746) ),
    inference(clausify,[status(thm)],[f_654_4]) ).

cnf(f_654_9,plain,
    ( hBOOL(U_1748)
    | ~ sP192(U_1748,U_1746) ),
    inference(clausify,[status(thm)],[f_654_4]) ).

cnf(f_654_10,plain,
    ( ~ hBOOL(U_1746)
    | ~ sP192(U_1748,U_1746) ),
    inference(clausify,[status(thm)],[f_654_4]) ).

cnf(f_654_11,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1746),U_1748))
    | ~ sP193(U_1748,U_1746) ),
    inference(clausify,[status(thm)],[f_654_4]) ).

cnf(f_654_12,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,U_1748),U_1746))
    | ~ sP193(U_1748,U_1746) ),
    inference(clausify,[status(thm)],[f_654_4]) ).

cnf(f_654_13,plain,
    ( hBOOL(U_1749)
    | ~ hBOOL(U_1747)
    | ~ sP194(U_1747,U_1749) ),
    inference(clausify,[status(thm)],[f_654_4]) ).

cnf(f_654_14,plain,
    ( hBOOL(U_1747)
    | ~ hBOOL(U_1749)
    | ~ sP194(U_1747,U_1749) ),
    inference(clausify,[status(thm)],[f_654_4]) ).

fof(f_655_1,plain,
    ! [X_3,Y_2] :
      ( ( X_3 = Y_2
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_3))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_3),Y_2)) )
        | X_3 != Y_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_551_order__eq__iff]) ).

fof(f_655_2,plain,
    ! [U_1751,U_1750] :
      ( ( U_1751 = U_1750
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1750),U_1751))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1751),U_1750)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1750),U_1751))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1751),U_1750)) )
        | U_1751 != U_1750 ) ),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

fof(f_655_3,plain,
    ( ! [U_1755,U_1753] :
        ( U_1755 = U_1753
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1753),U_1755))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1755),U_1753)) )
    & ! [U_1754,U_1752] :
        ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1752),U_1754))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1754),U_1752)) )
        | U_1754 != U_1752 ) ),
    inference(miniscope,[status(thm)],[f_655_2]) ).

fof(f_655_4,plain,
    ( ! [U_1752,U_1754] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1752),U_1754))
        | ~ sP195(U_1752,U_1754) )
    & ! [U_1752,U_1754] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1754),U_1752))
        | ~ sP195(U_1752,U_1754) )
    & ! [U_1753,U_1755] :
        ( U_1755 = U_1753
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1753),U_1755))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1755),U_1753)) )
    & ! [U_1752,U_1754] :
        ( sP195(U_1752,U_1754)
        | U_1754 != U_1752 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP195])],[f_655_3]) ).

cnf(f_655_5,plain,
    ( sP195(U_1752,U_1754)
    | U_1754 != U_1752 ),
    inference(clausify,[status(thm)],[f_655_4]) ).

cnf(f_655_6,plain,
    ( U_1755 = U_1753
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1753),U_1755))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1755),U_1753)) ),
    inference(clausify,[status(thm)],[f_655_4]) ).

cnf(f_655_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1754),U_1752))
    | ~ sP195(U_1752,U_1754) ),
    inference(clausify,[status(thm)],[f_655_4]) ).

cnf(f_655_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1752),U_1754))
    | ~ sP195(U_1752,U_1754) ),
    inference(clausify,[status(thm)],[f_655_4]) ).

fof(f_656_1,plain,
    ! [X_3,Y_2] :
      ( ( ( X_3 = Y_2
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) )
        & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Y_2),X_3))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_3),Y_2)) )
          | X_3 != Y_2 ) )
      | ~ is_fun_pname_bool(Y_2)
      | ~ is_fun_pname_bool(X_3) ),
    inference(fof_nnf,[status(thm)],[fact_552_order__eq__iff]) ).

fof(f_656_2,plain,
    ! [U_1757,U_1756] :
      ( ( ( U_1757 = U_1756
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1756),U_1757))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1757),U_1756)) )
        & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1756),U_1757))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1757),U_1756)) )
          | U_1757 != U_1756 ) )
      | ~ is_fun_pname_bool(U_1756)
      | ~ is_fun_pname_bool(U_1757) ),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

fof(f_656_3,plain,
    ( ! [U_1756,U_1757] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1756),U_1757))
        | ~ sP196(U_1756,U_1757) )
    & ! [U_1756,U_1757] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1757),U_1756))
        | ~ sP196(U_1756,U_1757) )
    & ! [U_1756,U_1757] :
        ( U_1757 = U_1756
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1756),U_1757))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1757),U_1756))
        | ~ sP197(U_1756,U_1757) )
    & ! [U_1756,U_1757] :
        ( sP196(U_1756,U_1757)
        | U_1757 != U_1756
        | ~ sP197(U_1756,U_1757) )
    & ! [U_1756,U_1757] :
        ( sP197(U_1756,U_1757)
        | ~ is_fun_pname_bool(U_1756)
        | ~ is_fun_pname_bool(U_1757) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP196,sP197])],[f_656_2]) ).

cnf(f_656_4,plain,
    ( sP197(U_1756,U_1757)
    | ~ is_fun_pname_bool(U_1756)
    | ~ is_fun_pname_bool(U_1757) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

cnf(f_656_5,plain,
    ( sP196(U_1756,U_1757)
    | U_1757 != U_1756
    | ~ sP197(U_1756,U_1757) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

cnf(f_656_6,plain,
    ( U_1757 = U_1756
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1756),U_1757))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1757),U_1756))
    | ~ sP197(U_1756,U_1757) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

cnf(f_656_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1757),U_1756))
    | ~ sP196(U_1756,U_1757) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

cnf(f_656_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1756),U_1757))
    | ~ sP196(U_1756,U_1757) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

fof(f_657_1,plain,
    ! [X_3,Y_2] :
      ( ( X_3 = Y_2
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_3))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),Y_2)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_3))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),Y_2)) )
        | X_3 != Y_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_553_order__eq__iff]) ).

fof(f_657_2,plain,
    ! [U_1759,U_1758] :
      ( ( U_1759 = U_1758
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1758),U_1759))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1759),U_1758)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1758),U_1759))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1759),U_1758)) )
        | U_1759 != U_1758 ) ),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

fof(f_657_3,plain,
    ( ! [U_1763,U_1761] :
        ( U_1763 = U_1761
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1761),U_1763))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1763),U_1761)) )
    & ! [U_1762,U_1760] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1760),U_1762))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1762),U_1760)) )
        | U_1762 != U_1760 ) ),
    inference(miniscope,[status(thm)],[f_657_2]) ).

fof(f_657_4,plain,
    ( ! [U_1760,U_1762] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1760),U_1762))
        | ~ sP198(U_1760,U_1762) )
    & ! [U_1760,U_1762] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1762),U_1760))
        | ~ sP198(U_1760,U_1762) )
    & ! [U_1761,U_1763] :
        ( U_1763 = U_1761
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1761),U_1763))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1763),U_1761)) )
    & ! [U_1760,U_1762] :
        ( sP198(U_1760,U_1762)
        | U_1762 != U_1760 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP198])],[f_657_3]) ).

cnf(f_657_5,plain,
    ( sP198(U_1760,U_1762)
    | U_1762 != U_1760 ),
    inference(clausify,[status(thm)],[f_657_4]) ).

cnf(f_657_6,plain,
    ( U_1763 = U_1761
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1761),U_1763))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1763),U_1761)) ),
    inference(clausify,[status(thm)],[f_657_4]) ).

cnf(f_657_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1762),U_1760))
    | ~ sP198(U_1760,U_1762) ),
    inference(clausify,[status(thm)],[f_657_4]) ).

cnf(f_657_8,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1760),U_1762))
    | ~ sP198(U_1760,U_1762) ),
    inference(clausify,[status(thm)],[f_657_4]) ).

fof(f_658_1,plain,
    ! [X_3,Y_2] :
      ( ( ( X_3 = Y_2
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) )
        & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_2),X_3))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_3),Y_2)) )
          | X_3 != Y_2 ) )
      | ~ is_fun_a_bool(Y_2)
      | ~ is_fun_a_bool(X_3) ),
    inference(fof_nnf,[status(thm)],[fact_554_order__eq__iff]) ).

fof(f_658_2,plain,
    ! [U_1765,U_1764] :
      ( ( ( U_1765 = U_1764
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1764),U_1765))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1765),U_1764)) )
        & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1764),U_1765))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1765),U_1764)) )
          | U_1765 != U_1764 ) )
      | ~ is_fun_a_bool(U_1764)
      | ~ is_fun_a_bool(U_1765) ),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

fof(f_658_3,plain,
    ( ! [U_1765,U_1764] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1764),U_1765))
        | ~ sP199(U_1765,U_1764) )
    & ! [U_1765,U_1764] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1765),U_1764))
        | ~ sP199(U_1765,U_1764) )
    & ! [U_1765,U_1764] :
        ( U_1765 = U_1764
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1764),U_1765))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1765),U_1764))
        | ~ sP200(U_1765,U_1764) )
    & ! [U_1765,U_1764] :
        ( sP199(U_1765,U_1764)
        | U_1765 != U_1764
        | ~ sP200(U_1765,U_1764) )
    & ! [U_1765,U_1764] :
        ( sP200(U_1765,U_1764)
        | ~ is_fun_a_bool(U_1764)
        | ~ is_fun_a_bool(U_1765) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199,sP200])],[f_658_2]) ).

cnf(f_658_4,plain,
    ( sP200(U_1765,U_1764)
    | ~ is_fun_a_bool(U_1764)
    | ~ is_fun_a_bool(U_1765) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

cnf(f_658_5,plain,
    ( sP199(U_1765,U_1764)
    | U_1765 != U_1764
    | ~ sP200(U_1765,U_1764) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

cnf(f_658_6,plain,
    ( U_1765 = U_1764
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1764),U_1765))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1765),U_1764))
    | ~ sP200(U_1765,U_1764) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

cnf(f_658_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1765),U_1764))
    | ~ sP199(U_1765,U_1764) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

cnf(f_658_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1764),U_1765))
    | ~ sP199(U_1765,U_1764) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

fof(f_659_1,plain,
    ! [X_2,Y_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_555_linorder__linear]) ).

fof(f_659_2,plain,
    ! [U_1767,U_1766] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1766),U_1767))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1767),U_1766)) ),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

fof(f_659_3,plain,
    ! [U_1767,U_1766] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1766),U_1767))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1767),U_1766)) ),
    inference(definitional_conversion,[status(esa)],[f_659_2]) ).

cnf(f_659_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1766),U_1767))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1767),U_1766)) ),
    inference(clausify,[status(thm)],[f_659_3]) ).

fof(f_660_1,plain,
    ! [Pa,A_1,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(Pa,F_1))
      | ? [A_2,F_2] :
          ( ~ hBOOL(hAPP_f54304608l_bool(Pa,insert_nat(A_2,F_2)))
          & hBOOL(hAPP_f54304608l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),F_2))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A_1))
          & 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_1))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_556_finite__subset__induct]) ).

fof(f_660_2,plain,
    ! [U_1772,U_1771,U_1770] :
      ( hBOOL(hAPP_f54304608l_bool(U_1772,U_1770))
      | ? [U_1769,U_1768] :
          ( ~ hBOOL(hAPP_f54304608l_bool(U_1772,insert_nat(U_1769,U_1768)))
          & hBOOL(hAPP_f54304608l_bool(U_1772,U_1768))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1769),U_1768))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1769),U_1771))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1768)) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_1772,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1770),U_1771))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1770)) ),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

fof(f_660_3,plain,
    ! [U_1772,U_1771,U_1770] :
      ( hBOOL(hAPP_f54304608l_bool(U_1772,U_1770))
      | ? [U_1768] :
          ( ~ hBOOL(hAPP_f54304608l_bool(U_1772,insert_nat(sK103(U_1772,U_1771,U_1770),U_1768)))
          & hBOOL(hAPP_f54304608l_bool(U_1772,U_1768))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK103(U_1772,U_1771,U_1770)),U_1768))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK103(U_1772,U_1771,U_1770)),U_1771))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1768)) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_1772,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1770),U_1771))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1770)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_1769,sK103(U_1772,U_1771,U_1770))],[f_660_2]) ).

fof(f_660_4,plain,
    ! [U_1772,U_1771,U_1770] :
      ( hBOOL(hAPP_f54304608l_bool(U_1772,U_1770))
      | ( ~ hBOOL(hAPP_f54304608l_bool(U_1772,insert_nat(sK103(U_1772,U_1771,U_1770),sK104(U_1772,U_1771,U_1770))))
        & hBOOL(hAPP_f54304608l_bool(U_1772,sK104(U_1772,U_1771,U_1770)))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK103(U_1772,U_1771,U_1770)),sK104(U_1772,U_1771,U_1770)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK103(U_1772,U_1771,U_1770)),U_1771))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK104(U_1772,U_1771,U_1770))) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_1772,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1770),U_1771))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1770)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_1768,sK104(U_1772,U_1771,U_1770))],[f_660_3]) ).

fof(f_660_5,plain,
    ( ! [U_1770,U_1771,U_1772] :
        ( ~ hBOOL(hAPP_f54304608l_bool(U_1772,insert_nat(sK103(U_1772,U_1771,U_1770),sK104(U_1772,U_1771,U_1770))))
        | ~ sP201(U_1770,U_1771,U_1772) )
    & ! [U_1770,U_1771,U_1772] :
        ( hBOOL(hAPP_f54304608l_bool(U_1772,sK104(U_1772,U_1771,U_1770)))
        | ~ sP201(U_1770,U_1771,U_1772) )
    & ! [U_1770,U_1771,U_1772] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK103(U_1772,U_1771,U_1770)),sK104(U_1772,U_1771,U_1770)))
        | ~ sP201(U_1770,U_1771,U_1772) )
    & ! [U_1770,U_1771,U_1772] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK103(U_1772,U_1771,U_1770)),U_1771))
        | ~ sP201(U_1770,U_1771,U_1772) )
    & ! [U_1770,U_1771,U_1772] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK104(U_1772,U_1771,U_1770)))
        | ~ sP201(U_1770,U_1771,U_1772) )
    & ! [U_1770,U_1771,U_1772] :
        ( hBOOL(hAPP_f54304608l_bool(U_1772,U_1770))
        | sP201(U_1770,U_1771,U_1772)
        | ~ hBOOL(hAPP_f54304608l_bool(U_1772,bot_bot_fun_nat_bool))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1770),U_1771))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1770)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP201])],[f_660_4]) ).

cnf(f_660_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(U_1772,U_1770))
    | sP201(U_1770,U_1771,U_1772)
    | ~ hBOOL(hAPP_f54304608l_bool(U_1772,bot_bot_fun_nat_bool))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1770),U_1771))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1770)) ),
    inference(clausify,[status(thm)],[f_660_5]) ).

cnf(f_660_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK104(U_1772,U_1771,U_1770)))
    | ~ sP201(U_1770,U_1771,U_1772) ),
    inference(clausify,[status(thm)],[f_660_5]) ).

cnf(f_660_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK103(U_1772,U_1771,U_1770)),U_1771))
    | ~ sP201(U_1770,U_1771,U_1772) ),
    inference(clausify,[status(thm)],[f_660_5]) ).

cnf(f_660_9,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK103(U_1772,U_1771,U_1770)),sK104(U_1772,U_1771,U_1770)))
    | ~ sP201(U_1770,U_1771,U_1772) ),
    inference(clausify,[status(thm)],[f_660_5]) ).

cnf(f_660_10,plain,
    ( hBOOL(hAPP_f54304608l_bool(U_1772,sK104(U_1772,U_1771,U_1770)))
    | ~ sP201(U_1770,U_1771,U_1772) ),
    inference(clausify,[status(thm)],[f_660_5]) ).

cnf(f_660_11,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(U_1772,insert_nat(sK103(U_1772,U_1771,U_1770),sK104(U_1772,U_1771,U_1770))))
    | ~ sP201(U_1770,U_1771,U_1772) ),
    inference(clausify,[status(thm)],[f_660_5]) ).

fof(f_661_1,plain,
    ! [Pa,A_1,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(Pa,F_1))
      | ? [A_2,F_2] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(Pa,insert_pname(A_2,F_2)))
          & hBOOL(hAPP_f1664156314l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),F_2))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A_1))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
          & is_fun_pname_bool(F_2)
          & is_pname(A_2) )
      | ~ hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F_1),A_1))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_557_finite__subset__induct]) ).

fof(f_661_2,plain,
    ! [U_1777,U_1776,U_1775] :
      ( hBOOL(hAPP_f1664156314l_bool(U_1777,U_1775))
      | ? [U_1774,U_1773] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_1777,insert_pname(U_1774,U_1773)))
          & hBOOL(hAPP_f1664156314l_bool(U_1777,U_1773))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1774),U_1773))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1774),U_1776))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1773))
          & is_fun_pname_bool(U_1773)
          & is_pname(U_1774) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_1777,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1775),U_1776))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1775)) ),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

fof(f_661_3,plain,
    ! [U_1777,U_1776,U_1775] :
      ( hBOOL(hAPP_f1664156314l_bool(U_1777,U_1775))
      | ? [U_1773] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_1777,insert_pname(sK105(U_1777,U_1776,U_1775),U_1773)))
          & hBOOL(hAPP_f1664156314l_bool(U_1777,U_1773))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK105(U_1777,U_1776,U_1775)),U_1773))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK105(U_1777,U_1776,U_1775)),U_1776))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1773))
          & is_fun_pname_bool(U_1773)
          & is_pname(sK105(U_1777,U_1776,U_1775)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_1777,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1775),U_1776))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1775)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_1774,sK105(U_1777,U_1776,U_1775))],[f_661_2]) ).

fof(f_661_4,plain,
    ! [U_1777,U_1776,U_1775] :
      ( hBOOL(hAPP_f1664156314l_bool(U_1777,U_1775))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(U_1777,insert_pname(sK105(U_1777,U_1776,U_1775),sK106(U_1777,U_1776,U_1775))))
        & hBOOL(hAPP_f1664156314l_bool(U_1777,sK106(U_1777,U_1776,U_1775)))
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK105(U_1777,U_1776,U_1775)),sK106(U_1777,U_1776,U_1775)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK105(U_1777,U_1776,U_1775)),U_1776))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK106(U_1777,U_1776,U_1775)))
        & is_fun_pname_bool(sK106(U_1777,U_1776,U_1775))
        & is_pname(sK105(U_1777,U_1776,U_1775)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_1777,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1775),U_1776))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1775)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_1773,sK106(U_1777,U_1776,U_1775))],[f_661_3]) ).

fof(f_661_5,plain,
    ( ! [U_1777,U_1775,U_1776] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(U_1777,insert_pname(sK105(U_1777,U_1776,U_1775),sK106(U_1777,U_1776,U_1775))))
        | ~ sP202(U_1777,U_1775,U_1776) )
    & ! [U_1777,U_1775,U_1776] :
        ( hBOOL(hAPP_f1664156314l_bool(U_1777,sK106(U_1777,U_1776,U_1775)))
        | ~ sP202(U_1777,U_1775,U_1776) )
    & ! [U_1777,U_1775,U_1776] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK105(U_1777,U_1776,U_1775)),sK106(U_1777,U_1776,U_1775)))
        | ~ sP202(U_1777,U_1775,U_1776) )
    & ! [U_1777,U_1775,U_1776] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK105(U_1777,U_1776,U_1775)),U_1776))
        | ~ sP202(U_1777,U_1775,U_1776) )
    & ! [U_1777,U_1775,U_1776] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK106(U_1777,U_1776,U_1775)))
        | ~ sP202(U_1777,U_1775,U_1776) )
    & ! [U_1777,U_1775,U_1776] :
        ( is_fun_pname_bool(sK106(U_1777,U_1776,U_1775))
        | ~ sP202(U_1777,U_1775,U_1776) )
    & ! [U_1777,U_1775,U_1776] :
        ( is_pname(sK105(U_1777,U_1776,U_1775))
        | ~ sP202(U_1777,U_1775,U_1776) )
    & ! [U_1777,U_1775,U_1776] :
        ( hBOOL(hAPP_f1664156314l_bool(U_1777,U_1775))
        | sP202(U_1777,U_1775,U_1776)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_1777,bot_bo844097828e_bool))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1775),U_1776))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1775)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP202])],[f_661_4]) ).

cnf(f_661_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_1777,U_1775))
    | sP202(U_1777,U_1775,U_1776)
    | ~ hBOOL(hAPP_f1664156314l_bool(U_1777,bot_bo844097828e_bool))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1775),U_1776))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1775)) ),
    inference(clausify,[status(thm)],[f_661_5]) ).

cnf(f_661_7,plain,
    ( is_pname(sK105(U_1777,U_1776,U_1775))
    | ~ sP202(U_1777,U_1775,U_1776) ),
    inference(clausify,[status(thm)],[f_661_5]) ).

cnf(f_661_8,plain,
    ( is_fun_pname_bool(sK106(U_1777,U_1776,U_1775))
    | ~ sP202(U_1777,U_1775,U_1776) ),
    inference(clausify,[status(thm)],[f_661_5]) ).

cnf(f_661_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK106(U_1777,U_1776,U_1775)))
    | ~ sP202(U_1777,U_1775,U_1776) ),
    inference(clausify,[status(thm)],[f_661_5]) ).

cnf(f_661_10,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK105(U_1777,U_1776,U_1775)),U_1776))
    | ~ sP202(U_1777,U_1775,U_1776) ),
    inference(clausify,[status(thm)],[f_661_5]) ).

cnf(f_661_11,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK105(U_1777,U_1776,U_1775)),sK106(U_1777,U_1776,U_1775)))
    | ~ sP202(U_1777,U_1775,U_1776) ),
    inference(clausify,[status(thm)],[f_661_5]) ).

cnf(f_661_12,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_1777,sK106(U_1777,U_1776,U_1775)))
    | ~ sP202(U_1777,U_1775,U_1776) ),
    inference(clausify,[status(thm)],[f_661_5]) ).

cnf(f_661_13,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(U_1777,insert_pname(sK105(U_1777,U_1776,U_1775),sK106(U_1777,U_1776,U_1775))))
    | ~ sP202(U_1777,U_1775,U_1776) ),
    inference(clausify,[status(thm)],[f_661_5]) ).

fof(f_662_1,plain,
    ! [Pa,A_1,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(Pa,F_1))
      | ? [A_2,F_2] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(Pa,insert_a(A_2,F_2)))
          & hBOOL(hAPP_fun_a_bool_bool(Pa,F_2))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),F_2))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A_1))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_2))
          & is_fun_a_bool(F_2)
          & is_a(A_2) )
      | ~ 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_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_558_finite__subset__induct]) ).

fof(f_662_2,plain,
    ! [U_1782,U_1781,U_1780] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_1782,U_1780))
      | ? [U_1779,U_1778] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1782,insert_a(U_1779,U_1778)))
          & hBOOL(hAPP_fun_a_bool_bool(U_1782,U_1778))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1779),U_1778))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1779),U_1781))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_1778))
          & is_fun_a_bool(U_1778)
          & is_a(U_1779) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(U_1782,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1780),U_1781))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_1780)) ),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

fof(f_662_3,plain,
    ! [U_1782,U_1781,U_1780] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_1782,U_1780))
      | ? [U_1778] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1782,insert_a(sK107(U_1782,U_1781,U_1780),U_1778)))
          & hBOOL(hAPP_fun_a_bool_bool(U_1782,U_1778))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK107(U_1782,U_1781,U_1780)),U_1778))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK107(U_1782,U_1781,U_1780)),U_1781))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_1778))
          & is_fun_a_bool(U_1778)
          & is_a(sK107(U_1782,U_1781,U_1780)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(U_1782,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1780),U_1781))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_1780)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_1779,sK107(U_1782,U_1781,U_1780))],[f_662_2]) ).

fof(f_662_4,plain,
    ! [U_1782,U_1781,U_1780] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_1782,U_1780))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1782,insert_a(sK107(U_1782,U_1781,U_1780),sK108(U_1782,U_1781,U_1780))))
        & hBOOL(hAPP_fun_a_bool_bool(U_1782,sK108(U_1782,U_1781,U_1780)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK107(U_1782,U_1781,U_1780)),sK108(U_1782,U_1781,U_1780)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK107(U_1782,U_1781,U_1780)),U_1781))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK108(U_1782,U_1781,U_1780)))
        & is_fun_a_bool(sK108(U_1782,U_1781,U_1780))
        & is_a(sK107(U_1782,U_1781,U_1780)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(U_1782,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1780),U_1781))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_1780)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_1778,sK108(U_1782,U_1781,U_1780))],[f_662_3]) ).

fof(f_662_5,plain,
    ( ! [U_1782,U_1781,U_1780] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1782,insert_a(sK107(U_1782,U_1781,U_1780),sK108(U_1782,U_1781,U_1780))))
        | ~ sP203(U_1782,U_1781,U_1780) )
    & ! [U_1782,U_1781,U_1780] :
        ( hBOOL(hAPP_fun_a_bool_bool(U_1782,sK108(U_1782,U_1781,U_1780)))
        | ~ sP203(U_1782,U_1781,U_1780) )
    & ! [U_1782,U_1781,U_1780] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK107(U_1782,U_1781,U_1780)),sK108(U_1782,U_1781,U_1780)))
        | ~ sP203(U_1782,U_1781,U_1780) )
    & ! [U_1782,U_1781,U_1780] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK107(U_1782,U_1781,U_1780)),U_1781))
        | ~ sP203(U_1782,U_1781,U_1780) )
    & ! [U_1782,U_1781,U_1780] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK108(U_1782,U_1781,U_1780)))
        | ~ sP203(U_1782,U_1781,U_1780) )
    & ! [U_1782,U_1781,U_1780] :
        ( is_fun_a_bool(sK108(U_1782,U_1781,U_1780))
        | ~ sP203(U_1782,U_1781,U_1780) )
    & ! [U_1782,U_1781,U_1780] :
        ( is_a(sK107(U_1782,U_1781,U_1780))
        | ~ sP203(U_1782,U_1781,U_1780) )
    & ! [U_1782,U_1781,U_1780] :
        ( hBOOL(hAPP_fun_a_bool_bool(U_1782,U_1780))
        | sP203(U_1782,U_1781,U_1780)
        | ~ hBOOL(hAPP_fun_a_bool_bool(U_1782,bot_bot_fun_a_bool))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1780),U_1781))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_1780)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP203])],[f_662_4]) ).

cnf(f_662_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(U_1782,U_1780))
    | sP203(U_1782,U_1781,U_1780)
    | ~ hBOOL(hAPP_fun_a_bool_bool(U_1782,bot_bot_fun_a_bool))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1780),U_1781))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_1780)) ),
    inference(clausify,[status(thm)],[f_662_5]) ).

cnf(f_662_7,plain,
    ( is_a(sK107(U_1782,U_1781,U_1780))
    | ~ sP203(U_1782,U_1781,U_1780) ),
    inference(clausify,[status(thm)],[f_662_5]) ).

cnf(f_662_8,plain,
    ( is_fun_a_bool(sK108(U_1782,U_1781,U_1780))
    | ~ sP203(U_1782,U_1781,U_1780) ),
    inference(clausify,[status(thm)],[f_662_5]) ).

cnf(f_662_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK108(U_1782,U_1781,U_1780)))
    | ~ sP203(U_1782,U_1781,U_1780) ),
    inference(clausify,[status(thm)],[f_662_5]) ).

cnf(f_662_10,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK107(U_1782,U_1781,U_1780)),U_1781))
    | ~ sP203(U_1782,U_1781,U_1780) ),
    inference(clausify,[status(thm)],[f_662_5]) ).

cnf(f_662_11,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK107(U_1782,U_1781,U_1780)),sK108(U_1782,U_1781,U_1780)))
    | ~ sP203(U_1782,U_1781,U_1780) ),
    inference(clausify,[status(thm)],[f_662_5]) ).

cnf(f_662_12,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(U_1782,sK108(U_1782,U_1781,U_1780)))
    | ~ sP203(U_1782,U_1781,U_1780) ),
    inference(clausify,[status(thm)],[f_662_5]) ).

cnf(f_662_13,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(U_1782,insert_a(sK107(U_1782,U_1781,U_1780),sK108(U_1782,U_1781,U_1780))))
    | ~ sP203(U_1782,U_1781,U_1780) ),
    inference(clausify,[status(thm)],[f_662_5]) ).

fof(f_663_1,plain,
    ! [Pa,A_1,F_1] :
      ( hBOOL(hAPP_f1637334154l_bool(Pa,F_1))
      | ? [A_2,F_2] :
          ( ~ hBOOL(hAPP_f1637334154l_bool(Pa,insert_fun_nat_bool(A_2,F_2)))
          & hBOOL(hAPP_f1637334154l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,A_2),F_2))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,A_2),A_1))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_2)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(Pa,bot_bo1701429464l_bool))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,F_1),A_1))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_559_finite__subset__induct]) ).

fof(f_663_2,plain,
    ! [U_1787,U_1786,U_1785] :
      ( hBOOL(hAPP_f1637334154l_bool(U_1787,U_1785))
      | ? [U_1784,U_1783] :
          ( ~ hBOOL(hAPP_f1637334154l_bool(U_1787,insert_fun_nat_bool(U_1784,U_1783)))
          & hBOOL(hAPP_f1637334154l_bool(U_1787,U_1783))
          & ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_1784),U_1783))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_1784),U_1786))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1783)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(U_1787,bot_bo1701429464l_bool))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_1785),U_1786))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1785)) ),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

fof(f_663_3,plain,
    ! [U_1787,U_1786,U_1785] :
      ( hBOOL(hAPP_f1637334154l_bool(U_1787,U_1785))
      | ? [U_1783] :
          ( ~ hBOOL(hAPP_f1637334154l_bool(U_1787,insert_fun_nat_bool(sK109(U_1787,U_1786,U_1785),U_1783)))
          & hBOOL(hAPP_f1637334154l_bool(U_1787,U_1783))
          & ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK109(U_1787,U_1786,U_1785)),U_1783))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK109(U_1787,U_1786,U_1785)),U_1786))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1783)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(U_1787,bot_bo1701429464l_bool))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_1785),U_1786))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1785)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_1784,sK109(U_1787,U_1786,U_1785))],[f_663_2]) ).

fof(f_663_4,plain,
    ! [U_1787,U_1786,U_1785] :
      ( hBOOL(hAPP_f1637334154l_bool(U_1787,U_1785))
      | ( ~ hBOOL(hAPP_f1637334154l_bool(U_1787,insert_fun_nat_bool(sK109(U_1787,U_1786,U_1785),sK110(U_1787,U_1786,U_1785))))
        & hBOOL(hAPP_f1637334154l_bool(U_1787,sK110(U_1787,U_1786,U_1785)))
        & ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK109(U_1787,U_1786,U_1785)),sK110(U_1787,U_1786,U_1785)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK109(U_1787,U_1786,U_1785)),U_1786))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK110(U_1787,U_1786,U_1785))) )
      | ~ hBOOL(hAPP_f1637334154l_bool(U_1787,bot_bo1701429464l_bool))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_1785),U_1786))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1785)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_1783,sK110(U_1787,U_1786,U_1785))],[f_663_3]) ).

fof(f_663_5,plain,
    ( ! [U_1787,U_1786,U_1785] :
        ( ~ hBOOL(hAPP_f1637334154l_bool(U_1787,insert_fun_nat_bool(sK109(U_1787,U_1786,U_1785),sK110(U_1787,U_1786,U_1785))))
        | ~ sP204(U_1787,U_1786,U_1785) )
    & ! [U_1787,U_1786,U_1785] :
        ( hBOOL(hAPP_f1637334154l_bool(U_1787,sK110(U_1787,U_1786,U_1785)))
        | ~ sP204(U_1787,U_1786,U_1785) )
    & ! [U_1787,U_1786,U_1785] :
        ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK109(U_1787,U_1786,U_1785)),sK110(U_1787,U_1786,U_1785)))
        | ~ sP204(U_1787,U_1786,U_1785) )
    & ! [U_1787,U_1786,U_1785] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK109(U_1787,U_1786,U_1785)),U_1786))
        | ~ sP204(U_1787,U_1786,U_1785) )
    & ! [U_1787,U_1786,U_1785] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK110(U_1787,U_1786,U_1785)))
        | ~ sP204(U_1787,U_1786,U_1785) )
    & ! [U_1787,U_1786,U_1785] :
        ( hBOOL(hAPP_f1637334154l_bool(U_1787,U_1785))
        | sP204(U_1787,U_1786,U_1785)
        | ~ hBOOL(hAPP_f1637334154l_bool(U_1787,bot_bo1701429464l_bool))
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_1785),U_1786))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1785)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_663_4]) ).

cnf(f_663_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(U_1787,U_1785))
    | sP204(U_1787,U_1786,U_1785)
    | ~ hBOOL(hAPP_f1637334154l_bool(U_1787,bot_bo1701429464l_bool))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_1785),U_1786))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1785)) ),
    inference(clausify,[status(thm)],[f_663_5]) ).

cnf(f_663_7,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK110(U_1787,U_1786,U_1785)))
    | ~ sP204(U_1787,U_1786,U_1785) ),
    inference(clausify,[status(thm)],[f_663_5]) ).

cnf(f_663_8,plain,
    ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK109(U_1787,U_1786,U_1785)),U_1786))
    | ~ sP204(U_1787,U_1786,U_1785) ),
    inference(clausify,[status(thm)],[f_663_5]) ).

cnf(f_663_9,plain,
    ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK109(U_1787,U_1786,U_1785)),sK110(U_1787,U_1786,U_1785)))
    | ~ sP204(U_1787,U_1786,U_1785) ),
    inference(clausify,[status(thm)],[f_663_5]) ).

cnf(f_663_10,plain,
    ( hBOOL(hAPP_f1637334154l_bool(U_1787,sK110(U_1787,U_1786,U_1785)))
    | ~ sP204(U_1787,U_1786,U_1785) ),
    inference(clausify,[status(thm)],[f_663_5]) ).

cnf(f_663_11,plain,
    ( ~ hBOOL(hAPP_f1637334154l_bool(U_1787,insert_fun_nat_bool(sK109(U_1787,U_1786,U_1785),sK110(U_1787,U_1786,U_1785))))
    | ~ sP204(U_1787,U_1786,U_1785) ),
    inference(clausify,[status(thm)],[f_663_5]) ).

fof(f_664_1,plain,
    ! [Pa,A_1,F_1] :
      ( hBOOL(hAPP_f1935102916l_bool(Pa,F_1))
      | ? [A_2,F_2] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(Pa,insert1325755072e_bool(A_2,F_2)))
          & hBOOL(hAPP_f1935102916l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),F_2))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A_1))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2))
          & is_fun1661590463l_bool(F_2)
          & is_fun_pname_bool(A_2) )
      | ~ hBOOL(hAPP_f1935102916l_bool(Pa,bot_bo1649642514l_bool))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,F_1),A_1))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_560_finite__subset__induct]) ).

fof(f_664_2,plain,
    ! [U_1792,U_1791,U_1790] :
      ( hBOOL(hAPP_f1935102916l_bool(U_1792,U_1790))
      | ? [U_1789,U_1788] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(U_1792,insert1325755072e_bool(U_1789,U_1788)))
          & hBOOL(hAPP_f1935102916l_bool(U_1792,U_1788))
          & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_1789),U_1788))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_1789),U_1791))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1788))
          & is_fun1661590463l_bool(U_1788)
          & is_fun_pname_bool(U_1789) )
      | ~ hBOOL(hAPP_f1935102916l_bool(U_1792,bot_bo1649642514l_bool))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_1790),U_1791))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1790)) ),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

fof(f_664_3,plain,
    ! [U_1792,U_1791,U_1790] :
      ( hBOOL(hAPP_f1935102916l_bool(U_1792,U_1790))
      | ? [U_1788] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(U_1792,insert1325755072e_bool(sK111(U_1792,U_1791,U_1790),U_1788)))
          & hBOOL(hAPP_f1935102916l_bool(U_1792,U_1788))
          & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK111(U_1792,U_1791,U_1790)),U_1788))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK111(U_1792,U_1791,U_1790)),U_1791))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1788))
          & is_fun1661590463l_bool(U_1788)
          & is_fun_pname_bool(sK111(U_1792,U_1791,U_1790)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(U_1792,bot_bo1649642514l_bool))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_1790),U_1791))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1790)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_1789,sK111(U_1792,U_1791,U_1790))],[f_664_2]) ).

fof(f_664_4,plain,
    ! [U_1792,U_1791,U_1790] :
      ( hBOOL(hAPP_f1935102916l_bool(U_1792,U_1790))
      | ( ~ hBOOL(hAPP_f1935102916l_bool(U_1792,insert1325755072e_bool(sK111(U_1792,U_1791,U_1790),sK112(U_1792,U_1791,U_1790))))
        & hBOOL(hAPP_f1935102916l_bool(U_1792,sK112(U_1792,U_1791,U_1790)))
        & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK111(U_1792,U_1791,U_1790)),sK112(U_1792,U_1791,U_1790)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK111(U_1792,U_1791,U_1790)),U_1791))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK112(U_1792,U_1791,U_1790)))
        & is_fun1661590463l_bool(sK112(U_1792,U_1791,U_1790))
        & is_fun_pname_bool(sK111(U_1792,U_1791,U_1790)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(U_1792,bot_bo1649642514l_bool))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_1790),U_1791))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1790)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_1788,sK112(U_1792,U_1791,U_1790))],[f_664_3]) ).

fof(f_664_5,plain,
    ( ! [U_1792,U_1791,U_1790] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(U_1792,insert1325755072e_bool(sK111(U_1792,U_1791,U_1790),sK112(U_1792,U_1791,U_1790))))
        | ~ sP205(U_1792,U_1791,U_1790) )
    & ! [U_1792,U_1791,U_1790] :
        ( hBOOL(hAPP_f1935102916l_bool(U_1792,sK112(U_1792,U_1791,U_1790)))
        | ~ sP205(U_1792,U_1791,U_1790) )
    & ! [U_1792,U_1791,U_1790] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK111(U_1792,U_1791,U_1790)),sK112(U_1792,U_1791,U_1790)))
        | ~ sP205(U_1792,U_1791,U_1790) )
    & ! [U_1792,U_1791,U_1790] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK111(U_1792,U_1791,U_1790)),U_1791))
        | ~ sP205(U_1792,U_1791,U_1790) )
    & ! [U_1792,U_1791,U_1790] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK112(U_1792,U_1791,U_1790)))
        | ~ sP205(U_1792,U_1791,U_1790) )
    & ! [U_1792,U_1791,U_1790] :
        ( is_fun1661590463l_bool(sK112(U_1792,U_1791,U_1790))
        | ~ sP205(U_1792,U_1791,U_1790) )
    & ! [U_1792,U_1791,U_1790] :
        ( is_fun_pname_bool(sK111(U_1792,U_1791,U_1790))
        | ~ sP205(U_1792,U_1791,U_1790) )
    & ! [U_1792,U_1791,U_1790] :
        ( hBOOL(hAPP_f1935102916l_bool(U_1792,U_1790))
        | sP205(U_1792,U_1791,U_1790)
        | ~ hBOOL(hAPP_f1935102916l_bool(U_1792,bot_bo1649642514l_bool))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_1790),U_1791))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1790)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_664_4]) ).

cnf(f_664_6,plain,
    ( hBOOL(hAPP_f1935102916l_bool(U_1792,U_1790))
    | sP205(U_1792,U_1791,U_1790)
    | ~ hBOOL(hAPP_f1935102916l_bool(U_1792,bot_bo1649642514l_bool))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_1790),U_1791))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1790)) ),
    inference(clausify,[status(thm)],[f_664_5]) ).

cnf(f_664_7,plain,
    ( is_fun_pname_bool(sK111(U_1792,U_1791,U_1790))
    | ~ sP205(U_1792,U_1791,U_1790) ),
    inference(clausify,[status(thm)],[f_664_5]) ).

cnf(f_664_8,plain,
    ( is_fun1661590463l_bool(sK112(U_1792,U_1791,U_1790))
    | ~ sP205(U_1792,U_1791,U_1790) ),
    inference(clausify,[status(thm)],[f_664_5]) ).

cnf(f_664_9,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK112(U_1792,U_1791,U_1790)))
    | ~ sP205(U_1792,U_1791,U_1790) ),
    inference(clausify,[status(thm)],[f_664_5]) ).

cnf(f_664_10,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK111(U_1792,U_1791,U_1790)),U_1791))
    | ~ sP205(U_1792,U_1791,U_1790) ),
    inference(clausify,[status(thm)],[f_664_5]) ).

cnf(f_664_11,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK111(U_1792,U_1791,U_1790)),sK112(U_1792,U_1791,U_1790)))
    | ~ sP205(U_1792,U_1791,U_1790) ),
    inference(clausify,[status(thm)],[f_664_5]) ).

cnf(f_664_12,plain,
    ( hBOOL(hAPP_f1935102916l_bool(U_1792,sK112(U_1792,U_1791,U_1790)))
    | ~ sP205(U_1792,U_1791,U_1790) ),
    inference(clausify,[status(thm)],[f_664_5]) ).

cnf(f_664_13,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(U_1792,insert1325755072e_bool(sK111(U_1792,U_1791,U_1790),sK112(U_1792,U_1791,U_1790))))
    | ~ sP205(U_1792,U_1791,U_1790) ),
    inference(clausify,[status(thm)],[f_664_5]) ).

fof(f_665_1,plain,
    ! [Pa,A_1,F_1] :
      ( hBOOL(hAPP_f621171935l_bool(Pa,F_1))
      | ? [A_2,F_2] :
          ( ~ hBOOL(hAPP_f621171935l_bool(Pa,insert_fun_a_bool(A_2,F_2)))
          & hBOOL(hAPP_f621171935l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,A_2),F_2))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,A_2),A_1))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_2))
          & is_fun949378684l_bool(F_2)
          & is_fun_a_bool(A_2) )
      | ~ hBOOL(hAPP_f621171935l_bool(Pa,bot_bo1389914601l_bool))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,F_1),A_1))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_561_finite__subset__induct]) ).

fof(f_665_2,plain,
    ! [U_1797,U_1796,U_1795] :
      ( hBOOL(hAPP_f621171935l_bool(U_1797,U_1795))
      | ? [U_1794,U_1793] :
          ( ~ hBOOL(hAPP_f621171935l_bool(U_1797,insert_fun_a_bool(U_1794,U_1793)))
          & hBOOL(hAPP_f621171935l_bool(U_1797,U_1793))
          & ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_1794),U_1793))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_1794),U_1796))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1793))
          & is_fun949378684l_bool(U_1793)
          & is_fun_a_bool(U_1794) )
      | ~ hBOOL(hAPP_f621171935l_bool(U_1797,bot_bo1389914601l_bool))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_1795),U_1796))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1795)) ),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

fof(f_665_3,plain,
    ! [U_1797,U_1796,U_1795] :
      ( hBOOL(hAPP_f621171935l_bool(U_1797,U_1795))
      | ? [U_1793] :
          ( ~ hBOOL(hAPP_f621171935l_bool(U_1797,insert_fun_a_bool(sK113(U_1797,U_1796,U_1795),U_1793)))
          & hBOOL(hAPP_f621171935l_bool(U_1797,U_1793))
          & ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK113(U_1797,U_1796,U_1795)),U_1793))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK113(U_1797,U_1796,U_1795)),U_1796))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1793))
          & is_fun949378684l_bool(U_1793)
          & is_fun_a_bool(sK113(U_1797,U_1796,U_1795)) )
      | ~ hBOOL(hAPP_f621171935l_bool(U_1797,bot_bo1389914601l_bool))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_1795),U_1796))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1795)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_1794,sK113(U_1797,U_1796,U_1795))],[f_665_2]) ).

fof(f_665_4,plain,
    ! [U_1797,U_1796,U_1795] :
      ( hBOOL(hAPP_f621171935l_bool(U_1797,U_1795))
      | ( ~ hBOOL(hAPP_f621171935l_bool(U_1797,insert_fun_a_bool(sK113(U_1797,U_1796,U_1795),sK114(U_1797,U_1796,U_1795))))
        & hBOOL(hAPP_f621171935l_bool(U_1797,sK114(U_1797,U_1796,U_1795)))
        & ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK113(U_1797,U_1796,U_1795)),sK114(U_1797,U_1796,U_1795)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK113(U_1797,U_1796,U_1795)),U_1796))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK114(U_1797,U_1796,U_1795)))
        & is_fun949378684l_bool(sK114(U_1797,U_1796,U_1795))
        & is_fun_a_bool(sK113(U_1797,U_1796,U_1795)) )
      | ~ hBOOL(hAPP_f621171935l_bool(U_1797,bot_bo1389914601l_bool))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_1795),U_1796))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1795)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_1793,sK114(U_1797,U_1796,U_1795))],[f_665_3]) ).

fof(f_665_5,plain,
    ( ! [U_1796,U_1795,U_1797] :
        ( ~ hBOOL(hAPP_f621171935l_bool(U_1797,insert_fun_a_bool(sK113(U_1797,U_1796,U_1795),sK114(U_1797,U_1796,U_1795))))
        | ~ sP206(U_1796,U_1795,U_1797) )
    & ! [U_1796,U_1795,U_1797] :
        ( hBOOL(hAPP_f621171935l_bool(U_1797,sK114(U_1797,U_1796,U_1795)))
        | ~ sP206(U_1796,U_1795,U_1797) )
    & ! [U_1796,U_1795,U_1797] :
        ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK113(U_1797,U_1796,U_1795)),sK114(U_1797,U_1796,U_1795)))
        | ~ sP206(U_1796,U_1795,U_1797) )
    & ! [U_1796,U_1795,U_1797] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK113(U_1797,U_1796,U_1795)),U_1796))
        | ~ sP206(U_1796,U_1795,U_1797) )
    & ! [U_1796,U_1795,U_1797] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK114(U_1797,U_1796,U_1795)))
        | ~ sP206(U_1796,U_1795,U_1797) )
    & ! [U_1796,U_1795,U_1797] :
        ( is_fun949378684l_bool(sK114(U_1797,U_1796,U_1795))
        | ~ sP206(U_1796,U_1795,U_1797) )
    & ! [U_1796,U_1795,U_1797] :
        ( is_fun_a_bool(sK113(U_1797,U_1796,U_1795))
        | ~ sP206(U_1796,U_1795,U_1797) )
    & ! [U_1796,U_1795,U_1797] :
        ( hBOOL(hAPP_f621171935l_bool(U_1797,U_1795))
        | sP206(U_1796,U_1795,U_1797)
        | ~ hBOOL(hAPP_f621171935l_bool(U_1797,bot_bo1389914601l_bool))
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_1795),U_1796))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1795)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206])],[f_665_4]) ).

cnf(f_665_6,plain,
    ( hBOOL(hAPP_f621171935l_bool(U_1797,U_1795))
    | sP206(U_1796,U_1795,U_1797)
    | ~ hBOOL(hAPP_f621171935l_bool(U_1797,bot_bo1389914601l_bool))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_1795),U_1796))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1795)) ),
    inference(clausify,[status(thm)],[f_665_5]) ).

cnf(f_665_7,plain,
    ( is_fun_a_bool(sK113(U_1797,U_1796,U_1795))
    | ~ sP206(U_1796,U_1795,U_1797) ),
    inference(clausify,[status(thm)],[f_665_5]) ).

cnf(f_665_8,plain,
    ( is_fun949378684l_bool(sK114(U_1797,U_1796,U_1795))
    | ~ sP206(U_1796,U_1795,U_1797) ),
    inference(clausify,[status(thm)],[f_665_5]) ).

cnf(f_665_9,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK114(U_1797,U_1796,U_1795)))
    | ~ sP206(U_1796,U_1795,U_1797) ),
    inference(clausify,[status(thm)],[f_665_5]) ).

cnf(f_665_10,plain,
    ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK113(U_1797,U_1796,U_1795)),U_1796))
    | ~ sP206(U_1796,U_1795,U_1797) ),
    inference(clausify,[status(thm)],[f_665_5]) ).

cnf(f_665_11,plain,
    ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK113(U_1797,U_1796,U_1795)),sK114(U_1797,U_1796,U_1795)))
    | ~ sP206(U_1796,U_1795,U_1797) ),
    inference(clausify,[status(thm)],[f_665_5]) ).

cnf(f_665_12,plain,
    ( hBOOL(hAPP_f621171935l_bool(U_1797,sK114(U_1797,U_1796,U_1795)))
    | ~ sP206(U_1796,U_1795,U_1797) ),
    inference(clausify,[status(thm)],[f_665_5]) ).

cnf(f_665_13,plain,
    ( ~ hBOOL(hAPP_f621171935l_bool(U_1797,insert_fun_a_bool(sK113(U_1797,U_1796,U_1795),sK114(U_1797,U_1796,U_1795))))
    | ~ sP206(U_1796,U_1795,U_1797) ),
    inference(clausify,[status(thm)],[f_665_5]) ).

fof(f_666_1,plain,
    ! [Pn,G] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(G),insert_a(hAPP_pname_a(mgt_call,Pn),bot_bot_fun_a_bool)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(p(insert_a(hAPP_pname_a(mgt_call,Pn),G)),insert_a(mgt(the_com(body(Pn))),bot_bot_fun_a_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_562_assms_I2_J]) ).

fof(f_666_2,plain,
    ! [U_1799,U_1798] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_1798),insert_a(hAPP_pname_a(mgt_call,U_1799),bot_bot_fun_a_bool)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(p(insert_a(hAPP_pname_a(mgt_call,U_1799),U_1798)),insert_a(mgt(the_com(body(U_1799))),bot_bot_fun_a_bool))) ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

fof(f_666_3,plain,
    ! [U_1799,U_1798] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_1798),insert_a(hAPP_pname_a(mgt_call,U_1799),bot_bot_fun_a_bool)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(p(insert_a(hAPP_pname_a(mgt_call,U_1799),U_1798)),insert_a(mgt(the_com(body(U_1799))),bot_bot_fun_a_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_666_2]) ).

cnf(f_666_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(p(U_1798),insert_a(hAPP_pname_a(mgt_call,U_1799),bot_bot_fun_a_bool)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(p(insert_a(hAPP_pname_a(mgt_call,U_1799),U_1798)),insert_a(mgt(the_com(body(U_1799))),bot_bot_fun_a_bool))) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

fof(f_667_1,plain,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f1637334154l_bool(Pa,F_1))
      | ? [X_1,F_2] :
          ( ~ hBOOL(hAPP_f1637334154l_bool(Pa,insert_fun_nat_bool(X_1,F_2)))
          & hBOOL(hAPP_f1637334154l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),F_2))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_2)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(Pa,bot_bo1701429464l_bool))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_563_finite__induct]) ).

fof(f_667_2,plain,
    ! [U_1803,U_1802] :
      ( hBOOL(hAPP_f1637334154l_bool(U_1803,U_1802))
      | ? [U_1801,U_1800] :
          ( ~ hBOOL(hAPP_f1637334154l_bool(U_1803,insert_fun_nat_bool(U_1801,U_1800)))
          & hBOOL(hAPP_f1637334154l_bool(U_1803,U_1800))
          & ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_1801),U_1800))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1800)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(U_1803,bot_bo1701429464l_bool))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1802)) ),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

fof(f_667_3,plain,
    ! [U_1803,U_1802] :
      ( hBOOL(hAPP_f1637334154l_bool(U_1803,U_1802))
      | ? [U_1800] :
          ( ~ hBOOL(hAPP_f1637334154l_bool(U_1803,insert_fun_nat_bool(sK115(U_1803,U_1802),U_1800)))
          & hBOOL(hAPP_f1637334154l_bool(U_1803,U_1800))
          & ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK115(U_1803,U_1802)),U_1800))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1800)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(U_1803,bot_bo1701429464l_bool))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1802)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_1801,sK115(U_1803,U_1802))],[f_667_2]) ).

fof(f_667_4,plain,
    ! [U_1803,U_1802] :
      ( hBOOL(hAPP_f1637334154l_bool(U_1803,U_1802))
      | ( ~ hBOOL(hAPP_f1637334154l_bool(U_1803,insert_fun_nat_bool(sK115(U_1803,U_1802),sK116(U_1803,U_1802))))
        & hBOOL(hAPP_f1637334154l_bool(U_1803,sK116(U_1803,U_1802)))
        & ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK115(U_1803,U_1802)),sK116(U_1803,U_1802)))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK116(U_1803,U_1802))) )
      | ~ hBOOL(hAPP_f1637334154l_bool(U_1803,bot_bo1701429464l_bool))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1802)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_1800,sK116(U_1803,U_1802))],[f_667_3]) ).

fof(f_667_5,plain,
    ( ! [U_1802,U_1803] :
        ( ~ hBOOL(hAPP_f1637334154l_bool(U_1803,insert_fun_nat_bool(sK115(U_1803,U_1802),sK116(U_1803,U_1802))))
        | ~ sP207(U_1802,U_1803) )
    & ! [U_1802,U_1803] :
        ( hBOOL(hAPP_f1637334154l_bool(U_1803,sK116(U_1803,U_1802)))
        | ~ sP207(U_1802,U_1803) )
    & ! [U_1802,U_1803] :
        ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK115(U_1803,U_1802)),sK116(U_1803,U_1802)))
        | ~ sP207(U_1802,U_1803) )
    & ! [U_1802,U_1803] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK116(U_1803,U_1802)))
        | ~ sP207(U_1802,U_1803) )
    & ! [U_1802,U_1803] :
        ( hBOOL(hAPP_f1637334154l_bool(U_1803,U_1802))
        | sP207(U_1802,U_1803)
        | ~ hBOOL(hAPP_f1637334154l_bool(U_1803,bot_bo1701429464l_bool))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1802)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207])],[f_667_4]) ).

cnf(f_667_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(U_1803,U_1802))
    | sP207(U_1802,U_1803)
    | ~ hBOOL(hAPP_f1637334154l_bool(U_1803,bot_bo1701429464l_bool))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_1802)) ),
    inference(clausify,[status(thm)],[f_667_5]) ).

cnf(f_667_7,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK116(U_1803,U_1802)))
    | ~ sP207(U_1802,U_1803) ),
    inference(clausify,[status(thm)],[f_667_5]) ).

cnf(f_667_8,plain,
    ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,sK115(U_1803,U_1802)),sK116(U_1803,U_1802)))
    | ~ sP207(U_1802,U_1803) ),
    inference(clausify,[status(thm)],[f_667_5]) ).

cnf(f_667_9,plain,
    ( hBOOL(hAPP_f1637334154l_bool(U_1803,sK116(U_1803,U_1802)))
    | ~ sP207(U_1802,U_1803) ),
    inference(clausify,[status(thm)],[f_667_5]) ).

cnf(f_667_10,plain,
    ( ~ hBOOL(hAPP_f1637334154l_bool(U_1803,insert_fun_nat_bool(sK115(U_1803,U_1802),sK116(U_1803,U_1802))))
    | ~ sP207(U_1802,U_1803) ),
    inference(clausify,[status(thm)],[f_667_5]) ).

fof(f_668_1,plain,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f1935102916l_bool(Pa,F_1))
      | ? [X_1,F_2] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(Pa,insert1325755072e_bool(X_1,F_2)))
          & hBOOL(hAPP_f1935102916l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),F_2))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_2))
          & is_fun1661590463l_bool(F_2)
          & is_fun_pname_bool(X_1) )
      | ~ hBOOL(hAPP_f1935102916l_bool(Pa,bot_bo1649642514l_bool))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_564_finite__induct]) ).

fof(f_668_2,plain,
    ! [U_1807,U_1806] :
      ( hBOOL(hAPP_f1935102916l_bool(U_1807,U_1806))
      | ? [U_1805,U_1804] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(U_1807,insert1325755072e_bool(U_1805,U_1804)))
          & hBOOL(hAPP_f1935102916l_bool(U_1807,U_1804))
          & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_1805),U_1804))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1804))
          & is_fun1661590463l_bool(U_1804)
          & is_fun_pname_bool(U_1805) )
      | ~ hBOOL(hAPP_f1935102916l_bool(U_1807,bot_bo1649642514l_bool))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1806)) ),
    inference(variable_rename,[status(thm)],[f_668_1]) ).

fof(f_668_3,plain,
    ! [U_1807,U_1806] :
      ( hBOOL(hAPP_f1935102916l_bool(U_1807,U_1806))
      | ? [U_1804] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(U_1807,insert1325755072e_bool(sK117(U_1807,U_1806),U_1804)))
          & hBOOL(hAPP_f1935102916l_bool(U_1807,U_1804))
          & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK117(U_1807,U_1806)),U_1804))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1804))
          & is_fun1661590463l_bool(U_1804)
          & is_fun_pname_bool(sK117(U_1807,U_1806)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(U_1807,bot_bo1649642514l_bool))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1806)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_1805,sK117(U_1807,U_1806))],[f_668_2]) ).

fof(f_668_4,plain,
    ! [U_1807,U_1806] :
      ( hBOOL(hAPP_f1935102916l_bool(U_1807,U_1806))
      | ( ~ hBOOL(hAPP_f1935102916l_bool(U_1807,insert1325755072e_bool(sK117(U_1807,U_1806),sK118(U_1807,U_1806))))
        & hBOOL(hAPP_f1935102916l_bool(U_1807,sK118(U_1807,U_1806)))
        & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK117(U_1807,U_1806)),sK118(U_1807,U_1806)))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK118(U_1807,U_1806)))
        & is_fun1661590463l_bool(sK118(U_1807,U_1806))
        & is_fun_pname_bool(sK117(U_1807,U_1806)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(U_1807,bot_bo1649642514l_bool))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1806)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_1804,sK118(U_1807,U_1806))],[f_668_3]) ).

fof(f_668_5,plain,
    ( ! [U_1806,U_1807] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(U_1807,insert1325755072e_bool(sK117(U_1807,U_1806),sK118(U_1807,U_1806))))
        | ~ sP208(U_1806,U_1807) )
    & ! [U_1806,U_1807] :
        ( hBOOL(hAPP_f1935102916l_bool(U_1807,sK118(U_1807,U_1806)))
        | ~ sP208(U_1806,U_1807) )
    & ! [U_1806,U_1807] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK117(U_1807,U_1806)),sK118(U_1807,U_1806)))
        | ~ sP208(U_1806,U_1807) )
    & ! [U_1806,U_1807] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK118(U_1807,U_1806)))
        | ~ sP208(U_1806,U_1807) )
    & ! [U_1806,U_1807] :
        ( is_fun1661590463l_bool(sK118(U_1807,U_1806))
        | ~ sP208(U_1806,U_1807) )
    & ! [U_1806,U_1807] :
        ( is_fun_pname_bool(sK117(U_1807,U_1806))
        | ~ sP208(U_1806,U_1807) )
    & ! [U_1806,U_1807] :
        ( hBOOL(hAPP_f1935102916l_bool(U_1807,U_1806))
        | sP208(U_1806,U_1807)
        | ~ hBOOL(hAPP_f1935102916l_bool(U_1807,bot_bo1649642514l_bool))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1806)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208])],[f_668_4]) ).

cnf(f_668_6,plain,
    ( hBOOL(hAPP_f1935102916l_bool(U_1807,U_1806))
    | sP208(U_1806,U_1807)
    | ~ hBOOL(hAPP_f1935102916l_bool(U_1807,bot_bo1649642514l_bool))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_1806)) ),
    inference(clausify,[status(thm)],[f_668_5]) ).

cnf(f_668_7,plain,
    ( is_fun_pname_bool(sK117(U_1807,U_1806))
    | ~ sP208(U_1806,U_1807) ),
    inference(clausify,[status(thm)],[f_668_5]) ).

cnf(f_668_8,plain,
    ( is_fun1661590463l_bool(sK118(U_1807,U_1806))
    | ~ sP208(U_1806,U_1807) ),
    inference(clausify,[status(thm)],[f_668_5]) ).

cnf(f_668_9,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK118(U_1807,U_1806)))
    | ~ sP208(U_1806,U_1807) ),
    inference(clausify,[status(thm)],[f_668_5]) ).

cnf(f_668_10,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK117(U_1807,U_1806)),sK118(U_1807,U_1806)))
    | ~ sP208(U_1806,U_1807) ),
    inference(clausify,[status(thm)],[f_668_5]) ).

cnf(f_668_11,plain,
    ( hBOOL(hAPP_f1935102916l_bool(U_1807,sK118(U_1807,U_1806)))
    | ~ sP208(U_1806,U_1807) ),
    inference(clausify,[status(thm)],[f_668_5]) ).

cnf(f_668_12,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(U_1807,insert1325755072e_bool(sK117(U_1807,U_1806),sK118(U_1807,U_1806))))
    | ~ sP208(U_1806,U_1807) ),
    inference(clausify,[status(thm)],[f_668_5]) ).

fof(f_669_1,plain,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f621171935l_bool(Pa,F_1))
      | ? [X_1,F_2] :
          ( ~ hBOOL(hAPP_f621171935l_bool(Pa,insert_fun_a_bool(X_1,F_2)))
          & hBOOL(hAPP_f621171935l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),F_2))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_2))
          & is_fun949378684l_bool(F_2)
          & is_fun_a_bool(X_1) )
      | ~ hBOOL(hAPP_f621171935l_bool(Pa,bot_bo1389914601l_bool))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_565_finite__induct]) ).

fof(f_669_2,plain,
    ! [U_1811,U_1810] :
      ( hBOOL(hAPP_f621171935l_bool(U_1811,U_1810))
      | ? [U_1809,U_1808] :
          ( ~ hBOOL(hAPP_f621171935l_bool(U_1811,insert_fun_a_bool(U_1809,U_1808)))
          & hBOOL(hAPP_f621171935l_bool(U_1811,U_1808))
          & ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_1809),U_1808))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1808))
          & is_fun949378684l_bool(U_1808)
          & is_fun_a_bool(U_1809) )
      | ~ hBOOL(hAPP_f621171935l_bool(U_1811,bot_bo1389914601l_bool))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1810)) ),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

fof(f_669_3,plain,
    ! [U_1811,U_1810] :
      ( hBOOL(hAPP_f621171935l_bool(U_1811,U_1810))
      | ? [U_1808] :
          ( ~ hBOOL(hAPP_f621171935l_bool(U_1811,insert_fun_a_bool(sK119(U_1811,U_1810),U_1808)))
          & hBOOL(hAPP_f621171935l_bool(U_1811,U_1808))
          & ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK119(U_1811,U_1810)),U_1808))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1808))
          & is_fun949378684l_bool(U_1808)
          & is_fun_a_bool(sK119(U_1811,U_1810)) )
      | ~ hBOOL(hAPP_f621171935l_bool(U_1811,bot_bo1389914601l_bool))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1810)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_1809,sK119(U_1811,U_1810))],[f_669_2]) ).

fof(f_669_4,plain,
    ! [U_1811,U_1810] :
      ( hBOOL(hAPP_f621171935l_bool(U_1811,U_1810))
      | ( ~ hBOOL(hAPP_f621171935l_bool(U_1811,insert_fun_a_bool(sK119(U_1811,U_1810),sK120(U_1811,U_1810))))
        & hBOOL(hAPP_f621171935l_bool(U_1811,sK120(U_1811,U_1810)))
        & ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK119(U_1811,U_1810)),sK120(U_1811,U_1810)))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK120(U_1811,U_1810)))
        & is_fun949378684l_bool(sK120(U_1811,U_1810))
        & is_fun_a_bool(sK119(U_1811,U_1810)) )
      | ~ hBOOL(hAPP_f621171935l_bool(U_1811,bot_bo1389914601l_bool))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1810)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_1808,sK120(U_1811,U_1810))],[f_669_3]) ).

fof(f_669_5,plain,
    ( ! [U_1810,U_1811] :
        ( ~ hBOOL(hAPP_f621171935l_bool(U_1811,insert_fun_a_bool(sK119(U_1811,U_1810),sK120(U_1811,U_1810))))
        | ~ sP209(U_1810,U_1811) )
    & ! [U_1810,U_1811] :
        ( hBOOL(hAPP_f621171935l_bool(U_1811,sK120(U_1811,U_1810)))
        | ~ sP209(U_1810,U_1811) )
    & ! [U_1810,U_1811] :
        ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK119(U_1811,U_1810)),sK120(U_1811,U_1810)))
        | ~ sP209(U_1810,U_1811) )
    & ! [U_1810,U_1811] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK120(U_1811,U_1810)))
        | ~ sP209(U_1810,U_1811) )
    & ! [U_1810,U_1811] :
        ( is_fun949378684l_bool(sK120(U_1811,U_1810))
        | ~ sP209(U_1810,U_1811) )
    & ! [U_1810,U_1811] :
        ( is_fun_a_bool(sK119(U_1811,U_1810))
        | ~ sP209(U_1810,U_1811) )
    & ! [U_1810,U_1811] :
        ( hBOOL(hAPP_f621171935l_bool(U_1811,U_1810))
        | sP209(U_1810,U_1811)
        | ~ hBOOL(hAPP_f621171935l_bool(U_1811,bot_bo1389914601l_bool))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1810)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209])],[f_669_4]) ).

cnf(f_669_6,plain,
    ( hBOOL(hAPP_f621171935l_bool(U_1811,U_1810))
    | sP209(U_1810,U_1811)
    | ~ hBOOL(hAPP_f621171935l_bool(U_1811,bot_bo1389914601l_bool))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_1810)) ),
    inference(clausify,[status(thm)],[f_669_5]) ).

cnf(f_669_7,plain,
    ( is_fun_a_bool(sK119(U_1811,U_1810))
    | ~ sP209(U_1810,U_1811) ),
    inference(clausify,[status(thm)],[f_669_5]) ).

cnf(f_669_8,plain,
    ( is_fun949378684l_bool(sK120(U_1811,U_1810))
    | ~ sP209(U_1810,U_1811) ),
    inference(clausify,[status(thm)],[f_669_5]) ).

cnf(f_669_9,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK120(U_1811,U_1810)))
    | ~ sP209(U_1810,U_1811) ),
    inference(clausify,[status(thm)],[f_669_5]) ).

cnf(f_669_10,plain,
    ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,sK119(U_1811,U_1810)),sK120(U_1811,U_1810)))
    | ~ sP209(U_1810,U_1811) ),
    inference(clausify,[status(thm)],[f_669_5]) ).

cnf(f_669_11,plain,
    ( hBOOL(hAPP_f621171935l_bool(U_1811,sK120(U_1811,U_1810)))
    | ~ sP209(U_1810,U_1811) ),
    inference(clausify,[status(thm)],[f_669_5]) ).

cnf(f_669_12,plain,
    ( ~ hBOOL(hAPP_f621171935l_bool(U_1811,insert_fun_a_bool(sK119(U_1811,U_1810),sK120(U_1811,U_1810))))
    | ~ sP209(U_1810,U_1811) ),
    inference(clausify,[status(thm)],[f_669_5]) ).

fof(f_670_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_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_2),hAPP_nat_nat(F,N_2))) ),
    inference(fof_nnf,[status(thm)],[fact_566_finite__less__ub]) ).

fof(f_670_2,plain,
    ! [U_1814,U_1813] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,U_1813)),U_1814))))
      | ? [U_1812] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1812),hAPP_nat_nat(U_1813,U_1812))) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

fof(f_670_3,plain,
    ! [U_1814,U_1813] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,U_1813)),U_1814))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK121(U_1814,U_1813)),hAPP_nat_nat(U_1813,sK121(U_1814,U_1813)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_1812,sK121(U_1814,U_1813))],[f_670_2]) ).

fof(f_670_4,plain,
    ! [U_1814,U_1813] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,U_1813)),U_1814))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK121(U_1814,U_1813)),hAPP_nat_nat(U_1813,sK121(U_1814,U_1813)))) ),
    inference(definitional_conversion,[status(esa)],[f_670_3]) ).

cnf(f_670_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_1813)),U_1814))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK121(U_1814,U_1813)),hAPP_nat_nat(U_1813,sK121(U_1814,U_1813)))) ),
    inference(clausify,[status(thm)],[f_670_4]) ).

fof(f_671_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_567_assms_I4_J]) ).

fof(f_671_2,plain,
    ! [U_1815] :
      ( hBOOL(wt(the_com(body(U_1815))))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1815),u)) ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

fof(f_671_3,plain,
    ! [U_1815] :
      ( hBOOL(wt(the_com(body(U_1815))))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1815),u)) ),
    inference(definitional_conversion,[status(esa)],[f_671_2]) ).

cnf(f_671_4,plain,
    ( hBOOL(wt(the_com(body(U_1815))))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1815),u)) ),
    inference(clausify,[status(thm)],[f_671_3]) ).

fof(f_672_1,plain,
    ! [M,N] : hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N),
    inference(fof_nnf,[status(thm)],[fact_568_diff__Suc__eq__diff__pred]) ).

fof(f_672_2,plain,
    ! [U_1817,U_1816] : hAPP_nat_nat(minus_minus_nat(U_1817),hAPP_nat_nat(suc,U_1816)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_1817),one_one_nat)),U_1816),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

fof(f_672_3,plain,
    ! [U_1816,U_1817] : hAPP_nat_nat(minus_minus_nat(U_1817),hAPP_nat_nat(suc,U_1816)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_1817),one_one_nat)),U_1816),
    inference(definitional_conversion,[status(esa)],[f_672_2]) ).

cnf(f_672_4,plain,
    hAPP_nat_nat(minus_minus_nat(U_1817),hAPP_nat_nat(suc,U_1816)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_1817),one_one_nat)),U_1816),
    inference(clausify,[status(thm)],[f_672_3]) ).

fof(f_673_1,plain,
    ! [N] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,N)),one_one_nat) = N,
    inference(fof_nnf,[status(thm)],[fact_569_diff__Suc__1]) ).

fof(f_673_2,plain,
    ! [U_1818] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_1818)),one_one_nat) = U_1818,
    inference(variable_rename,[status(thm)],[f_673_1]) ).

fof(f_673_3,plain,
    ! [U_1818] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_1818)),one_one_nat) = U_1818,
    inference(definitional_conversion,[status(esa)],[f_673_2]) ).

cnf(f_673_4,plain,
    hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_1818)),one_one_nat) = U_1818,
    inference(clausify,[status(thm)],[f_673_3]) ).

fof(f_674_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M_1)),Na)) )
      & ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M_1)),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_570_less__eq__nat_Osimps_I2_J]) ).

fof(f_674_2,plain,
    ! [U_1820,U_1819] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1820)),U_1819))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1820)),U_1819)) )
      & ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1820)),U_1819))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1820)),U_1819)) ) ),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

fof(f_674_3,plain,
    ( ! [U_1824,U_1822] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1824)),U_1822))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1824)),U_1822)) )
    & ! [U_1823,U_1821] :
        ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1823)),U_1821))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1823)),U_1821)) ) ),
    inference(miniscope,[status(thm)],[f_674_2]) ).

fof(f_674_4,plain,
    ( ! [U_1822,U_1824] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1824)),U_1822))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1824)),U_1822)) )
    & ! [U_1823,U_1821] :
        ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1823)),U_1821))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1823)),U_1821)) ) ),
    inference(definitional_conversion,[status(esa)],[f_674_3]) ).

cnf(f_674_5,plain,
    ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1823)),U_1821))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1823)),U_1821)) ),
    inference(clausify,[status(thm)],[f_674_4]) ).

cnf(f_674_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1824)),U_1822))
    | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1824)),U_1822)) ),
    inference(clausify,[status(thm)],[f_674_4]) ).

fof(f_675_1,plain,
    ! [M,N] : hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N)),
    inference(fof_nnf,[status(thm)],[fact_571_add__Suc__right]) ).

fof(f_675_2,plain,
    ! [U_1826,U_1825] : hAPP_nat_nat(plus_plus_nat(U_1826),hAPP_nat_nat(suc,U_1825)) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_1826),U_1825)),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

fof(f_675_3,plain,
    ! [U_1825,U_1826] : hAPP_nat_nat(plus_plus_nat(U_1826),hAPP_nat_nat(suc,U_1825)) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_1826),U_1825)),
    inference(definitional_conversion,[status(esa)],[f_675_2]) ).

cnf(f_675_4,plain,
    hAPP_nat_nat(plus_plus_nat(U_1826),hAPP_nat_nat(suc,U_1825)) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_1826),U_1825)),
    inference(clausify,[status(thm)],[f_675_3]) ).

fof(f_676_1,plain,
    ! [M,N] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),N)),
    inference(fof_nnf,[status(thm)],[fact_572_add__Suc]) ).

fof(f_676_2,plain,
    ! [U_1828,U_1827] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,U_1828)),U_1827) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_1828),U_1827)),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

fof(f_676_3,plain,
    ! [U_1827,U_1828] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,U_1828)),U_1827) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_1828),U_1827)),
    inference(definitional_conversion,[status(esa)],[f_676_2]) ).

cnf(f_676_4,plain,
    hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,U_1828)),U_1827) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_1828),U_1827)),
    inference(clausify,[status(thm)],[f_676_3]) ).

fof(f_677_1,plain,
    ! [M,N] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(suc,N)),
    inference(fof_nnf,[status(thm)],[fact_573_add__Suc__shift]) ).

fof(f_677_2,plain,
    ! [U_1830,U_1829] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,U_1830)),U_1829) = hAPP_nat_nat(plus_plus_nat(U_1830),hAPP_nat_nat(suc,U_1829)),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

fof(f_677_3,plain,
    ! [U_1829,U_1830] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,U_1830)),U_1829) = hAPP_nat_nat(plus_plus_nat(U_1830),hAPP_nat_nat(suc,U_1829)),
    inference(definitional_conversion,[status(esa)],[f_677_2]) ).

cnf(f_677_4,plain,
    hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,U_1830)),U_1829) = hAPP_nat_nat(plus_plus_nat(U_1830),hAPP_nat_nat(suc,U_1829)),
    inference(clausify,[status(thm)],[f_677_3]) ).

fof(f_678_1,plain,
    ! [M_1,K_2,Na] :
      ( ( hAPP_nat_nat(plus_plus_nat(M_1),K_2) = hAPP_nat_nat(plus_plus_nat(Na),K_2)
        | M_1 != Na )
      & ( M_1 = Na
        | hAPP_nat_nat(plus_plus_nat(M_1),K_2) != hAPP_nat_nat(plus_plus_nat(Na),K_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_574_nat__add__right__cancel]) ).

fof(f_678_2,plain,
    ! [U_1833,U_1832,U_1831] :
      ( ( hAPP_nat_nat(plus_plus_nat(U_1833),U_1832) = hAPP_nat_nat(plus_plus_nat(U_1831),U_1832)
        | U_1833 != U_1831 )
      & ( U_1833 = U_1831
        | hAPP_nat_nat(plus_plus_nat(U_1833),U_1832) != hAPP_nat_nat(plus_plus_nat(U_1831),U_1832) ) ),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

fof(f_678_3,plain,
    ( ! [U_1839,U_1837,U_1835] :
        ( hAPP_nat_nat(plus_plus_nat(U_1839),U_1837) = hAPP_nat_nat(plus_plus_nat(U_1835),U_1837)
        | U_1839 != U_1835 )
    & ! [U_1838,U_1836,U_1834] :
        ( U_1838 = U_1834
        | hAPP_nat_nat(plus_plus_nat(U_1838),U_1836) != hAPP_nat_nat(plus_plus_nat(U_1834),U_1836) ) ),
    inference(miniscope,[status(thm)],[f_678_2]) ).

fof(f_678_4,plain,
    ( ! [U_1835,U_1837,U_1839] :
        ( hAPP_nat_nat(plus_plus_nat(U_1839),U_1837) = hAPP_nat_nat(plus_plus_nat(U_1835),U_1837)
        | U_1839 != U_1835 )
    & ! [U_1838,U_1836,U_1834] :
        ( U_1838 = U_1834
        | hAPP_nat_nat(plus_plus_nat(U_1838),U_1836) != hAPP_nat_nat(plus_plus_nat(U_1834),U_1836) ) ),
    inference(definitional_conversion,[status(esa)],[f_678_3]) ).

cnf(f_678_5,plain,
    ( U_1838 = U_1834
    | hAPP_nat_nat(plus_plus_nat(U_1838),U_1836) != hAPP_nat_nat(plus_plus_nat(U_1834),U_1836) ),
    inference(clausify,[status(thm)],[f_678_4]) ).

cnf(f_678_6,plain,
    ( hAPP_nat_nat(plus_plus_nat(U_1839),U_1837) = hAPP_nat_nat(plus_plus_nat(U_1835),U_1837)
    | U_1839 != U_1835 ),
    inference(clausify,[status(thm)],[f_678_4]) ).

fof(f_679_1,plain,
    ! [K_2,M_1,Na] :
      ( ( hAPP_nat_nat(plus_plus_nat(K_2),M_1) = hAPP_nat_nat(plus_plus_nat(K_2),Na)
        | M_1 != Na )
      & ( M_1 = Na
        | hAPP_nat_nat(plus_plus_nat(K_2),M_1) != hAPP_nat_nat(plus_plus_nat(K_2),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_575_nat__add__left__cancel]) ).

fof(f_679_2,plain,
    ! [U_1842,U_1841,U_1840] :
      ( ( hAPP_nat_nat(plus_plus_nat(U_1842),U_1841) = hAPP_nat_nat(plus_plus_nat(U_1842),U_1840)
        | U_1841 != U_1840 )
      & ( U_1841 = U_1840
        | hAPP_nat_nat(plus_plus_nat(U_1842),U_1841) != hAPP_nat_nat(plus_plus_nat(U_1842),U_1840) ) ),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

fof(f_679_3,plain,
    ( ! [U_1848,U_1846,U_1844] :
        ( hAPP_nat_nat(plus_plus_nat(U_1848),U_1846) = hAPP_nat_nat(plus_plus_nat(U_1848),U_1844)
        | U_1846 != U_1844 )
    & ! [U_1847,U_1845,U_1843] :
        ( U_1845 = U_1843
        | hAPP_nat_nat(plus_plus_nat(U_1847),U_1845) != hAPP_nat_nat(plus_plus_nat(U_1847),U_1843) ) ),
    inference(miniscope,[status(thm)],[f_679_2]) ).

fof(f_679_4,plain,
    ( ! [U_1844,U_1846,U_1848] :
        ( hAPP_nat_nat(plus_plus_nat(U_1848),U_1846) = hAPP_nat_nat(plus_plus_nat(U_1848),U_1844)
        | U_1846 != U_1844 )
    & ! [U_1845,U_1847,U_1843] :
        ( U_1845 = U_1843
        | hAPP_nat_nat(plus_plus_nat(U_1847),U_1845) != hAPP_nat_nat(plus_plus_nat(U_1847),U_1843) ) ),
    inference(definitional_conversion,[status(esa)],[f_679_3]) ).

cnf(f_679_5,plain,
    ( U_1845 = U_1843
    | hAPP_nat_nat(plus_plus_nat(U_1847),U_1845) != hAPP_nat_nat(plus_plus_nat(U_1847),U_1843) ),
    inference(clausify,[status(thm)],[f_679_4]) ).

cnf(f_679_6,plain,
    ( hAPP_nat_nat(plus_plus_nat(U_1848),U_1846) = hAPP_nat_nat(plus_plus_nat(U_1848),U_1844)
    | U_1846 != U_1844 ),
    inference(clausify,[status(thm)],[f_679_4]) ).

fof(f_680_1,plain,
    ! [M,N,K] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(M),N)),K) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(plus_plus_nat(N),K)),
    inference(fof_nnf,[status(thm)],[fact_576_nat__add__assoc]) ).

fof(f_680_2,plain,
    ! [U_1851,U_1850,U_1849] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_1851),U_1850)),U_1849) = hAPP_nat_nat(plus_plus_nat(U_1851),hAPP_nat_nat(plus_plus_nat(U_1850),U_1849)),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

fof(f_680_3,plain,
    ! [U_1849,U_1850,U_1851] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_1851),U_1850)),U_1849) = hAPP_nat_nat(plus_plus_nat(U_1851),hAPP_nat_nat(plus_plus_nat(U_1850),U_1849)),
    inference(definitional_conversion,[status(esa)],[f_680_2]) ).

cnf(f_680_4,plain,
    hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_1851),U_1850)),U_1849) = hAPP_nat_nat(plus_plus_nat(U_1851),hAPP_nat_nat(plus_plus_nat(U_1850),U_1849)),
    inference(clausify,[status(thm)],[f_680_3]) ).

fof(f_681_1,plain,
    ! [X,Y,Z] : hAPP_nat_nat(plus_plus_nat(X),hAPP_nat_nat(plus_plus_nat(Y),Z)) = hAPP_nat_nat(plus_plus_nat(Y),hAPP_nat_nat(plus_plus_nat(X),Z)),
    inference(fof_nnf,[status(thm)],[fact_577_nat__add__left__commute]) ).

fof(f_681_2,plain,
    ! [U_1854,U_1853,U_1852] : hAPP_nat_nat(plus_plus_nat(U_1854),hAPP_nat_nat(plus_plus_nat(U_1853),U_1852)) = hAPP_nat_nat(plus_plus_nat(U_1853),hAPP_nat_nat(plus_plus_nat(U_1854),U_1852)),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

fof(f_681_3,plain,
    ! [U_1852,U_1853,U_1854] : hAPP_nat_nat(plus_plus_nat(U_1854),hAPP_nat_nat(plus_plus_nat(U_1853),U_1852)) = hAPP_nat_nat(plus_plus_nat(U_1853),hAPP_nat_nat(plus_plus_nat(U_1854),U_1852)),
    inference(definitional_conversion,[status(esa)],[f_681_2]) ).

cnf(f_681_4,plain,
    hAPP_nat_nat(plus_plus_nat(U_1854),hAPP_nat_nat(plus_plus_nat(U_1853),U_1852)) = hAPP_nat_nat(plus_plus_nat(U_1853),hAPP_nat_nat(plus_plus_nat(U_1854),U_1852)),
    inference(clausify,[status(thm)],[f_681_3]) ).

fof(f_682_1,plain,
    ! [M,N] : hAPP_nat_nat(plus_plus_nat(M),N) = hAPP_nat_nat(plus_plus_nat(N),M),
    inference(fof_nnf,[status(thm)],[fact_578_nat__add__commute]) ).

fof(f_682_2,plain,
    ! [U_1856,U_1855] : hAPP_nat_nat(plus_plus_nat(U_1856),U_1855) = hAPP_nat_nat(plus_plus_nat(U_1855),U_1856),
    inference(variable_rename,[status(thm)],[f_682_1]) ).

fof(f_682_3,plain,
    ! [U_1855,U_1856] : hAPP_nat_nat(plus_plus_nat(U_1856),U_1855) = hAPP_nat_nat(plus_plus_nat(U_1855),U_1856),
    inference(definitional_conversion,[status(esa)],[f_682_2]) ).

cnf(f_682_4,plain,
    hAPP_nat_nat(plus_plus_nat(U_1856),U_1855) = hAPP_nat_nat(plus_plus_nat(U_1855),U_1856),
    inference(clausify,[status(thm)],[f_682_3]) ).

fof(f_683_1,plain,
    ! [M,N] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),N)),N) = M,
    inference(fof_nnf,[status(thm)],[fact_579_diff__add__inverse2]) ).

fof(f_683_2,plain,
    ! [U_1858,U_1857] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1858),U_1857)),U_1857) = U_1858,
    inference(variable_rename,[status(thm)],[f_683_1]) ).

fof(f_683_3,plain,
    ! [U_1857,U_1858] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1858),U_1857)),U_1857) = U_1858,
    inference(definitional_conversion,[status(esa)],[f_683_2]) ).

cnf(f_683_4,plain,
    hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1858),U_1857)),U_1857) = U_1858,
    inference(clausify,[status(thm)],[f_683_3]) ).

fof(f_684_1,plain,
    ! [N,M] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N),M)),N) = M,
    inference(fof_nnf,[status(thm)],[fact_580_diff__add__inverse]) ).

fof(f_684_2,plain,
    ! [U_1860,U_1859] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1860),U_1859)),U_1860) = U_1859,
    inference(variable_rename,[status(thm)],[f_684_1]) ).

fof(f_684_3,plain,
    ! [U_1859,U_1860] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1860),U_1859)),U_1860) = U_1859,
    inference(definitional_conversion,[status(esa)],[f_684_2]) ).

cnf(f_684_4,plain,
    hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1860),U_1859)),U_1860) = U_1859,
    inference(clausify,[status(thm)],[f_684_3]) ).

fof(f_685_1,plain,
    ! [I,J_2,K] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I),J_2)),K) = hAPP_nat_nat(minus_minus_nat(I),hAPP_nat_nat(plus_plus_nat(J_2),K)),
    inference(fof_nnf,[status(thm)],[fact_581_diff__diff__left]) ).

fof(f_685_2,plain,
    ! [U_1863,U_1862,U_1861] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_1863),U_1862)),U_1861) = hAPP_nat_nat(minus_minus_nat(U_1863),hAPP_nat_nat(plus_plus_nat(U_1862),U_1861)),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

fof(f_685_3,plain,
    ! [U_1861,U_1862,U_1863] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_1863),U_1862)),U_1861) = hAPP_nat_nat(minus_minus_nat(U_1863),hAPP_nat_nat(plus_plus_nat(U_1862),U_1861)),
    inference(definitional_conversion,[status(esa)],[f_685_2]) ).

cnf(f_685_4,plain,
    hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_1863),U_1862)),U_1861) = hAPP_nat_nat(minus_minus_nat(U_1863),hAPP_nat_nat(plus_plus_nat(U_1862),U_1861)),
    inference(clausify,[status(thm)],[f_685_3]) ).

fof(f_686_1,plain,
    ! [K,M,N] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(K),M)),hAPP_nat_nat(plus_plus_nat(K),N)) = hAPP_nat_nat(minus_minus_nat(M),N),
    inference(fof_nnf,[status(thm)],[fact_582_diff__cancel]) ).

fof(f_686_2,plain,
    ! [U_1866,U_1865,U_1864] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1866),U_1865)),hAPP_nat_nat(plus_plus_nat(U_1866),U_1864)) = hAPP_nat_nat(minus_minus_nat(U_1865),U_1864),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

fof(f_686_3,plain,
    ! [U_1864,U_1865,U_1866] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1866),U_1865)),hAPP_nat_nat(plus_plus_nat(U_1866),U_1864)) = hAPP_nat_nat(minus_minus_nat(U_1865),U_1864),
    inference(definitional_conversion,[status(esa)],[f_686_2]) ).

cnf(f_686_4,plain,
    hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1866),U_1865)),hAPP_nat_nat(plus_plus_nat(U_1866),U_1864)) = hAPP_nat_nat(minus_minus_nat(U_1865),U_1864),
    inference(clausify,[status(thm)],[f_686_3]) ).

fof(f_687_1,plain,
    ! [M,K,N] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K)),hAPP_nat_nat(plus_plus_nat(N),K)) = hAPP_nat_nat(minus_minus_nat(M),N),
    inference(fof_nnf,[status(thm)],[fact_583_diff__cancel2]) ).

fof(f_687_2,plain,
    ! [U_1869,U_1868,U_1867] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1869),U_1868)),hAPP_nat_nat(plus_plus_nat(U_1867),U_1868)) = hAPP_nat_nat(minus_minus_nat(U_1869),U_1867),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

fof(f_687_3,plain,
    ! [U_1867,U_1868,U_1869] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1869),U_1868)),hAPP_nat_nat(plus_plus_nat(U_1867),U_1868)) = hAPP_nat_nat(minus_minus_nat(U_1869),U_1867),
    inference(definitional_conversion,[status(esa)],[f_687_2]) ).

cnf(f_687_4,plain,
    hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1869),U_1868)),hAPP_nat_nat(plus_plus_nat(U_1867),U_1868)) = hAPP_nat_nat(minus_minus_nat(U_1869),U_1867),
    inference(clausify,[status(thm)],[f_687_3]) ).

fof(f_688_1,plain,
    ! [N,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(plus_plus_nat(M),N))),
    inference(fof_nnf,[status(thm)],[fact_584_le__add2]) ).

fof(f_688_2,plain,
    ! [U_1871,U_1870] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1871),hAPP_nat_nat(plus_plus_nat(U_1870),U_1871))),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

fof(f_688_3,plain,
    ! [U_1870,U_1871] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1871),hAPP_nat_nat(plus_plus_nat(U_1870),U_1871))),
    inference(definitional_conversion,[status(esa)],[f_688_2]) ).

cnf(f_688_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1871),hAPP_nat_nat(plus_plus_nat(U_1870),U_1871))),
    inference(clausify,[status(thm)],[f_688_3]) ).

fof(f_689_1,plain,
    ! [N,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(plus_plus_nat(N),M))),
    inference(fof_nnf,[status(thm)],[fact_585_le__add1]) ).

fof(f_689_2,plain,
    ! [U_1873,U_1872] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1873),hAPP_nat_nat(plus_plus_nat(U_1873),U_1872))),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

fof(f_689_3,plain,
    ! [U_1872,U_1873] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1873),hAPP_nat_nat(plus_plus_nat(U_1873),U_1872))),
    inference(definitional_conversion,[status(esa)],[f_689_2]) ).

cnf(f_689_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1873),hAPP_nat_nat(plus_plus_nat(U_1873),U_1872))),
    inference(clausify,[status(thm)],[f_689_3]) ).

fof(f_690_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ! [K_1] : Na != hAPP_nat_nat(plus_plus_nat(M_1),K_1) )
      & ( ? [K_1] : Na = hAPP_nat_nat(plus_plus_nat(M_1),K_1)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_586_le__iff__add]) ).

fof(f_690_2,plain,
    ! [U_1877,U_1876] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1877),U_1876))
        | ! [U_1875] : U_1876 != hAPP_nat_nat(plus_plus_nat(U_1877),U_1875) )
      & ( ? [U_1874] : U_1876 = hAPP_nat_nat(plus_plus_nat(U_1877),U_1874)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1877),U_1876)) ) ),
    inference(variable_rename,[status(thm)],[f_690_1]) ).

fof(f_690_3,plain,
    ( ! [U_1881,U_1879] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1881),U_1879))
        | ! [U_1875] : U_1879 != hAPP_nat_nat(plus_plus_nat(U_1881),U_1875) )
    & ! [U_1880,U_1878] :
        ( ? [U_1874] : U_1878 = hAPP_nat_nat(plus_plus_nat(U_1880),U_1874)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1880),U_1878)) ) ),
    inference(miniscope,[status(thm)],[f_690_2]) ).

fof(f_690_4,plain,
    ( ! [U_1881,U_1879] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1881),U_1879))
        | ! [U_1875] : U_1879 != hAPP_nat_nat(plus_plus_nat(U_1881),U_1875) )
    & ! [U_1880,U_1878] :
        ( U_1878 = hAPP_nat_nat(plus_plus_nat(U_1880),sK122(U_1880,U_1878))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1880),U_1878)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_1874,sK122(U_1880,U_1878))],[f_690_3]) ).

fof(f_690_5,plain,
    ( ! [U_1875,U_1879,U_1881] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1881),U_1879))
        | U_1879 != hAPP_nat_nat(plus_plus_nat(U_1881),U_1875) )
    & ! [U_1880,U_1878] :
        ( U_1878 = hAPP_nat_nat(plus_plus_nat(U_1880),sK122(U_1880,U_1878))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1880),U_1878)) ) ),
    inference(definitional_conversion,[status(esa)],[f_690_4]) ).

cnf(f_690_6,plain,
    ( U_1878 = hAPP_nat_nat(plus_plus_nat(U_1880),sK122(U_1880,U_1878))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1880),U_1878)) ),
    inference(clausify,[status(thm)],[f_690_5]) ).

cnf(f_690_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1881),U_1879))
    | U_1879 != hAPP_nat_nat(plus_plus_nat(U_1881),U_1875) ),
    inference(clausify,[status(thm)],[f_690_5]) ).

fof(f_691_1,plain,
    ! [K_2,M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(K_2),M_1)),hAPP_nat_nat(plus_plus_nat(K_2),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(K_2),M_1)),hAPP_nat_nat(plus_plus_nat(K_2),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_587_nat__add__left__cancel__le]) ).

fof(f_691_2,plain,
    ! [U_1884,U_1883,U_1882] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1884),U_1883)),hAPP_nat_nat(plus_plus_nat(U_1884),U_1882)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1883),U_1882)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1883),U_1882))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1884),U_1883)),hAPP_nat_nat(plus_plus_nat(U_1884),U_1882))) ) ),
    inference(variable_rename,[status(thm)],[f_691_1]) ).

fof(f_691_3,plain,
    ( ! [U_1890,U_1888,U_1886] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1890),U_1888)),hAPP_nat_nat(plus_plus_nat(U_1890),U_1886)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1888),U_1886)) )
    & ! [U_1889,U_1887,U_1885] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1887),U_1885))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1889),U_1887)),hAPP_nat_nat(plus_plus_nat(U_1889),U_1885))) ) ),
    inference(miniscope,[status(thm)],[f_691_2]) ).

fof(f_691_4,plain,
    ( ! [U_1886,U_1888,U_1890] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1890),U_1888)),hAPP_nat_nat(plus_plus_nat(U_1890),U_1886)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1888),U_1886)) )
    & ! [U_1889,U_1887,U_1885] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1887),U_1885))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1889),U_1887)),hAPP_nat_nat(plus_plus_nat(U_1889),U_1885))) ) ),
    inference(definitional_conversion,[status(esa)],[f_691_3]) ).

cnf(f_691_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1887),U_1885))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1889),U_1887)),hAPP_nat_nat(plus_plus_nat(U_1889),U_1885))) ),
    inference(clausify,[status(thm)],[f_691_4]) ).

cnf(f_691_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1890),U_1888)),hAPP_nat_nat(plus_plus_nat(U_1890),U_1886)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1888),U_1886)) ),
    inference(clausify,[status(thm)],[f_691_4]) ).

fof(f_692_1,plain,
    ! [M,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(plus_plus_nat(J_2),M)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_588_trans__le__add1]) ).

fof(f_692_2,plain,
    ! [U_1893,U_1892,U_1891] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1892),hAPP_nat_nat(plus_plus_nat(U_1891),U_1893)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1892),U_1891)) ),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

fof(f_692_3,plain,
    ! [U_1892,U_1891,U_1893] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1892),hAPP_nat_nat(plus_plus_nat(U_1891),U_1893)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1892),U_1891)) ),
    inference(definitional_conversion,[status(esa)],[f_692_2]) ).

cnf(f_692_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1892),hAPP_nat_nat(plus_plus_nat(U_1891),U_1893)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1892),U_1891)) ),
    inference(clausify,[status(thm)],[f_692_3]) ).

fof(f_693_1,plain,
    ! [M,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(plus_plus_nat(M),J_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_589_trans__le__add2]) ).

fof(f_693_2,plain,
    ! [U_1896,U_1895,U_1894] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1895),hAPP_nat_nat(plus_plus_nat(U_1896),U_1894)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1895),U_1894)) ),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

fof(f_693_3,plain,
    ! [U_1894,U_1895,U_1896] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1895),hAPP_nat_nat(plus_plus_nat(U_1896),U_1894)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1895),U_1894)) ),
    inference(definitional_conversion,[status(esa)],[f_693_2]) ).

cnf(f_693_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1895),hAPP_nat_nat(plus_plus_nat(U_1896),U_1894)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1895),U_1894)) ),
    inference(clausify,[status(thm)],[f_693_3]) ).

fof(f_694_1,plain,
    ! [K,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),K)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_590_add__le__mono1]) ).

fof(f_694_2,plain,
    ! [U_1899,U_1898,U_1897] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1898),U_1899)),hAPP_nat_nat(plus_plus_nat(U_1897),U_1899)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1898),U_1897)) ),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

fof(f_694_3,plain,
    ! [U_1897,U_1898,U_1899] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1898),U_1899)),hAPP_nat_nat(plus_plus_nat(U_1897),U_1899)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1898),U_1897)) ),
    inference(definitional_conversion,[status(esa)],[f_694_2]) ).

cnf(f_694_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1898),U_1899)),hAPP_nat_nat(plus_plus_nat(U_1897),U_1899)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1898),U_1897)) ),
    inference(clausify,[status(thm)],[f_694_3]) ).

fof(f_695_1,plain,
    ! [K,L,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),L)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),L))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_591_add__le__mono]) ).

fof(f_695_2,plain,
    ! [U_1903,U_1902,U_1901,U_1900] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1901),U_1903)),hAPP_nat_nat(plus_plus_nat(U_1900),U_1902)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1903),U_1902))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1901),U_1900)) ),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

fof(f_695_3,plain,
    ! [U_1900,U_1901,U_1902,U_1903] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1901),U_1903)),hAPP_nat_nat(plus_plus_nat(U_1900),U_1902)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1903),U_1902))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1901),U_1900)) ),
    inference(definitional_conversion,[status(esa)],[f_695_2]) ).

cnf(f_695_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1901),U_1903)),hAPP_nat_nat(plus_plus_nat(U_1900),U_1902)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1903),U_1902))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1901),U_1900)) ),
    inference(clausify,[status(thm)],[f_695_3]) ).

fof(f_696_1,plain,
    ! [M,K,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_592_add__leD2]) ).

fof(f_696_2,plain,
    ! [U_1906,U_1905,U_1904] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1905),U_1904))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1906),U_1905)),U_1904)) ),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

fof(f_696_3,plain,
    ! [U_1905,U_1904,U_1906] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1905),U_1904))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1906),U_1905)),U_1904)) ),
    inference(definitional_conversion,[status(esa)],[f_696_2]) ).

cnf(f_696_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1905),U_1904))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1906),U_1905)),U_1904)) ),
    inference(clausify,[status(thm)],[f_696_3]) ).

fof(f_697_1,plain,
    ! [M,K,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_593_add__leD1]) ).

fof(f_697_2,plain,
    ! [U_1909,U_1908,U_1907] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1909),U_1907))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1909),U_1908)),U_1907)) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

fof(f_697_3,plain,
    ! [U_1907,U_1908,U_1909] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1909),U_1907))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1909),U_1908)),U_1907)) ),
    inference(definitional_conversion,[status(esa)],[f_697_2]) ).

cnf(f_697_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1909),U_1907))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1909),U_1908)),U_1907)) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

fof(f_698_1,plain,
    ! [M,K,N] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_594_add__leE]) ).

fof(f_698_2,plain,
    ! [U_1912,U_1911,U_1910] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1911),U_1910))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1912),U_1910)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1912),U_1911)),U_1910)) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

fof(f_698_3,plain,
    ( ! [U_1910,U_1911,U_1912] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1911),U_1910))
        | ~ sP210(U_1910,U_1911,U_1912) )
    & ! [U_1910,U_1911,U_1912] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1912),U_1910))
        | ~ sP210(U_1910,U_1911,U_1912) )
    & ! [U_1910,U_1911,U_1912] :
        ( sP210(U_1910,U_1911,U_1912)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1912),U_1911)),U_1910)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210])],[f_698_2]) ).

cnf(f_698_4,plain,
    ( sP210(U_1910,U_1911,U_1912)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1912),U_1911)),U_1910)) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

cnf(f_698_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1912),U_1910))
    | ~ sP210(U_1910,U_1911,U_1912) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

cnf(f_698_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1911),U_1910))
    | ~ sP210(U_1910,U_1911,U_1912) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

fof(f_699_1,plain,
    ! [I,K,J_2] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J_2),I)),K) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J_2),K)),I)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_595_diff__add__assoc2]) ).

fof(f_699_2,plain,
    ! [U_1915,U_1914,U_1913] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1913),U_1915)),U_1914) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_1913),U_1914)),U_1915)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1914),U_1913)) ),
    inference(variable_rename,[status(thm)],[f_699_1]) ).

fof(f_699_3,plain,
    ! [U_1913,U_1914,U_1915] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1913),U_1915)),U_1914) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_1913),U_1914)),U_1915)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1914),U_1913)) ),
    inference(definitional_conversion,[status(esa)],[f_699_2]) ).

cnf(f_699_4,plain,
    ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1913),U_1915)),U_1914) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_1913),U_1914)),U_1915)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1914),U_1913)) ),
    inference(clausify,[status(thm)],[f_699_3]) ).

fof(f_700_1,plain,
    ! [I,K,J_2] :
      ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J_2),K)),I) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J_2),I)),K)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_596_add__diff__assoc2]) ).

fof(f_700_2,plain,
    ! [U_1918,U_1917,U_1916] :
      ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_1916),U_1917)),U_1918) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1916),U_1918)),U_1917)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1917),U_1916)) ),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

fof(f_700_3,plain,
    ! [U_1916,U_1917,U_1918] :
      ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_1916),U_1917)),U_1918) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1916),U_1918)),U_1917)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1917),U_1916)) ),
    inference(definitional_conversion,[status(esa)],[f_700_2]) ).

cnf(f_700_4,plain,
    ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_1916),U_1917)),U_1918) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1916),U_1918)),U_1917)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1917),U_1916)) ),
    inference(clausify,[status(thm)],[f_700_3]) ).

fof(f_701_1,plain,
    ! [I,K,J_2] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),J_2)),K) = hAPP_nat_nat(plus_plus_nat(I),hAPP_nat_nat(minus_minus_nat(J_2),K))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_597_diff__add__assoc]) ).

fof(f_701_2,plain,
    ! [U_1921,U_1920,U_1919] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1921),U_1919)),U_1920) = hAPP_nat_nat(plus_plus_nat(U_1921),hAPP_nat_nat(minus_minus_nat(U_1919),U_1920))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1920),U_1919)) ),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

fof(f_701_3,plain,
    ! [U_1919,U_1920,U_1921] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1921),U_1919)),U_1920) = hAPP_nat_nat(plus_plus_nat(U_1921),hAPP_nat_nat(minus_minus_nat(U_1919),U_1920))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1920),U_1919)) ),
    inference(definitional_conversion,[status(esa)],[f_701_2]) ).

cnf(f_701_4,plain,
    ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1921),U_1919)),U_1920) = hAPP_nat_nat(plus_plus_nat(U_1921),hAPP_nat_nat(minus_minus_nat(U_1919),U_1920))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1920),U_1919)) ),
    inference(clausify,[status(thm)],[f_701_3]) ).

fof(f_702_1,plain,
    ! [K_2,I_1,J_1] :
      ( ( ( hAPP_nat_nat(minus_minus_nat(J_1),I_1) = K_2
          | J_1 != hAPP_nat_nat(plus_plus_nat(K_2),I_1) )
        & ( J_1 = hAPP_nat_nat(plus_plus_nat(K_2),I_1)
          | hAPP_nat_nat(minus_minus_nat(J_1),I_1) != K_2 ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_598_le__imp__diff__is__add]) ).

fof(f_702_2,plain,
    ! [U_1924,U_1923,U_1922] :
      ( ( ( hAPP_nat_nat(minus_minus_nat(U_1922),U_1923) = U_1924
          | U_1922 != hAPP_nat_nat(plus_plus_nat(U_1924),U_1923) )
        & ( U_1922 = hAPP_nat_nat(plus_plus_nat(U_1924),U_1923)
          | hAPP_nat_nat(minus_minus_nat(U_1922),U_1923) != U_1924 ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1923),U_1922)) ),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

fof(f_702_3,plain,
    ( ! [U_1922,U_1923,U_1924] :
        ( hAPP_nat_nat(minus_minus_nat(U_1922),U_1923) = U_1924
        | U_1922 != hAPP_nat_nat(plus_plus_nat(U_1924),U_1923)
        | ~ sP211(U_1922,U_1923,U_1924) )
    & ! [U_1922,U_1923,U_1924] :
        ( U_1922 = hAPP_nat_nat(plus_plus_nat(U_1924),U_1923)
        | hAPP_nat_nat(minus_minus_nat(U_1922),U_1923) != U_1924
        | ~ sP211(U_1922,U_1923,U_1924) )
    & ! [U_1922,U_1923,U_1924] :
        ( sP211(U_1922,U_1923,U_1924)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1923),U_1922)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP211])],[f_702_2]) ).

cnf(f_702_4,plain,
    ( sP211(U_1922,U_1923,U_1924)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1923),U_1922)) ),
    inference(clausify,[status(thm)],[f_702_3]) ).

cnf(f_702_5,plain,
    ( U_1922 = hAPP_nat_nat(plus_plus_nat(U_1924),U_1923)
    | hAPP_nat_nat(minus_minus_nat(U_1922),U_1923) != U_1924
    | ~ sP211(U_1922,U_1923,U_1924) ),
    inference(clausify,[status(thm)],[f_702_3]) ).

cnf(f_702_6,plain,
    ( hAPP_nat_nat(minus_minus_nat(U_1922),U_1923) = U_1924
    | U_1922 != hAPP_nat_nat(plus_plus_nat(U_1924),U_1923)
    | ~ sP211(U_1922,U_1923,U_1924) ),
    inference(clausify,[status(thm)],[f_702_3]) ).

fof(f_703_1,plain,
    ! [N,M] :
      ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),N)),N) = M
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) ),
    inference(fof_nnf,[status(thm)],[fact_599_le__add__diff__inverse2]) ).

fof(f_703_2,plain,
    ! [U_1926,U_1925] :
      ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_1925),U_1926)),U_1926) = U_1925
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1926),U_1925)) ),
    inference(variable_rename,[status(thm)],[f_703_1]) ).

fof(f_703_3,plain,
    ! [U_1926,U_1925] :
      ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_1925),U_1926)),U_1926) = U_1925
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1926),U_1925)) ),
    inference(definitional_conversion,[status(esa)],[f_703_2]) ).

cnf(f_703_4,plain,
    ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_1925),U_1926)),U_1926) = U_1925
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1926),U_1925)) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

fof(f_704_1,plain,
    ! [I_1,K_2,J_1] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_2)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_2)),J_1)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_2)),J_1))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_2))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_600_le__diff__conv2]) ).

fof(f_704_2,plain,
    ! [U_1929,U_1928,U_1927] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1929),hAPP_nat_nat(minus_minus_nat(U_1927),U_1928)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1929),U_1928)),U_1927)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1929),U_1928)),U_1927))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1929),hAPP_nat_nat(minus_minus_nat(U_1927),U_1928))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1928),U_1927)) ),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

fof(f_704_3,plain,
    ( ! [U_1927,U_1928,U_1929] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1929),hAPP_nat_nat(minus_minus_nat(U_1927),U_1928)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1929),U_1928)),U_1927))
        | ~ sP212(U_1927,U_1928,U_1929) )
    & ! [U_1927,U_1928,U_1929] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1929),U_1928)),U_1927))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1929),hAPP_nat_nat(minus_minus_nat(U_1927),U_1928)))
        | ~ sP212(U_1927,U_1928,U_1929) )
    & ! [U_1927,U_1928,U_1929] :
        ( sP212(U_1927,U_1928,U_1929)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1928),U_1927)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212])],[f_704_2]) ).

cnf(f_704_4,plain,
    ( sP212(U_1927,U_1928,U_1929)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1928),U_1927)) ),
    inference(clausify,[status(thm)],[f_704_3]) ).

cnf(f_704_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1929),U_1928)),U_1927))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1929),hAPP_nat_nat(minus_minus_nat(U_1927),U_1928)))
    | ~ sP212(U_1927,U_1928,U_1929) ),
    inference(clausify,[status(thm)],[f_704_3]) ).

cnf(f_704_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1929),hAPP_nat_nat(minus_minus_nat(U_1927),U_1928)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_1929),U_1928)),U_1927))
    | ~ sP212(U_1927,U_1928,U_1929) ),
    inference(clausify,[status(thm)],[f_704_3]) ).

fof(f_705_1,plain,
    ! [I,K,J_2] :
      ( hAPP_nat_nat(plus_plus_nat(I),hAPP_nat_nat(minus_minus_nat(J_2),K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),J_2)),K)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_601_add__diff__assoc]) ).

fof(f_705_2,plain,
    ! [U_1932,U_1931,U_1930] :
      ( hAPP_nat_nat(plus_plus_nat(U_1932),hAPP_nat_nat(minus_minus_nat(U_1930),U_1931)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1932),U_1930)),U_1931)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1931),U_1930)) ),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

fof(f_705_3,plain,
    ! [U_1930,U_1932,U_1931] :
      ( hAPP_nat_nat(plus_plus_nat(U_1932),hAPP_nat_nat(minus_minus_nat(U_1930),U_1931)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1932),U_1930)),U_1931)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1931),U_1930)) ),
    inference(definitional_conversion,[status(esa)],[f_705_2]) ).

cnf(f_705_4,plain,
    ( hAPP_nat_nat(plus_plus_nat(U_1932),hAPP_nat_nat(minus_minus_nat(U_1930),U_1931)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1932),U_1930)),U_1931)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1931),U_1930)) ),
    inference(clausify,[status(thm)],[f_705_3]) ).

fof(f_706_1,plain,
    ! [N,M] :
      ( hAPP_nat_nat(plus_plus_nat(N),hAPP_nat_nat(minus_minus_nat(M),N)) = M
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) ),
    inference(fof_nnf,[status(thm)],[fact_602_le__add__diff__inverse]) ).

fof(f_706_2,plain,
    ! [U_1934,U_1933] :
      ( hAPP_nat_nat(plus_plus_nat(U_1934),hAPP_nat_nat(minus_minus_nat(U_1933),U_1934)) = U_1933
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1934),U_1933)) ),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

fof(f_706_3,plain,
    ! [U_1933,U_1934] :
      ( hAPP_nat_nat(plus_plus_nat(U_1934),hAPP_nat_nat(minus_minus_nat(U_1933),U_1934)) = U_1933
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1934),U_1933)) ),
    inference(definitional_conversion,[status(esa)],[f_706_2]) ).

cnf(f_706_4,plain,
    ( hAPP_nat_nat(plus_plus_nat(U_1934),hAPP_nat_nat(minus_minus_nat(U_1933),U_1934)) = U_1933
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1934),U_1933)) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

fof(f_707_1,plain,
    ! [M,K,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N),M)),K)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) ),
    inference(fof_nnf,[status(thm)],[fact_603_le__add__diff]) ).

fof(f_707_2,plain,
    ! [U_1937,U_1936,U_1935] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1937),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1935),U_1937)),U_1936)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1936),U_1935)) ),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

fof(f_707_3,plain,
    ! [U_1935,U_1936,U_1937] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1937),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1935),U_1937)),U_1936)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1936),U_1935)) ),
    inference(definitional_conversion,[status(esa)],[f_707_2]) ).

cnf(f_707_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1937),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1935),U_1937)),U_1936)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1936),U_1935)) ),
    inference(clausify,[status(thm)],[f_707_3]) ).

fof(f_708_1,plain,
    ! [J_1,K_2,I_1] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(J_1),K_2)),I_1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_nat_nat(plus_plus_nat(I_1),K_2))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_nat_nat(plus_plus_nat(I_1),K_2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(J_1),K_2)),I_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_604_le__diff__conv]) ).

fof(f_708_2,plain,
    ! [U_1940,U_1939,U_1938] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_1940),U_1939)),U_1938))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1940),hAPP_nat_nat(plus_plus_nat(U_1938),U_1939))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1940),hAPP_nat_nat(plus_plus_nat(U_1938),U_1939)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_1940),U_1939)),U_1938)) ) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

fof(f_708_3,plain,
    ( ! [U_1946,U_1944,U_1942] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_1946),U_1944)),U_1942))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1946),hAPP_nat_nat(plus_plus_nat(U_1942),U_1944))) )
    & ! [U_1945,U_1943,U_1941] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1945),hAPP_nat_nat(plus_plus_nat(U_1941),U_1943)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_1945),U_1943)),U_1941)) ) ),
    inference(miniscope,[status(thm)],[f_708_2]) ).

fof(f_708_4,plain,
    ( ! [U_1942,U_1944,U_1946] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_1946),U_1944)),U_1942))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1946),hAPP_nat_nat(plus_plus_nat(U_1942),U_1944))) )
    & ! [U_1945,U_1943,U_1941] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1945),hAPP_nat_nat(plus_plus_nat(U_1941),U_1943)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_1945),U_1943)),U_1941)) ) ),
    inference(definitional_conversion,[status(esa)],[f_708_3]) ).

cnf(f_708_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1945),hAPP_nat_nat(plus_plus_nat(U_1941),U_1943)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_1945),U_1943)),U_1941)) ),
    inference(clausify,[status(thm)],[f_708_4]) ).

cnf(f_708_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_1946),U_1944)),U_1942))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1946),hAPP_nat_nat(plus_plus_nat(U_1942),U_1944))) ),
    inference(clausify,[status(thm)],[f_708_4]) ).

fof(f_709_1,plain,
    ! [I,K,J_2] :
      ( hAPP_nat_nat(minus_minus_nat(I),hAPP_nat_nat(minus_minus_nat(J_2),K)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I),K)),J_2)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_605_diff__diff__right]) ).

fof(f_709_2,plain,
    ! [U_1949,U_1948,U_1947] :
      ( hAPP_nat_nat(minus_minus_nat(U_1949),hAPP_nat_nat(minus_minus_nat(U_1947),U_1948)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1949),U_1948)),U_1947)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1948),U_1947)) ),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

fof(f_709_3,plain,
    ! [U_1948,U_1947,U_1949] :
      ( hAPP_nat_nat(minus_minus_nat(U_1949),hAPP_nat_nat(minus_minus_nat(U_1947),U_1948)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1949),U_1948)),U_1947)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1948),U_1947)) ),
    inference(definitional_conversion,[status(esa)],[f_709_2]) ).

cnf(f_709_4,plain,
    ( hAPP_nat_nat(minus_minus_nat(U_1949),hAPP_nat_nat(minus_minus_nat(U_1947),U_1948)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1949),U_1948)),U_1947)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1948),U_1947)) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

fof(f_710_1,plain,
    ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(plus_plus_nat(N),one_one_nat),
    inference(fof_nnf,[status(thm)],[fact_606_Suc__eq__plus1]) ).

fof(f_710_2,plain,
    ! [U_1950] : hAPP_nat_nat(suc,U_1950) = hAPP_nat_nat(plus_plus_nat(U_1950),one_one_nat),
    inference(variable_rename,[status(thm)],[f_710_1]) ).

fof(f_710_3,plain,
    ! [U_1950] : hAPP_nat_nat(suc,U_1950) = hAPP_nat_nat(plus_plus_nat(U_1950),one_one_nat),
    inference(definitional_conversion,[status(esa)],[f_710_2]) ).

cnf(f_710_4,plain,
    hAPP_nat_nat(suc,U_1950) = hAPP_nat_nat(plus_plus_nat(U_1950),one_one_nat),
    inference(clausify,[status(thm)],[f_710_3]) ).

fof(f_711_1,plain,
    ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(plus_plus_nat(one_one_nat),N),
    inference(fof_nnf,[status(thm)],[fact_607_Suc__eq__plus1__left]) ).

fof(f_711_2,plain,
    ! [U_1951] : hAPP_nat_nat(suc,U_1951) = hAPP_nat_nat(plus_plus_nat(one_one_nat),U_1951),
    inference(variable_rename,[status(thm)],[f_711_1]) ).

fof(f_711_3,plain,
    ! [U_1951] : hAPP_nat_nat(suc,U_1951) = hAPP_nat_nat(plus_plus_nat(one_one_nat),U_1951),
    inference(definitional_conversion,[status(esa)],[f_711_2]) ).

cnf(f_711_4,plain,
    hAPP_nat_nat(suc,U_1951) = hAPP_nat_nat(plus_plus_nat(one_one_nat),U_1951),
    inference(clausify,[status(thm)],[f_711_3]) ).

fof(f_712_1,plain,
    ! [M,K,J_2] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J_2),K))),M) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,J_2)),hAPP_nat_nat(plus_plus_nat(K),M))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_608_diff__Suc__diff__eq2]) ).

fof(f_712_2,plain,
    ! [U_1954,U_1953,U_1952] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(U_1952),U_1953))),U_1954) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_1952)),hAPP_nat_nat(plus_plus_nat(U_1953),U_1954))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1953),U_1952)) ),
    inference(variable_rename,[status(thm)],[f_712_1]) ).

fof(f_712_3,plain,
    ! [U_1952,U_1953,U_1954] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(U_1952),U_1953))),U_1954) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_1952)),hAPP_nat_nat(plus_plus_nat(U_1953),U_1954))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1953),U_1952)) ),
    inference(definitional_conversion,[status(esa)],[f_712_2]) ).

cnf(f_712_4,plain,
    ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(U_1952),U_1953))),U_1954) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_1952)),hAPP_nat_nat(plus_plus_nat(U_1953),U_1954))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1953),U_1952)) ),
    inference(clausify,[status(thm)],[f_712_3]) ).

fof(f_713_1,plain,
    ! [M,K,J_2] :
      ( hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(J_2),K))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K)),hAPP_nat_nat(suc,J_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_609_diff__Suc__diff__eq1]) ).

fof(f_713_2,plain,
    ! [U_1957,U_1956,U_1955] :
      ( hAPP_nat_nat(minus_minus_nat(U_1957),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(U_1955),U_1956))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1957),U_1956)),hAPP_nat_nat(suc,U_1955))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1956),U_1955)) ),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

fof(f_713_3,plain,
    ! [U_1955,U_1956,U_1957] :
      ( hAPP_nat_nat(minus_minus_nat(U_1957),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(U_1955),U_1956))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1957),U_1956)),hAPP_nat_nat(suc,U_1955))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1956),U_1955)) ),
    inference(definitional_conversion,[status(esa)],[f_713_2]) ).

cnf(f_713_4,plain,
    ( hAPP_nat_nat(minus_minus_nat(U_1957),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(U_1955),U_1956))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_1957),U_1956)),hAPP_nat_nat(suc,U_1955))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1956),U_1955)) ),
    inference(clausify,[status(thm)],[f_713_3]) ).

fof(f_714_1,plain,
    ! [Z,X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_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_610_termination__basic__simps_I3_J]) ).

fof(f_714_2,plain,
    ! [U_1960,U_1959,U_1958] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1959),hAPP_nat_nat(plus_plus_nat(U_1958),U_1960)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1959),U_1958)) ),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

fof(f_714_3,plain,
    ! [U_1958,U_1959,U_1960] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1959),hAPP_nat_nat(plus_plus_nat(U_1958),U_1960)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1959),U_1958)) ),
    inference(definitional_conversion,[status(esa)],[f_714_2]) ).

cnf(f_714_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1959),hAPP_nat_nat(plus_plus_nat(U_1958),U_1960)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1959),U_1958)) ),
    inference(clausify,[status(thm)],[f_714_3]) ).

fof(f_715_1,plain,
    ! [Y,X,Z] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_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_611_termination__basic__simps_I4_J]) ).

fof(f_715_2,plain,
    ! [U_1963,U_1962,U_1961] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1962),hAPP_nat_nat(plus_plus_nat(U_1963),U_1961)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1962),U_1961)) ),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

fof(f_715_3,plain,
    ! [U_1961,U_1962,U_1963] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1962),hAPP_nat_nat(plus_plus_nat(U_1963),U_1961)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1962),U_1961)) ),
    inference(definitional_conversion,[status(esa)],[f_715_2]) ).

cnf(f_715_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1962),hAPP_nat_nat(plus_plus_nat(U_1963),U_1961)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1962),U_1961)) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

fof(f_716_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_612_lessI]) ).

fof(f_716_2,plain,
    ! [U_1964] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1964),hAPP_nat_nat(suc,U_1964))),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

fof(f_716_3,plain,
    ! [U_1964] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1964),hAPP_nat_nat(suc,U_1964))),
    inference(definitional_conversion,[status(esa)],[f_716_2]) ).

cnf(f_716_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1964),hAPP_nat_nat(suc,U_1964))),
    inference(clausify,[status(thm)],[f_716_3]) ).

fof(f_717_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_613_Suc__mono]) ).

fof(f_717_2,plain,
    ! [U_1966,U_1965] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_1966)),hAPP_nat_nat(suc,U_1965)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1966),U_1965)) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

fof(f_717_3,plain,
    ! [U_1965,U_1966] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_1966)),hAPP_nat_nat(suc,U_1965)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1966),U_1965)) ),
    inference(definitional_conversion,[status(esa)],[f_717_2]) ).

cnf(f_717_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_1966)),hAPP_nat_nat(suc,U_1965)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1966),U_1965)) ),
    inference(clausify,[status(thm)],[f_717_3]) ).

fof(f_718_1,plain,
    ! [K_2] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),K_2)))),
    inference(fof_nnf,[status(thm)],[fact_614_finite__Collect__less__nat]) ).

fof(f_718_2,plain,
    ! [U_1967] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_1967)))),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

fof(f_718_3,plain,
    ! [U_1967] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_1967)))),
    inference(definitional_conversion,[status(esa)],[f_718_2]) ).

cnf(f_718_4,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_1967)))),
    inference(clausify,[status(thm)],[f_718_3]) ).

fof(f_719_1,plain,
    ! [Z,X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_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_615_termination__basic__simps_I1_J]) ).

fof(f_719_2,plain,
    ! [U_1970,U_1969,U_1968] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1969),hAPP_nat_nat(plus_plus_nat(U_1968),U_1970)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1969),U_1968)) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

fof(f_719_3,plain,
    ! [U_1968,U_1969,U_1970] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1969),hAPP_nat_nat(plus_plus_nat(U_1968),U_1970)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1969),U_1968)) ),
    inference(definitional_conversion,[status(esa)],[f_719_2]) ).

cnf(f_719_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1969),hAPP_nat_nat(plus_plus_nat(U_1968),U_1970)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1969),U_1968)) ),
    inference(clausify,[status(thm)],[f_719_3]) ).

fof(f_720_1,plain,
    ! [Y,X,Z] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_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_616_termination__basic__simps_I2_J]) ).

fof(f_720_2,plain,
    ! [U_1973,U_1972,U_1971] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1972),hAPP_nat_nat(plus_plus_nat(U_1973),U_1971)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1972),U_1971)) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

fof(f_720_3,plain,
    ! [U_1971,U_1972,U_1973] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1972),hAPP_nat_nat(plus_plus_nat(U_1973),U_1971)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1972),U_1971)) ),
    inference(definitional_conversion,[status(esa)],[f_720_2]) ).

cnf(f_720_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1972),hAPP_nat_nat(plus_plus_nat(U_1973),U_1971)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1972),U_1971)) ),
    inference(clausify,[status(thm)],[f_720_3]) ).

fof(f_721_1,plain,
    ! [I,J_2,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),J_2)),K)) ),
    inference(fof_nnf,[status(thm)],[fact_617_add__lessD1]) ).

fof(f_721_2,plain,
    ! [U_1976,U_1975,U_1974] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1976),U_1974))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_1976),U_1975)),U_1974)) ),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

fof(f_721_3,plain,
    ! [U_1974,U_1975,U_1976] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1976),U_1974))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_1976),U_1975)),U_1974)) ),
    inference(definitional_conversion,[status(esa)],[f_721_2]) ).

cnf(f_721_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1976),U_1974))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_1976),U_1975)),U_1974)) ),
    inference(clausify,[status(thm)],[f_721_3]) ).

fof(f_722_1,plain,
    ! [M,N,K,L] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
      | hAPP_nat_nat(plus_plus_nat(M),L) != hAPP_nat_nat(plus_plus_nat(K),N)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L)) ),
    inference(fof_nnf,[status(thm)],[fact_618_less__add__eq__less]) ).

fof(f_722_2,plain,
    ! [U_1980,U_1979,U_1978,U_1977] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1980),U_1979))
      | hAPP_nat_nat(plus_plus_nat(U_1980),U_1977) != hAPP_nat_nat(plus_plus_nat(U_1978),U_1979)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1978),U_1977)) ),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

fof(f_722_3,plain,
    ! [U_1977,U_1978,U_1979,U_1980] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1980),U_1979))
      | hAPP_nat_nat(plus_plus_nat(U_1980),U_1977) != hAPP_nat_nat(plus_plus_nat(U_1978),U_1979)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1978),U_1977)) ),
    inference(definitional_conversion,[status(esa)],[f_722_2]) ).

cnf(f_722_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1980),U_1979))
    | hAPP_nat_nat(plus_plus_nat(U_1980),U_1977) != hAPP_nat_nat(plus_plus_nat(U_1978),U_1979)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1978),U_1977)) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

fof(f_723_1,plain,
    ! [K,L,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),L)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_619_add__less__mono]) ).

fof(f_723_2,plain,
    ! [U_1984,U_1983,U_1982,U_1981] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_1982),U_1984)),hAPP_nat_nat(plus_plus_nat(U_1981),U_1983)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1984),U_1983))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1982),U_1981)) ),
    inference(variable_rename,[status(thm)],[f_723_1]) ).

fof(f_723_3,plain,
    ! [U_1981,U_1982,U_1983,U_1984] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_1982),U_1984)),hAPP_nat_nat(plus_plus_nat(U_1981),U_1983)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1984),U_1983))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1982),U_1981)) ),
    inference(definitional_conversion,[status(esa)],[f_723_2]) ).

cnf(f_723_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_1982),U_1984)),hAPP_nat_nat(plus_plus_nat(U_1981),U_1983)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1984),U_1983))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1982),U_1981)) ),
    inference(clausify,[status(thm)],[f_723_3]) ).

fof(f_724_1,plain,
    ! [K,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),K)),hAPP_nat_nat(plus_plus_nat(J_2),K)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_620_add__less__mono1]) ).

fof(f_724_2,plain,
    ! [U_1987,U_1986,U_1985] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_1986),U_1987)),hAPP_nat_nat(plus_plus_nat(U_1985),U_1987)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1986),U_1985)) ),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

fof(f_724_3,plain,
    ! [U_1985,U_1986,U_1987] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_1986),U_1987)),hAPP_nat_nat(plus_plus_nat(U_1985),U_1987)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1986),U_1985)) ),
    inference(definitional_conversion,[status(esa)],[f_724_2]) ).

cnf(f_724_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_1986),U_1987)),hAPP_nat_nat(plus_plus_nat(U_1985),U_1987)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1986),U_1985)) ),
    inference(clausify,[status(thm)],[f_724_3]) ).

fof(f_725_1,plain,
    ! [M,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(plus_plus_nat(M),J_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_621_trans__less__add2]) ).

fof(f_725_2,plain,
    ! [U_1990,U_1989,U_1988] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1989),hAPP_nat_nat(plus_plus_nat(U_1990),U_1988)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1989),U_1988)) ),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

fof(f_725_3,plain,
    ! [U_1988,U_1989,U_1990] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1989),hAPP_nat_nat(plus_plus_nat(U_1990),U_1988)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1989),U_1988)) ),
    inference(definitional_conversion,[status(esa)],[f_725_2]) ).

cnf(f_725_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1989),hAPP_nat_nat(plus_plus_nat(U_1990),U_1988)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1989),U_1988)) ),
    inference(clausify,[status(thm)],[f_725_3]) ).

fof(f_726_1,plain,
    ! [M,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(plus_plus_nat(J_2),M)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_622_trans__less__add1]) ).

fof(f_726_2,plain,
    ! [U_1993,U_1992,U_1991] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1992),hAPP_nat_nat(plus_plus_nat(U_1991),U_1993)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1992),U_1991)) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

fof(f_726_3,plain,
    ! [U_1991,U_1992,U_1993] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1992),hAPP_nat_nat(plus_plus_nat(U_1991),U_1993)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1992),U_1991)) ),
    inference(definitional_conversion,[status(esa)],[f_726_2]) ).

cnf(f_726_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1992),hAPP_nat_nat(plus_plus_nat(U_1991),U_1993)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1992),U_1991)) ),
    inference(clausify,[status(thm)],[f_726_3]) ).

fof(f_727_1,plain,
    ! [K_2,M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(K_2),M_1)),hAPP_nat_nat(plus_plus_nat(K_2),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(K_2),M_1)),hAPP_nat_nat(plus_plus_nat(K_2),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_623_nat__add__left__cancel__less]) ).

fof(f_727_2,plain,
    ! [U_1996,U_1995,U_1994] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_1996),U_1995)),hAPP_nat_nat(plus_plus_nat(U_1996),U_1994)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1995),U_1994)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1995),U_1994))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_1996),U_1995)),hAPP_nat_nat(plus_plus_nat(U_1996),U_1994))) ) ),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

fof(f_727_3,plain,
    ( ! [U_2002,U_2000,U_1998] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2002),U_2000)),hAPP_nat_nat(plus_plus_nat(U_2002),U_1998)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2000),U_1998)) )
    & ! [U_2001,U_1999,U_1997] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1999),U_1997))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2001),U_1999)),hAPP_nat_nat(plus_plus_nat(U_2001),U_1997))) ) ),
    inference(miniscope,[status(thm)],[f_727_2]) ).

fof(f_727_4,plain,
    ( ! [U_1998,U_2000,U_2002] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2002),U_2000)),hAPP_nat_nat(plus_plus_nat(U_2002),U_1998)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2000),U_1998)) )
    & ! [U_1999,U_2001,U_1997] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1999),U_1997))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2001),U_1999)),hAPP_nat_nat(plus_plus_nat(U_2001),U_1997))) ) ),
    inference(definitional_conversion,[status(esa)],[f_727_3]) ).

cnf(f_727_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1999),U_1997))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2001),U_1999)),hAPP_nat_nat(plus_plus_nat(U_2001),U_1997))) ),
    inference(clausify,[status(thm)],[f_727_4]) ).

cnf(f_727_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2002),U_2000)),hAPP_nat_nat(plus_plus_nat(U_2002),U_1998)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2000),U_1998)) ),
    inference(clausify,[status(thm)],[f_727_4]) ).

fof(f_728_1,plain,
    ! [J_2,I] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(J_2),I)),I)),
    inference(fof_nnf,[status(thm)],[fact_624_not__add__less2]) ).

fof(f_728_2,plain,
    ! [U_2004,U_2003] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2004),U_2003)),U_2003)),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

fof(f_728_3,plain,
    ! [U_2003,U_2004] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2004),U_2003)),U_2003)),
    inference(definitional_conversion,[status(esa)],[f_728_2]) ).

cnf(f_728_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2004),U_2003)),U_2003)),
    inference(clausify,[status(thm)],[f_728_3]) ).

fof(f_729_1,plain,
    ! [I,J_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I),J_2)),I)),
    inference(fof_nnf,[status(thm)],[fact_625_not__add__less1]) ).

fof(f_729_2,plain,
    ! [U_2006,U_2005] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2006),U_2005)),U_2006)),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

fof(f_729_3,plain,
    ! [U_2005,U_2006] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2006),U_2005)),U_2006)),
    inference(definitional_conversion,[status(esa)],[f_729_2]) ).

cnf(f_729_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2006),U_2005)),U_2006)),
    inference(clausify,[status(thm)],[f_729_3]) ).

fof(f_730_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_626_Suc__less__SucD]) ).

fof(f_730_2,plain,
    ! [U_2008,U_2007] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2008),U_2007))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2008)),hAPP_nat_nat(suc,U_2007))) ),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

fof(f_730_3,plain,
    ! [U_2007,U_2008] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2008),U_2007))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2008)),hAPP_nat_nat(suc,U_2007))) ),
    inference(definitional_conversion,[status(esa)],[f_730_2]) ).

cnf(f_730_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2008),U_2007))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2008)),hAPP_nat_nat(suc,U_2007))) ),
    inference(clausify,[status(thm)],[f_730_3]) ).

fof(f_731_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_627_Suc__lessD]) ).

fof(f_731_2,plain,
    ! [U_2010,U_2009] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2010),U_2009))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2010)),U_2009)) ),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

fof(f_731_3,plain,
    ! [U_2009,U_2010] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2010),U_2009))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2010)),U_2009)) ),
    inference(definitional_conversion,[status(esa)],[f_731_2]) ).

cnf(f_731_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2010),U_2009))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2010)),U_2009)) ),
    inference(clausify,[status(thm)],[f_731_3]) ).

fof(f_732_1,plain,
    ! [M,N] :
      ( M = N
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_628_less__SucE]) ).

fof(f_732_2,plain,
    ! [U_2012,U_2011] :
      ( U_2012 = U_2011
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2012),U_2011))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2012),hAPP_nat_nat(suc,U_2011))) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

fof(f_732_3,plain,
    ! [U_2011,U_2012] :
      ( U_2012 = U_2011
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2012),U_2011))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2012),hAPP_nat_nat(suc,U_2011))) ),
    inference(definitional_conversion,[status(esa)],[f_732_2]) ).

cnf(f_732_4,plain,
    ( U_2012 = U_2011
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2012),U_2011))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2012),hAPP_nat_nat(suc,U_2011))) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

fof(f_733_1,plain,
    ! [K,I,J_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_629_less__trans__Suc]) ).

fof(f_733_2,plain,
    ! [U_2015,U_2014,U_2013] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2014)),U_2015))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2013),U_2015))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2014),U_2013)) ),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

fof(f_733_3,plain,
    ! [U_2013,U_2014,U_2015] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2014)),U_2015))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2013),U_2015))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2014),U_2013)) ),
    inference(definitional_conversion,[status(esa)],[f_733_2]) ).

cnf(f_733_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2014)),U_2015))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2013),U_2015))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2014),U_2013)) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

fof(f_734_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N))
      | hAPP_nat_nat(suc,M) = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_630_Suc__lessI]) ).

fof(f_734_2,plain,
    ! [U_2017,U_2016] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2017)),U_2016))
      | hAPP_nat_nat(suc,U_2017) = U_2016
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2017),U_2016)) ),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

fof(f_734_3,plain,
    ! [U_2016,U_2017] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2017)),U_2016))
      | hAPP_nat_nat(suc,U_2017) = U_2016
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2017),U_2016)) ),
    inference(definitional_conversion,[status(esa)],[f_734_2]) ).

cnf(f_734_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2017)),U_2016))
    | hAPP_nat_nat(suc,U_2017) = U_2016
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2017),U_2016)) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

fof(f_735_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_631_less__SucI]) ).

fof(f_735_2,plain,
    ! [U_2019,U_2018] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2019),hAPP_nat_nat(suc,U_2018)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2019),U_2018)) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

fof(f_735_3,plain,
    ! [U_2018,U_2019] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2019),hAPP_nat_nat(suc,U_2018)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2019),U_2018)) ),
    inference(definitional_conversion,[status(esa)],[f_735_2]) ).

cnf(f_735_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2019),hAPP_nat_nat(suc,U_2018)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2019),U_2018)) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

fof(f_736_1,plain,
    ! [N,M] :
      ( M = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) ),
    inference(fof_nnf,[status(thm)],[fact_632_less__antisym]) ).

fof(f_736_2,plain,
    ! [U_2021,U_2020] :
      ( U_2020 = U_2021
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2021),hAPP_nat_nat(suc,U_2020)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2021),U_2020)) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

fof(f_736_3,plain,
    ! [U_2020,U_2021] :
      ( U_2020 = U_2021
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2021),hAPP_nat_nat(suc,U_2020)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2021),U_2020)) ),
    inference(definitional_conversion,[status(esa)],[f_736_2]) ).

cnf(f_736_4,plain,
    ( U_2020 = U_2021
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2021),hAPP_nat_nat(suc,U_2020)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2021),U_2020)) ),
    inference(clausify,[status(thm)],[f_736_3]) ).

fof(f_737_1,plain,
    ! [Na,M_1] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
          | Na != M_1 )
        & ( Na = M_1
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_633_not__less__less__Suc__eq]) ).

fof(f_737_2,plain,
    ! [U_2023,U_2022] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2023),hAPP_nat_nat(suc,U_2022)))
          | U_2023 != U_2022 )
        & ( U_2023 = U_2022
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2023),hAPP_nat_nat(suc,U_2022))) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2023),U_2022)) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

fof(f_737_3,plain,
    ( ! [U_2022,U_2023] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2023),hAPP_nat_nat(suc,U_2022)))
        | U_2023 != U_2022
        | ~ sP213(U_2022,U_2023) )
    & ! [U_2022,U_2023] :
        ( U_2023 = U_2022
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2023),hAPP_nat_nat(suc,U_2022)))
        | ~ sP213(U_2022,U_2023) )
    & ! [U_2022,U_2023] :
        ( sP213(U_2022,U_2023)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2023),U_2022)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213])],[f_737_2]) ).

cnf(f_737_4,plain,
    ( sP213(U_2022,U_2023)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2023),U_2022)) ),
    inference(clausify,[status(thm)],[f_737_3]) ).

cnf(f_737_5,plain,
    ( U_2023 = U_2022
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2023),hAPP_nat_nat(suc,U_2022)))
    | ~ sP213(U_2022,U_2023) ),
    inference(clausify,[status(thm)],[f_737_3]) ).

cnf(f_737_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2023),hAPP_nat_nat(suc,U_2022)))
    | U_2023 != U_2022
    | ~ sP213(U_2022,U_2023) ),
    inference(clausify,[status(thm)],[f_737_3]) ).

fof(f_738_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_634_Suc__less__eq]) ).

fof(f_738_2,plain,
    ! [U_2025,U_2024] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2025)),hAPP_nat_nat(suc,U_2024)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2025),U_2024)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2025),U_2024))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2025)),hAPP_nat_nat(suc,U_2024))) ) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

fof(f_738_3,plain,
    ( ! [U_2029,U_2027] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2029)),hAPP_nat_nat(suc,U_2027)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2029),U_2027)) )
    & ! [U_2028,U_2026] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2028),U_2026))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2028)),hAPP_nat_nat(suc,U_2026))) ) ),
    inference(miniscope,[status(thm)],[f_738_2]) ).

fof(f_738_4,plain,
    ( ! [U_2029,U_2027] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2029)),hAPP_nat_nat(suc,U_2027)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2029),U_2027)) )
    & ! [U_2028,U_2026] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2028),U_2026))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2028)),hAPP_nat_nat(suc,U_2026))) ) ),
    inference(definitional_conversion,[status(esa)],[f_738_3]) ).

cnf(f_738_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2028),U_2026))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2028)),hAPP_nat_nat(suc,U_2026))) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

cnf(f_738_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2029)),hAPP_nat_nat(suc,U_2027)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2029),U_2027)) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

fof(f_739_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
        | ( M_1 != Na
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) )
      & ( M_1 = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_635_less__Suc__eq]) ).

fof(f_739_2,plain,
    ! [U_2031,U_2030] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2031),hAPP_nat_nat(suc,U_2030)))
        | ( U_2031 != U_2030
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2031),U_2030)) ) )
      & ( U_2031 = U_2030
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2031),U_2030))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2031),hAPP_nat_nat(suc,U_2030))) ) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

fof(f_739_3,plain,
    ( ! [U_2035,U_2033] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2035),hAPP_nat_nat(suc,U_2033)))
        | ( U_2035 != U_2033
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2035),U_2033)) ) )
    & ! [U_2034,U_2032] :
        ( U_2034 = U_2032
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2034),U_2032))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2034),hAPP_nat_nat(suc,U_2032))) ) ),
    inference(miniscope,[status(thm)],[f_739_2]) ).

fof(f_739_4,plain,
    ( ! [U_2035,U_2033] :
        ( U_2035 != U_2033
        | ~ sP214(U_2035,U_2033) )
    & ! [U_2035,U_2033] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2035),U_2033))
        | ~ sP214(U_2035,U_2033) )
    & ! [U_2035,U_2033] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2035),hAPP_nat_nat(suc,U_2033)))
        | sP214(U_2035,U_2033) )
    & ! [U_2034,U_2032] :
        ( U_2034 = U_2032
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2034),U_2032))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2034),hAPP_nat_nat(suc,U_2032))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214])],[f_739_3]) ).

cnf(f_739_5,plain,
    ( U_2034 = U_2032
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2034),U_2032))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2034),hAPP_nat_nat(suc,U_2032))) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

cnf(f_739_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2035),hAPP_nat_nat(suc,U_2033)))
    | sP214(U_2035,U_2033) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

cnf(f_739_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2035),U_2033))
    | ~ sP214(U_2035,U_2033) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

cnf(f_739_8,plain,
    ( U_2035 != U_2033
    | ~ sP214(U_2035,U_2033) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

fof(f_740_1,plain,
    ! [M_1,Na] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_636_not__less__eq]) ).

fof(f_740_2,plain,
    ! [U_2037,U_2036] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2037),U_2036))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2036),hAPP_nat_nat(suc,U_2037))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2036),hAPP_nat_nat(suc,U_2037)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2037),U_2036)) ) ),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

fof(f_740_3,plain,
    ( ! [U_2041,U_2039] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2041),U_2039))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2039),hAPP_nat_nat(suc,U_2041))) )
    & ! [U_2040,U_2038] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2038),hAPP_nat_nat(suc,U_2040)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2040),U_2038)) ) ),
    inference(miniscope,[status(thm)],[f_740_2]) ).

fof(f_740_4,plain,
    ( ! [U_2039,U_2041] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2041),U_2039))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2039),hAPP_nat_nat(suc,U_2041))) )
    & ! [U_2040,U_2038] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2038),hAPP_nat_nat(suc,U_2040)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2040),U_2038)) ) ),
    inference(definitional_conversion,[status(esa)],[f_740_3]) ).

cnf(f_740_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2038),hAPP_nat_nat(suc,U_2040)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2040),U_2038)) ),
    inference(clausify,[status(thm)],[f_740_4]) ).

cnf(f_740_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2041),U_2039))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2039),hAPP_nat_nat(suc,U_2041))) ),
    inference(clausify,[status(thm)],[f_740_4]) ).

fof(f_741_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
      | ( M != N
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ),
    inference(fof_nnf,[status(thm)],[fact_637_less__or__eq__imp__le]) ).

fof(f_741_2,plain,
    ! [U_2043,U_2042] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2043),U_2042))
      | ( U_2043 != U_2042
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2043),U_2042)) ) ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

fof(f_741_3,plain,
    ( ! [U_2043,U_2042] :
        ( U_2043 != U_2042
        | ~ sP215(U_2043,U_2042) )
    & ! [U_2043,U_2042] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2043),U_2042))
        | ~ sP215(U_2043,U_2042) )
    & ! [U_2043,U_2042] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2043),U_2042))
        | sP215(U_2043,U_2042) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215])],[f_741_2]) ).

cnf(f_741_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2043),U_2042))
    | sP215(U_2043,U_2042) ),
    inference(clausify,[status(thm)],[f_741_3]) ).

cnf(f_741_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2043),U_2042))
    | ~ sP215(U_2043,U_2042) ),
    inference(clausify,[status(thm)],[f_741_3]) ).

cnf(f_741_6,plain,
    ( U_2043 != U_2042
    | ~ sP215(U_2043,U_2042) ),
    inference(clausify,[status(thm)],[f_741_3]) ).

fof(f_742_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
      | M = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_638_le__neq__implies__less]) ).

fof(f_742_2,plain,
    ! [U_2045,U_2044] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2045),U_2044))
      | U_2045 = U_2044
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2045),U_2044)) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

fof(f_742_3,plain,
    ! [U_2045,U_2044] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2045),U_2044))
      | U_2045 = U_2044
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2045),U_2044)) ),
    inference(definitional_conversion,[status(esa)],[f_742_2]) ).

cnf(f_742_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2045),U_2044))
    | U_2045 = U_2044
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2045),U_2044)) ),
    inference(clausify,[status(thm)],[f_742_3]) ).

fof(f_743_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_639_less__imp__le__nat]) ).

fof(f_743_2,plain,
    ! [U_2047,U_2046] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2047),U_2046))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2047),U_2046)) ),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

fof(f_743_3,plain,
    ! [U_2046,U_2047] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2047),U_2046))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2047),U_2046)) ),
    inference(definitional_conversion,[status(esa)],[f_743_2]) ).

cnf(f_743_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2047),U_2046))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2047),U_2046)) ),
    inference(clausify,[status(thm)],[f_743_3]) ).

fof(f_744_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ( M_1 != Na
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) )
      & ( M_1 = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_640_le__eq__less__or__eq]) ).

fof(f_744_2,plain,
    ! [U_2049,U_2048] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2049),U_2048))
        | ( U_2049 != U_2048
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2049),U_2048)) ) )
      & ( U_2049 = U_2048
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2049),U_2048))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2049),U_2048)) ) ),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

fof(f_744_3,plain,
    ( ! [U_2053,U_2051] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2053),U_2051))
        | ( U_2053 != U_2051
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2053),U_2051)) ) )
    & ! [U_2052,U_2050] :
        ( U_2052 = U_2050
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2052),U_2050))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2052),U_2050)) ) ),
    inference(miniscope,[status(thm)],[f_744_2]) ).

fof(f_744_4,plain,
    ( ! [U_2053,U_2051] :
        ( U_2053 != U_2051
        | ~ sP216(U_2053,U_2051) )
    & ! [U_2053,U_2051] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2053),U_2051))
        | ~ sP216(U_2053,U_2051) )
    & ! [U_2053,U_2051] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2053),U_2051))
        | sP216(U_2053,U_2051) )
    & ! [U_2052,U_2050] :
        ( U_2052 = U_2050
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2052),U_2050))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2052),U_2050)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216])],[f_744_3]) ).

cnf(f_744_5,plain,
    ( U_2052 = U_2050
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2052),U_2050))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2052),U_2050)) ),
    inference(clausify,[status(thm)],[f_744_4]) ).

cnf(f_744_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2053),U_2051))
    | sP216(U_2053,U_2051) ),
    inference(clausify,[status(thm)],[f_744_4]) ).

cnf(f_744_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2053),U_2051))
    | ~ sP216(U_2053,U_2051) ),
    inference(clausify,[status(thm)],[f_744_4]) ).

cnf(f_744_8,plain,
    ( U_2053 != U_2051
    | ~ sP216(U_2053,U_2051) ),
    inference(clausify,[status(thm)],[f_744_4]) ).

fof(f_745_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | M_1 = Na
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) )
      & ( ( M_1 != Na
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_641_nat__less__le]) ).

fof(f_745_2,plain,
    ! [U_2055,U_2054] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2055),U_2054))
        | U_2055 = U_2054
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2055),U_2054)) )
      & ( ( U_2055 != U_2054
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2055),U_2054)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2055),U_2054)) ) ),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

fof(f_745_3,plain,
    ( ! [U_2059,U_2057] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2059),U_2057))
        | U_2059 = U_2057
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2059),U_2057)) )
    & ! [U_2058,U_2056] :
        ( ( U_2058 != U_2056
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2058),U_2056)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2058),U_2056)) ) ),
    inference(miniscope,[status(thm)],[f_745_2]) ).

fof(f_745_4,plain,
    ( ! [U_2058,U_2056] :
        ( U_2058 != U_2056
        | ~ sP217(U_2058,U_2056) )
    & ! [U_2058,U_2056] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2058),U_2056))
        | ~ sP217(U_2058,U_2056) )
    & ! [U_2059,U_2057] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2059),U_2057))
        | U_2059 = U_2057
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2059),U_2057)) )
    & ! [U_2058,U_2056] :
        ( sP217(U_2058,U_2056)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2058),U_2056)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP217])],[f_745_3]) ).

cnf(f_745_5,plain,
    ( sP217(U_2058,U_2056)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2058),U_2056)) ),
    inference(clausify,[status(thm)],[f_745_4]) ).

cnf(f_745_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2059),U_2057))
    | U_2059 = U_2057
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2059),U_2057)) ),
    inference(clausify,[status(thm)],[f_745_4]) ).

cnf(f_745_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2058),U_2056))
    | ~ sP217(U_2058,U_2056) ),
    inference(clausify,[status(thm)],[f_745_4]) ).

cnf(f_745_8,plain,
    ( U_2058 != U_2056
    | ~ sP217(U_2058,U_2056) ),
    inference(clausify,[status(thm)],[f_745_4]) ).

fof(f_746_1,plain,
    ! [L,M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(L),N)),hAPP_nat_nat(minus_minus_nat(L),M)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),L))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_642_diff__less__mono2]) ).

fof(f_746_2,plain,
    ! [U_2062,U_2061,U_2060] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2062),U_2060)),hAPP_nat_nat(minus_minus_nat(U_2062),U_2061)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2061),U_2062))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2061),U_2060)) ),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

fof(f_746_3,plain,
    ! [U_2061,U_2062,U_2060] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2062),U_2060)),hAPP_nat_nat(minus_minus_nat(U_2062),U_2061)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2061),U_2062))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2061),U_2060)) ),
    inference(definitional_conversion,[status(esa)],[f_746_2]) ).

cnf(f_746_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2062),U_2060)),hAPP_nat_nat(minus_minus_nat(U_2062),U_2061)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2061),U_2062))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2061),U_2060)) ),
    inference(clausify,[status(thm)],[f_746_3]) ).

fof(f_747_1,plain,
    ! [N,J_2,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(J_2),N)),K))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K)) ),
    inference(fof_nnf,[status(thm)],[fact_643_less__imp__diff__less]) ).

fof(f_747_2,plain,
    ! [U_2065,U_2064,U_2063] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2064),U_2065)),U_2063))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2064),U_2063)) ),
    inference(variable_rename,[status(thm)],[f_747_1]) ).

fof(f_747_3,plain,
    ! [U_2064,U_2063,U_2065] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2064),U_2065)),U_2063))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2064),U_2063)) ),
    inference(definitional_conversion,[status(esa)],[f_747_2]) ).

cnf(f_747_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2064),U_2065)),U_2063))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2064),U_2063)) ),
    inference(clausify,[status(thm)],[f_747_3]) ).

fof(f_748_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_644_termination__basic__simps_I5_J]) ).

fof(f_748_2,plain,
    ! [U_2067,U_2066] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2067),U_2066))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2067),U_2066)) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

fof(f_748_3,plain,
    ! [U_2066,U_2067] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2067),U_2066))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2067),U_2066)) ),
    inference(definitional_conversion,[status(esa)],[f_748_2]) ).

cnf(f_748_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2067),U_2066))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2067),U_2066)) ),
    inference(clausify,[status(thm)],[f_748_3]) ).

fof(f_749_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)),
    inference(fof_nnf,[status(thm)],[fact_645_less__not__refl]) ).

fof(f_749_2,plain,
    ! [U_2068] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2068),U_2068)),
    inference(variable_rename,[status(thm)],[f_749_1]) ).

fof(f_749_3,plain,
    ! [U_2068] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2068),U_2068)),
    inference(definitional_conversion,[status(esa)],[f_749_2]) ).

cnf(f_749_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2068),U_2068)),
    inference(clausify,[status(thm)],[f_749_3]) ).

fof(f_750_1,plain,
    ! [M_1,Na] :
      ( ( M_1 != Na
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | M_1 = Na ) ),
    inference(fof_nnf,[status(thm)],[fact_646_nat__neq__iff]) ).

fof(f_750_2,plain,
    ! [U_2070,U_2069] :
      ( ( U_2070 != U_2069
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2069),U_2070))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2070),U_2069)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2069),U_2070))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2070),U_2069))
        | U_2070 = U_2069 ) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

fof(f_750_3,plain,
    ( ! [U_2074,U_2072] :
        ( U_2074 != U_2072
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2072),U_2074))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2074),U_2072)) ) )
    & ! [U_2073,U_2071] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2071),U_2073))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2073),U_2071))
        | U_2073 = U_2071 ) ),
    inference(miniscope,[status(thm)],[f_750_2]) ).

fof(f_750_4,plain,
    ( ! [U_2074,U_2072] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2072),U_2074))
        | ~ sP218(U_2074,U_2072) )
    & ! [U_2074,U_2072] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2074),U_2072))
        | ~ sP218(U_2074,U_2072) )
    & ! [U_2074,U_2072] :
        ( U_2074 != U_2072
        | sP218(U_2074,U_2072) )
    & ! [U_2073,U_2071] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2071),U_2073))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2073),U_2071))
        | U_2073 = U_2071 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP218])],[f_750_3]) ).

cnf(f_750_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2071),U_2073))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2073),U_2071))
    | U_2073 = U_2071 ),
    inference(clausify,[status(thm)],[f_750_4]) ).

cnf(f_750_6,plain,
    ( U_2074 != U_2072
    | sP218(U_2074,U_2072) ),
    inference(clausify,[status(thm)],[f_750_4]) ).

cnf(f_750_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2074),U_2072))
    | ~ sP218(U_2074,U_2072) ),
    inference(clausify,[status(thm)],[f_750_4]) ).

cnf(f_750_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2072),U_2074))
    | ~ sP218(U_2074,U_2072) ),
    inference(clausify,[status(thm)],[f_750_4]) ).

fof(f_751_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_647_linorder__neqE__nat]) ).

fof(f_751_2,plain,
    ! [U_2076,U_2075] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2075),U_2076))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2076),U_2075))
      | U_2076 = U_2075 ),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

fof(f_751_3,plain,
    ! [U_2076,U_2075] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2075),U_2076))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2076),U_2075))
      | U_2076 = U_2075 ),
    inference(definitional_conversion,[status(esa)],[f_751_2]) ).

cnf(f_751_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2075),U_2076))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2076),U_2075))
    | U_2076 = U_2075 ),
    inference(clausify,[status(thm)],[f_751_3]) ).

fof(f_752_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)),
    inference(fof_nnf,[status(thm)],[fact_648_less__irrefl__nat]) ).

fof(f_752_2,plain,
    ! [U_2077] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2077),U_2077)),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

fof(f_752_3,plain,
    ! [U_2077] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2077),U_2077)),
    inference(definitional_conversion,[status(esa)],[f_752_2]) ).

cnf(f_752_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2077),U_2077)),
    inference(clausify,[status(thm)],[f_752_3]) ).

fof(f_753_1,plain,
    ! [N,M] :
      ( M != N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) ),
    inference(fof_nnf,[status(thm)],[fact_649_less__not__refl2]) ).

fof(f_753_2,plain,
    ! [U_2079,U_2078] :
      ( U_2078 != U_2079
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2079),U_2078)) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

fof(f_753_3,plain,
    ! [U_2079,U_2078] :
      ( U_2078 != U_2079
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2079),U_2078)) ),
    inference(definitional_conversion,[status(esa)],[f_753_2]) ).

cnf(f_753_4,plain,
    ( U_2078 != U_2079
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2079),U_2078)) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

fof(f_754_1,plain,
    ! [S,T] :
      ( S != T
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) ),
    inference(fof_nnf,[status(thm)],[fact_650_less__not__refl3]) ).

fof(f_754_2,plain,
    ! [U_2081,U_2080] :
      ( U_2081 != U_2080
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2081),U_2080)) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

fof(f_754_3,plain,
    ! [U_2081,U_2080] :
      ( U_2081 != U_2080
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2081),U_2080)) ),
    inference(definitional_conversion,[status(esa)],[f_754_2]) ).

cnf(f_754_4,plain,
    ( U_2081 != U_2080
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2081),U_2080)) ),
    inference(clausify,[status(thm)],[f_754_3]) ).

fof(f_755_1,plain,
    ! [Pa,M_1,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1))
        & M_1 = Na )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_651_nat__less__cases]) ).

fof(f_755_2,plain,
    ! [U_2084,U_2083,U_2082] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2084,U_2082),U_2083))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2084,U_2082),U_2083))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2082),U_2083)) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2084,U_2082),U_2083))
        & U_2083 = U_2082 )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2084,U_2082),U_2083))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2083),U_2082)) ) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

fof(f_755_3,plain,
    ( ! [U_2082,U_2083,U_2084] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2084,U_2082),U_2083))
        | ~ sP221(U_2082,U_2083,U_2084) )
    & ! [U_2082,U_2083,U_2084] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2082),U_2083))
        | ~ sP221(U_2082,U_2083,U_2084) )
    & ! [U_2082,U_2083,U_2084] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2084,U_2082),U_2083))
        | ~ sP220(U_2082,U_2083,U_2084) )
    & ! [U_2082,U_2083,U_2084] :
        ( U_2083 = U_2082
        | ~ sP220(U_2082,U_2083,U_2084) )
    & ! [U_2082,U_2083,U_2084] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2084,U_2082),U_2083))
        | ~ sP219(U_2082,U_2083,U_2084) )
    & ! [U_2082,U_2083,U_2084] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2083),U_2082))
        | ~ sP219(U_2082,U_2083,U_2084) )
    & ! [U_2082,U_2083,U_2084] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2084,U_2082),U_2083))
        | sP221(U_2082,U_2083,U_2084)
        | sP220(U_2082,U_2083,U_2084)
        | sP219(U_2082,U_2083,U_2084) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219,sP220,sP221])],[f_755_2]) ).

cnf(f_755_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2084,U_2082),U_2083))
    | sP221(U_2082,U_2083,U_2084)
    | sP220(U_2082,U_2083,U_2084)
    | sP219(U_2082,U_2083,U_2084) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

cnf(f_755_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2083),U_2082))
    | ~ sP219(U_2082,U_2083,U_2084) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

cnf(f_755_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2084,U_2082),U_2083))
    | ~ sP219(U_2082,U_2083,U_2084) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

cnf(f_755_7,plain,
    ( U_2083 = U_2082
    | ~ sP220(U_2082,U_2083,U_2084) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

cnf(f_755_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2084,U_2082),U_2083))
    | ~ sP220(U_2082,U_2083,U_2084) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

cnf(f_755_9,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2082),U_2083))
    | ~ sP221(U_2082,U_2083,U_2084) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

cnf(f_755_10,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2084,U_2082),U_2083))
    | ~ sP221(U_2082,U_2083,U_2084) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

fof(f_756_1,plain,
    ! [N_1] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1))
        | ! [M_2] :
          ? [X_1] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),M_2))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1)) ) )
      & ( ? [M_2] :
          ! [X_1] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),M_2))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_652_finite__nat__set__iff__bounded]) ).

fof(f_756_2,plain,
    ! [U_2089] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2089))
        | ! [U_2088] :
          ? [U_2087] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2087),U_2088))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2087),U_2089)) ) )
      & ( ? [U_2086] :
          ! [U_2085] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2085),U_2086))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2085),U_2089)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2089)) ) ),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

fof(f_756_3,plain,
    ( ! [U_2091] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2091))
        | ! [U_2088] :
          ? [U_2087] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2087),U_2088))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2087),U_2091)) ) )
    & ! [U_2090] :
        ( ? [U_2086] :
          ! [U_2085] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2085),U_2086))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2085),U_2090)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2090)) ) ),
    inference(miniscope,[status(thm)],[f_756_2]) ).

fof(f_756_4,plain,
    ( ! [U_2091] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2091))
        | ! [U_2088] :
          ? [U_2087] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2087),U_2088))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2087),U_2091)) ) )
    & ! [U_2090] :
        ( ! [U_2085] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2085),sK123(U_2090)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2085),U_2090)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2090)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_2086,sK123(U_2090))],[f_756_3]) ).

fof(f_756_5,plain,
    ( ! [U_2091] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2091))
        | ! [U_2088] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK124(U_2091,U_2088)),U_2088))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK124(U_2091,U_2088)),U_2091)) ) )
    & ! [U_2090] :
        ( ! [U_2085] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2085),sK123(U_2090)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2085),U_2090)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2090)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_2087,sK124(U_2091,U_2088))],[f_756_4]) ).

fof(f_756_6,plain,
    ( ! [U_2088,U_2091] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK124(U_2091,U_2088)),U_2088))
        | ~ sP222(U_2088,U_2091) )
    & ! [U_2088,U_2091] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK124(U_2091,U_2088)),U_2091))
        | ~ sP222(U_2088,U_2091) )
    & ! [U_2088,U_2091] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2091))
        | sP222(U_2088,U_2091) )
    & ! [U_2085,U_2090] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2085),sK123(U_2090)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2085),U_2090))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2090)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP222])],[f_756_5]) ).

cnf(f_756_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2085),sK123(U_2090)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2085),U_2090))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2090)) ),
    inference(clausify,[status(thm)],[f_756_6]) ).

cnf(f_756_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2091))
    | sP222(U_2088,U_2091) ),
    inference(clausify,[status(thm)],[f_756_6]) ).

cnf(f_756_9,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK124(U_2091,U_2088)),U_2091))
    | ~ sP222(U_2088,U_2091) ),
    inference(clausify,[status(thm)],[f_756_6]) ).

cnf(f_756_10,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK124(U_2091,U_2088)),U_2088))
    | ~ sP222(U_2088,U_2091) ),
    inference(clausify,[status(thm)],[f_756_6]) ).

fof(f_757_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_653_card__Collect__less__nat]) ).

fof(f_757_2,plain,
    ! [U_2092] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2092))) = U_2092,
    inference(variable_rename,[status(thm)],[f_757_1]) ).

fof(f_757_3,plain,
    ! [U_2092] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2092))) = U_2092,
    inference(definitional_conversion,[status(esa)],[f_757_2]) ).

cnf(f_757_4,plain,
    hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2092))) = U_2092,
    inference(clausify,[status(thm)],[f_757_3]) ).

fof(f_758_1,plain,
    ! [Pa,I_1] : 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_1))))),
    inference(fof_nnf,[status(thm)],[fact_654_finite__M__bounded__by__nat]) ).

fof(f_758_2,plain,
    ! [U_2094,U_2093] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_2094),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2093))))),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

fof(f_758_3,plain,
    ! [U_2093,U_2094] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_2094),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2093))))),
    inference(definitional_conversion,[status(esa)],[f_758_2]) ).

cnf(f_758_4,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_2094),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2093))))),
    inference(clausify,[status(thm)],[f_758_3]) ).

fof(f_759_1,plain,
    ! [I,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(I),M)))),
    inference(fof_nnf,[status(thm)],[fact_655_less__add__Suc1]) ).

fof(f_759_2,plain,
    ! [U_2096,U_2095] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2096),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2096),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_nat,U_2096),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2096),U_2095)))),
    inference(definitional_conversion,[status(esa)],[f_759_2]) ).

cnf(f_759_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2096),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2096),U_2095)))),
    inference(clausify,[status(thm)],[f_759_3]) ).

fof(f_760_1,plain,
    ! [I,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),I)))),
    inference(fof_nnf,[status(thm)],[fact_656_less__add__Suc2]) ).

fof(f_760_2,plain,
    ! [U_2098,U_2097] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2098),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2097),U_2098)))),
    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_nat,U_2098),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2097),U_2098)))),
    inference(definitional_conversion,[status(esa)],[f_760_2]) ).

cnf(f_760_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2098),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2097),U_2098)))),
    inference(clausify,[status(thm)],[f_760_3]) ).

fof(f_761_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ! [K_1] : Na != hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M_1),K_1)) )
      & ( ? [K_1] : Na = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M_1),K_1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_657_less__iff__Suc__add]) ).

fof(f_761_2,plain,
    ! [U_2102,U_2101] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2102),U_2101))
        | ! [U_2100] : U_2101 != hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2102),U_2100)) )
      & ( ? [U_2099] : U_2101 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2102),U_2099))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2102),U_2101)) ) ),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

fof(f_761_3,plain,
    ( ! [U_2106,U_2104] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2106),U_2104))
        | ! [U_2100] : U_2104 != hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2106),U_2100)) )
    & ! [U_2105,U_2103] :
        ( ? [U_2099] : U_2103 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2105),U_2099))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2105),U_2103)) ) ),
    inference(miniscope,[status(thm)],[f_761_2]) ).

fof(f_761_4,plain,
    ( ! [U_2106,U_2104] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2106),U_2104))
        | ! [U_2100] : U_2104 != hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2106),U_2100)) )
    & ! [U_2105,U_2103] :
        ( U_2103 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2105),sK125(U_2105,U_2103)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2105),U_2103)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_2099,sK125(U_2105,U_2103))],[f_761_3]) ).

fof(f_761_5,plain,
    ( ! [U_2100,U_2104,U_2106] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2106),U_2104))
        | U_2104 != hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2106),U_2100)) )
    & ! [U_2105,U_2103] :
        ( U_2103 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2105),sK125(U_2105,U_2103)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2105),U_2103)) ) ),
    inference(definitional_conversion,[status(esa)],[f_761_4]) ).

cnf(f_761_6,plain,
    ( U_2103 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2105),sK125(U_2105,U_2103)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2105),U_2103)) ),
    inference(clausify,[status(thm)],[f_761_5]) ).

cnf(f_761_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2106),U_2104))
    | U_2104 != hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2106),U_2100)) ),
    inference(clausify,[status(thm)],[f_761_5]) ).

fof(f_762_1,plain,
    ! [Na,M_1] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_658_less__eq__Suc__le]) ).

fof(f_762_2,plain,
    ! [U_2108,U_2107] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2108),U_2107))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2108)),U_2107)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2108)),U_2107))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2108),U_2107)) ) ),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

fof(f_762_3,plain,
    ( ! [U_2112,U_2110] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2112),U_2110))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2112)),U_2110)) )
    & ! [U_2111,U_2109] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2111)),U_2109))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2111),U_2109)) ) ),
    inference(miniscope,[status(thm)],[f_762_2]) ).

fof(f_762_4,plain,
    ( ! [U_2110,U_2112] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2112),U_2110))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2112)),U_2110)) )
    & ! [U_2111,U_2109] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2111)),U_2109))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2111),U_2109)) ) ),
    inference(definitional_conversion,[status(esa)],[f_762_3]) ).

cnf(f_762_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2111)),U_2109))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2111),U_2109)) ),
    inference(clausify,[status(thm)],[f_762_4]) ).

cnf(f_762_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2112),U_2110))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2112)),U_2110)) ),
    inference(clausify,[status(thm)],[f_762_4]) ).

fof(f_763_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_659_less__Suc__eq__le]) ).

fof(f_763_2,plain,
    ! [U_2114,U_2113] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2114),hAPP_nat_nat(suc,U_2113)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2114),U_2113)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2114),U_2113))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2114),hAPP_nat_nat(suc,U_2113))) ) ),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

fof(f_763_3,plain,
    ( ! [U_2118,U_2116] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2118),hAPP_nat_nat(suc,U_2116)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2118),U_2116)) )
    & ! [U_2117,U_2115] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2117),U_2115))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2117),hAPP_nat_nat(suc,U_2115))) ) ),
    inference(miniscope,[status(thm)],[f_763_2]) ).

fof(f_763_4,plain,
    ( ! [U_2116,U_2118] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2118),hAPP_nat_nat(suc,U_2116)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2118),U_2116)) )
    & ! [U_2117,U_2115] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2117),U_2115))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2117),hAPP_nat_nat(suc,U_2115))) ) ),
    inference(definitional_conversion,[status(esa)],[f_763_3]) ).

cnf(f_763_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2117),U_2115))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2117),hAPP_nat_nat(suc,U_2115))) ),
    inference(clausify,[status(thm)],[f_763_4]) ).

cnf(f_763_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2118),hAPP_nat_nat(suc,U_2116)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2118),U_2116)) ),
    inference(clausify,[status(thm)],[f_763_4]) ).

fof(f_764_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_660_Suc__le__eq]) ).

fof(f_764_2,plain,
    ! [U_2120,U_2119] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2120)),U_2119))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2120),U_2119)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2120),U_2119))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2120)),U_2119)) ) ),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

fof(f_764_3,plain,
    ( ! [U_2124,U_2122] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2124)),U_2122))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2124),U_2122)) )
    & ! [U_2123,U_2121] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2123),U_2121))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2123)),U_2121)) ) ),
    inference(miniscope,[status(thm)],[f_764_2]) ).

fof(f_764_4,plain,
    ( ! [U_2122,U_2124] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2124)),U_2122))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2124),U_2122)) )
    & ! [U_2123,U_2121] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2123),U_2121))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2123)),U_2121)) ) ),
    inference(definitional_conversion,[status(esa)],[f_764_3]) ).

cnf(f_764_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2123),U_2121))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2123)),U_2121)) ),
    inference(clausify,[status(thm)],[f_764_4]) ).

cnf(f_764_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2124)),U_2122))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2124),U_2122)) ),
    inference(clausify,[status(thm)],[f_764_4]) ).

fof(f_765_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_661_le__imp__less__Suc]) ).

fof(f_765_2,plain,
    ! [U_2126,U_2125] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2126),hAPP_nat_nat(suc,U_2125)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2126),U_2125)) ),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

fof(f_765_3,plain,
    ! [U_2126,U_2125] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2126),hAPP_nat_nat(suc,U_2125)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2126),U_2125)) ),
    inference(definitional_conversion,[status(esa)],[f_765_2]) ).

cnf(f_765_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2126),hAPP_nat_nat(suc,U_2125)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2126),U_2125)) ),
    inference(clausify,[status(thm)],[f_765_3]) ).

fof(f_766_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_662_Suc__leI]) ).

fof(f_766_2,plain,
    ! [U_2128,U_2127] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2128)),U_2127))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2128),U_2127)) ),
    inference(variable_rename,[status(thm)],[f_766_1]) ).

fof(f_766_3,plain,
    ! [U_2127,U_2128] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2128)),U_2127))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2128),U_2127)) ),
    inference(definitional_conversion,[status(esa)],[f_766_2]) ).

cnf(f_766_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2128)),U_2127))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2128),U_2127)) ),
    inference(clausify,[status(thm)],[f_766_3]) ).

fof(f_767_1,plain,
    ! [M_1,Na] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
          | Na != M_1 )
        & ( Na = M_1
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ),
    inference(fof_nnf,[status(thm)],[fact_663_le__less__Suc__eq]) ).

fof(f_767_2,plain,
    ! [U_2130,U_2129] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2129),hAPP_nat_nat(suc,U_2130)))
          | U_2129 != U_2130 )
        & ( U_2129 = U_2130
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2129),hAPP_nat_nat(suc,U_2130))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2130),U_2129)) ),
    inference(variable_rename,[status(thm)],[f_767_1]) ).

fof(f_767_3,plain,
    ( ! [U_2129,U_2130] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2129),hAPP_nat_nat(suc,U_2130)))
        | U_2129 != U_2130
        | ~ sP223(U_2129,U_2130) )
    & ! [U_2129,U_2130] :
        ( U_2129 = U_2130
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2129),hAPP_nat_nat(suc,U_2130)))
        | ~ sP223(U_2129,U_2130) )
    & ! [U_2129,U_2130] :
        ( sP223(U_2129,U_2130)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2130),U_2129)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP223])],[f_767_2]) ).

cnf(f_767_4,plain,
    ( sP223(U_2129,U_2130)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2130),U_2129)) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

cnf(f_767_5,plain,
    ( U_2129 = U_2130
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2129),hAPP_nat_nat(suc,U_2130)))
    | ~ sP223(U_2129,U_2130) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

cnf(f_767_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2129),hAPP_nat_nat(suc,U_2130)))
    | U_2129 != U_2130
    | ~ sP223(U_2129,U_2130) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

fof(f_768_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_664_Suc__le__lessD]) ).

fof(f_768_2,plain,
    ! [U_2132,U_2131] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2132),U_2131))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2132)),U_2131)) ),
    inference(variable_rename,[status(thm)],[f_768_1]) ).

fof(f_768_3,plain,
    ! [U_2132,U_2131] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2132),U_2131))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2132)),U_2131)) ),
    inference(definitional_conversion,[status(esa)],[f_768_2]) ).

cnf(f_768_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2132),U_2131))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2132)),U_2131)) ),
    inference(clausify,[status(thm)],[f_768_3]) ).

fof(f_769_1,plain,
    ! [M,N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M),N)),hAPP_nat_nat(suc,M))),
    inference(fof_nnf,[status(thm)],[fact_665_diff__less__Suc]) ).

fof(f_769_2,plain,
    ! [U_2134,U_2133] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2134),U_2133)),hAPP_nat_nat(suc,U_2134))),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

fof(f_769_3,plain,
    ! [U_2133,U_2134] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2134),U_2133)),hAPP_nat_nat(suc,U_2134))),
    inference(definitional_conversion,[status(esa)],[f_769_2]) ).

cnf(f_769_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2134),U_2133)),hAPP_nat_nat(suc,U_2134))),
    inference(clausify,[status(thm)],[f_769_3]) ).

fof(f_770_1,plain,
    ! [M,N] :
      ( hAPP_nat_nat(plus_plus_nat(N),hAPP_nat_nat(minus_minus_nat(M),N)) = M
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_666_add__diff__inverse]) ).

fof(f_770_2,plain,
    ! [U_2136,U_2135] :
      ( hAPP_nat_nat(plus_plus_nat(U_2135),hAPP_nat_nat(minus_minus_nat(U_2136),U_2135)) = U_2136
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2136),U_2135)) ),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

fof(f_770_3,plain,
    ! [U_2135,U_2136] :
      ( hAPP_nat_nat(plus_plus_nat(U_2135),hAPP_nat_nat(minus_minus_nat(U_2136),U_2135)) = U_2136
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2136),U_2135)) ),
    inference(definitional_conversion,[status(esa)],[f_770_2]) ).

cnf(f_770_4,plain,
    ( hAPP_nat_nat(plus_plus_nat(U_2135),hAPP_nat_nat(minus_minus_nat(U_2136),U_2135)) = U_2136
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2136),U_2135)) ),
    inference(clausify,[status(thm)],[f_770_3]) ).

fof(f_771_1,plain,
    ! [I_1,J_1,K_2] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_2)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_2)),J_1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_2)),J_1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_667_less__diff__conv]) ).

fof(f_771_2,plain,
    ! [U_2139,U_2138,U_2137] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2139),hAPP_nat_nat(minus_minus_nat(U_2138),U_2137)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2139),U_2137)),U_2138)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2139),U_2137)),U_2138))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2139),hAPP_nat_nat(minus_minus_nat(U_2138),U_2137))) ) ),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

fof(f_771_3,plain,
    ( ! [U_2145,U_2143,U_2141] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2145),hAPP_nat_nat(minus_minus_nat(U_2143),U_2141)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2145),U_2141)),U_2143)) )
    & ! [U_2144,U_2142,U_2140] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2144),U_2140)),U_2142))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2144),hAPP_nat_nat(minus_minus_nat(U_2142),U_2140))) ) ),
    inference(miniscope,[status(thm)],[f_771_2]) ).

fof(f_771_4,plain,
    ( ! [U_2141,U_2143,U_2145] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2145),hAPP_nat_nat(minus_minus_nat(U_2143),U_2141)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2145),U_2141)),U_2143)) )
    & ! [U_2144,U_2142,U_2140] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2144),U_2140)),U_2142))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2144),hAPP_nat_nat(minus_minus_nat(U_2142),U_2140))) ) ),
    inference(definitional_conversion,[status(esa)],[f_771_3]) ).

cnf(f_771_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2144),U_2140)),U_2142))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2144),hAPP_nat_nat(minus_minus_nat(U_2142),U_2140))) ),
    inference(clausify,[status(thm)],[f_771_4]) ).

cnf(f_771_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2145),hAPP_nat_nat(minus_minus_nat(U_2143),U_2141)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2145),U_2141)),U_2143)) ),
    inference(clausify,[status(thm)],[f_771_4]) ).

fof(f_772_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(A),C)),hAPP_nat_nat(minus_minus_nat(B),C)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_668_diff__less__mono]) ).

fof(f_772_2,plain,
    ! [U_2148,U_2147,U_2146] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2147),U_2148)),hAPP_nat_nat(minus_minus_nat(U_2146),U_2148)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2148),U_2147))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2147),U_2146)) ),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

fof(f_772_3,plain,
    ! [U_2147,U_2146,U_2148] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2147),U_2148)),hAPP_nat_nat(minus_minus_nat(U_2146),U_2148)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2148),U_2147))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2147),U_2146)) ),
    inference(definitional_conversion,[status(esa)],[f_772_2]) ).

cnf(f_772_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2147),U_2148)),hAPP_nat_nat(minus_minus_nat(U_2146),U_2148)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2148),U_2147))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2147),U_2146)) ),
    inference(clausify,[status(thm)],[f_772_3]) ).

fof(f_773_1,plain,
    ! [Na,K_2,M_1] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M_1),K_2)),hAPP_nat_nat(minus_minus_nat(Na),K_2)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M_1),K_2)),hAPP_nat_nat(minus_minus_nat(Na),K_2))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_669_less__diff__iff]) ).

fof(f_773_2,plain,
    ! [U_2151,U_2150,U_2149] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2149),U_2150)),hAPP_nat_nat(minus_minus_nat(U_2151),U_2150)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2149),U_2151)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2149),U_2151))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2149),U_2150)),hAPP_nat_nat(minus_minus_nat(U_2151),U_2150))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2150),U_2151))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2150),U_2149)) ),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

fof(f_773_3,plain,
    ( ! [U_2149,U_2150,U_2151] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2149),U_2150)),hAPP_nat_nat(minus_minus_nat(U_2151),U_2150)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2149),U_2151))
        | ~ sP224(U_2149,U_2150,U_2151) )
    & ! [U_2149,U_2150,U_2151] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2149),U_2151))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2149),U_2150)),hAPP_nat_nat(minus_minus_nat(U_2151),U_2150)))
        | ~ sP224(U_2149,U_2150,U_2151) )
    & ! [U_2149,U_2150,U_2151] :
        ( sP224(U_2149,U_2150,U_2151)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2150),U_2151))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2150),U_2149)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP224])],[f_773_2]) ).

cnf(f_773_4,plain,
    ( sP224(U_2149,U_2150,U_2151)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2150),U_2151))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2150),U_2149)) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

cnf(f_773_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2149),U_2151))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2149),U_2150)),hAPP_nat_nat(minus_minus_nat(U_2151),U_2150)))
    | ~ sP224(U_2149,U_2150,U_2151) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

cnf(f_773_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2149),U_2150)),hAPP_nat_nat(minus_minus_nat(U_2151),U_2150)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2149),U_2151))
    | ~ sP224(U_2149,U_2150,U_2151) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

fof(f_774_1,plain,
    ! [X_1] : hAPP_n1699378549t_bool(ord_less_nat,X_1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_1)),
    inference(fof_nnf,[status(thm)],[fact_670_less__eq__Suc__le__raw]) ).

fof(f_774_2,plain,
    ! [U_2152] : hAPP_n1699378549t_bool(ord_less_nat,U_2152) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2152)),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

fof(f_774_3,plain,
    ! [U_2152] : hAPP_n1699378549t_bool(ord_less_nat,U_2152) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2152)),
    inference(definitional_conversion,[status(esa)],[f_774_2]) ).

cnf(f_774_4,plain,
    hAPP_n1699378549t_bool(ord_less_nat,U_2152) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2152)),
    inference(clausify,[status(thm)],[f_774_3]) ).

fof(f_775_1,plain,
    ! [M_1,K_2,F] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(F,M_1)),K_2)),hAPP_nat_nat(F,hAPP_nat_nat(plus_plus_nat(M_1),K_2))))
      | ? [M_2,N_2] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_2)),hAPP_nat_nat(F,N_2)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_671_mono__nat__linear__lb]) ).

fof(f_775_2,plain,
    ! [U_2157,U_2156,U_2155] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(U_2155,U_2157)),U_2156)),hAPP_nat_nat(U_2155,hAPP_nat_nat(plus_plus_nat(U_2157),U_2156))))
      | ? [U_2154,U_2153] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_2155,U_2154)),hAPP_nat_nat(U_2155,U_2153)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2154),U_2153)) ) ),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

fof(f_775_3,plain,
    ! [U_2157,U_2156,U_2155] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(U_2155,U_2157)),U_2156)),hAPP_nat_nat(U_2155,hAPP_nat_nat(plus_plus_nat(U_2157),U_2156))))
      | ? [U_2153] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_2155,sK126(U_2157,U_2156,U_2155))),hAPP_nat_nat(U_2155,U_2153)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK126(U_2157,U_2156,U_2155)),U_2153)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_2154,sK126(U_2157,U_2156,U_2155))],[f_775_2]) ).

fof(f_775_4,plain,
    ! [U_2157,U_2156,U_2155] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(U_2155,U_2157)),U_2156)),hAPP_nat_nat(U_2155,hAPP_nat_nat(plus_plus_nat(U_2157),U_2156))))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_2155,sK126(U_2157,U_2156,U_2155))),hAPP_nat_nat(U_2155,sK127(U_2157,U_2156,U_2155))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK126(U_2157,U_2156,U_2155)),sK127(U_2157,U_2156,U_2155))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_2153,sK127(U_2157,U_2156,U_2155))],[f_775_3]) ).

fof(f_775_5,plain,
    ( ! [U_2155,U_2156,U_2157] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_2155,sK126(U_2157,U_2156,U_2155))),hAPP_nat_nat(U_2155,sK127(U_2157,U_2156,U_2155))))
        | ~ sP225(U_2155,U_2156,U_2157) )
    & ! [U_2155,U_2156,U_2157] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK126(U_2157,U_2156,U_2155)),sK127(U_2157,U_2156,U_2155)))
        | ~ sP225(U_2155,U_2156,U_2157) )
    & ! [U_2155,U_2156,U_2157] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(U_2155,U_2157)),U_2156)),hAPP_nat_nat(U_2155,hAPP_nat_nat(plus_plus_nat(U_2157),U_2156))))
        | sP225(U_2155,U_2156,U_2157) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225])],[f_775_4]) ).

cnf(f_775_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(U_2155,U_2157)),U_2156)),hAPP_nat_nat(U_2155,hAPP_nat_nat(plus_plus_nat(U_2157),U_2156))))
    | sP225(U_2155,U_2156,U_2157) ),
    inference(clausify,[status(thm)],[f_775_5]) ).

cnf(f_775_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK126(U_2157,U_2156,U_2155)),sK127(U_2157,U_2156,U_2155)))
    | ~ sP225(U_2155,U_2156,U_2157) ),
    inference(clausify,[status(thm)],[f_775_5]) ).

cnf(f_775_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_2155,sK126(U_2157,U_2156,U_2155))),hAPP_nat_nat(U_2155,sK127(U_2157,U_2156,U_2155))))
    | ~ sP225(U_2155,U_2156,U_2157) ),
    inference(clausify,[status(thm)],[f_775_5]) ).

fof(f_776_1,plain,
    ! [Pa,I_1,J_1] :
      ( hBOOL(hAPP_nat_bool(Pa,I_1))
      | ? [I_2] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,I_2))
          & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_2)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,J_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_672_inc__induct]) ).

fof(f_776_2,plain,
    ! [U_2161,U_2160,U_2159] :
      ( hBOOL(hAPP_nat_bool(U_2161,U_2160))
      | ? [U_2158] :
          ( ~ hBOOL(hAPP_nat_bool(U_2161,U_2158))
          & hBOOL(hAPP_nat_bool(U_2161,hAPP_nat_nat(suc,U_2158)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2158),U_2159)) )
      | ~ hBOOL(hAPP_nat_bool(U_2161,U_2159))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2160),U_2159)) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

fof(f_776_3,plain,
    ! [U_2161,U_2160,U_2159] :
      ( hBOOL(hAPP_nat_bool(U_2161,U_2160))
      | ( ~ hBOOL(hAPP_nat_bool(U_2161,sK128(U_2161,U_2160,U_2159)))
        & hBOOL(hAPP_nat_bool(U_2161,hAPP_nat_nat(suc,sK128(U_2161,U_2160,U_2159))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK128(U_2161,U_2160,U_2159)),U_2159)) )
      | ~ hBOOL(hAPP_nat_bool(U_2161,U_2159))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2160),U_2159)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_2158,sK128(U_2161,U_2160,U_2159))],[f_776_2]) ).

fof(f_776_4,plain,
    ( ! [U_2159,U_2160,U_2161] :
        ( ~ hBOOL(hAPP_nat_bool(U_2161,sK128(U_2161,U_2160,U_2159)))
        | ~ sP226(U_2159,U_2160,U_2161) )
    & ! [U_2159,U_2160,U_2161] :
        ( hBOOL(hAPP_nat_bool(U_2161,hAPP_nat_nat(suc,sK128(U_2161,U_2160,U_2159))))
        | ~ sP226(U_2159,U_2160,U_2161) )
    & ! [U_2159,U_2160,U_2161] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK128(U_2161,U_2160,U_2159)),U_2159))
        | ~ sP226(U_2159,U_2160,U_2161) )
    & ! [U_2159,U_2160,U_2161] :
        ( hBOOL(hAPP_nat_bool(U_2161,U_2160))
        | sP226(U_2159,U_2160,U_2161)
        | ~ hBOOL(hAPP_nat_bool(U_2161,U_2159))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2160),U_2159)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226])],[f_776_3]) ).

cnf(f_776_5,plain,
    ( hBOOL(hAPP_nat_bool(U_2161,U_2160))
    | sP226(U_2159,U_2160,U_2161)
    | ~ hBOOL(hAPP_nat_bool(U_2161,U_2159))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2160),U_2159)) ),
    inference(clausify,[status(thm)],[f_776_4]) ).

cnf(f_776_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK128(U_2161,U_2160,U_2159)),U_2159))
    | ~ sP226(U_2159,U_2160,U_2161) ),
    inference(clausify,[status(thm)],[f_776_4]) ).

cnf(f_776_7,plain,
    ( hBOOL(hAPP_nat_bool(U_2161,hAPP_nat_nat(suc,sK128(U_2161,U_2160,U_2159))))
    | ~ sP226(U_2159,U_2160,U_2161) ),
    inference(clausify,[status(thm)],[f_776_4]) ).

cnf(f_776_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_2161,sK128(U_2161,U_2160,U_2159)))
    | ~ sP226(U_2159,U_2160,U_2161) ),
    inference(clausify,[status(thm)],[f_776_4]) ).

fof(f_777_1,plain,
    ! [M,N] :
      ( ? [K_1] : N = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(M),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_673_less__imp__Suc__add]) ).

fof(f_777_2,plain,
    ! [U_2164,U_2163] :
      ( ? [U_2162] : U_2163 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2164),U_2162))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2164),U_2163)) ),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

fof(f_777_3,plain,
    ! [U_2164,U_2163] :
      ( U_2163 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2164),sK129(U_2164,U_2163)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2164),U_2163)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_2162,sK129(U_2164,U_2163))],[f_777_2]) ).

fof(f_777_4,plain,
    ! [U_2163,U_2164] :
      ( U_2163 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2164),sK129(U_2164,U_2163)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2164),U_2163)) ),
    inference(definitional_conversion,[status(esa)],[f_777_3]) ).

cnf(f_777_5,plain,
    ( U_2163 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(U_2164),sK129(U_2164,U_2163)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2164),U_2163)) ),
    inference(clausify,[status(thm)],[f_777_4]) ).

fof(f_778_1,plain,
    ! [Na,N_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_1))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Na))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_674_bounded__nat__set__is__finite]) ).

fof(f_778_2,plain,
    ! [U_2167,U_2166] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2166))
      | ? [U_2165] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2165),U_2167))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2165),U_2166)) ) ),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

fof(f_778_3,plain,
    ! [U_2167,U_2166] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2166))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK130(U_2167,U_2166)),U_2167))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK130(U_2167,U_2166)),U_2166)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_2165,sK130(U_2167,U_2166))],[f_778_2]) ).

fof(f_778_4,plain,
    ( ! [U_2166,U_2167] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK130(U_2167,U_2166)),U_2167))
        | ~ sP227(U_2166,U_2167) )
    & ! [U_2166,U_2167] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK130(U_2167,U_2166)),U_2166))
        | ~ sP227(U_2166,U_2167) )
    & ! [U_2166,U_2167] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2166))
        | sP227(U_2166,U_2167) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227])],[f_778_3]) ).

cnf(f_778_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2166))
    | sP227(U_2166,U_2167) ),
    inference(clausify,[status(thm)],[f_778_4]) ).

cnf(f_778_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK130(U_2167,U_2166)),U_2166))
    | ~ sP227(U_2166,U_2167) ),
    inference(clausify,[status(thm)],[f_778_4]) ).

cnf(f_778_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK130(U_2167,U_2166)),U_2167))
    | ~ sP227(U_2166,U_2167) ),
    inference(clausify,[status(thm)],[f_778_4]) ).

fof(f_779_1,plain,
    ! [I_1,J_1,F] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
      | ? [I_2,J] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J)) ) ),
    inference(fof_nnf,[status(thm)],[fact_675_less__mono__imp__le__mono]) ).

fof(f_779_2,plain,
    ! [U_2172,U_2171,U_2170] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_2170,U_2172)),hAPP_nat_nat(U_2170,U_2171)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2172),U_2171))
      | ? [U_2169,U_2168] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_2170,U_2169)),hAPP_nat_nat(U_2170,U_2168)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2169),U_2168)) ) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

fof(f_779_3,plain,
    ! [U_2172,U_2171,U_2170] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_2170,U_2172)),hAPP_nat_nat(U_2170,U_2171)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2172),U_2171))
      | ? [U_2168] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_2170,sK131(U_2172,U_2171,U_2170))),hAPP_nat_nat(U_2170,U_2168)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK131(U_2172,U_2171,U_2170)),U_2168)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_2169,sK131(U_2172,U_2171,U_2170))],[f_779_2]) ).

fof(f_779_4,plain,
    ! [U_2172,U_2171,U_2170] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_2170,U_2172)),hAPP_nat_nat(U_2170,U_2171)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2172),U_2171))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_2170,sK131(U_2172,U_2171,U_2170))),hAPP_nat_nat(U_2170,sK132(U_2172,U_2171,U_2170))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK131(U_2172,U_2171,U_2170)),sK132(U_2172,U_2171,U_2170))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_2168,sK132(U_2172,U_2171,U_2170))],[f_779_3]) ).

fof(f_779_5,plain,
    ( ! [U_2170,U_2171,U_2172] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_2170,sK131(U_2172,U_2171,U_2170))),hAPP_nat_nat(U_2170,sK132(U_2172,U_2171,U_2170))))
        | ~ sP228(U_2170,U_2171,U_2172) )
    & ! [U_2170,U_2171,U_2172] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK131(U_2172,U_2171,U_2170)),sK132(U_2172,U_2171,U_2170)))
        | ~ sP228(U_2170,U_2171,U_2172) )
    & ! [U_2170,U_2171,U_2172] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_2170,U_2172)),hAPP_nat_nat(U_2170,U_2171)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2172),U_2171))
        | sP228(U_2170,U_2171,U_2172) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228])],[f_779_4]) ).

cnf(f_779_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_2170,U_2172)),hAPP_nat_nat(U_2170,U_2171)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2172),U_2171))
    | sP228(U_2170,U_2171,U_2172) ),
    inference(clausify,[status(thm)],[f_779_5]) ).

cnf(f_779_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK131(U_2172,U_2171,U_2170)),sK132(U_2172,U_2171,U_2170)))
    | ~ sP228(U_2170,U_2171,U_2172) ),
    inference(clausify,[status(thm)],[f_779_5]) ).

cnf(f_779_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_2170,sK131(U_2172,U_2171,U_2170))),hAPP_nat_nat(U_2170,sK132(U_2172,U_2171,U_2170))))
    | ~ sP228(U_2170,U_2171,U_2172) ),
    inference(clausify,[status(thm)],[f_779_5]) ).

fof(f_780_1,plain,
    ! [I,K] :
      ( ? [J] :
          ( K = hAPP_nat_nat(suc,J)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K)) ),
    inference(fof_nnf,[status(thm)],[fact_676_Suc__lessE]) ).

fof(f_780_2,plain,
    ! [U_2175,U_2174] :
      ( ? [U_2173] :
          ( U_2174 = hAPP_nat_nat(suc,U_2173)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2175),U_2173)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2175)),U_2174)) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

fof(f_780_3,plain,
    ! [U_2175,U_2174] :
      ( ( U_2174 = hAPP_nat_nat(suc,sK133(U_2175,U_2174))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2175),sK133(U_2175,U_2174))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2175)),U_2174)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_2173,sK133(U_2175,U_2174))],[f_780_2]) ).

fof(f_780_4,plain,
    ( ! [U_2174,U_2175] :
        ( U_2174 = hAPP_nat_nat(suc,sK133(U_2175,U_2174))
        | ~ sP229(U_2174,U_2175) )
    & ! [U_2174,U_2175] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2175),sK133(U_2175,U_2174)))
        | ~ sP229(U_2174,U_2175) )
    & ! [U_2174,U_2175] :
        ( sP229(U_2174,U_2175)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2175)),U_2174)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229])],[f_780_3]) ).

cnf(f_780_5,plain,
    ( sP229(U_2174,U_2175)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2175)),U_2174)) ),
    inference(clausify,[status(thm)],[f_780_4]) ).

cnf(f_780_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2175),sK133(U_2175,U_2174)))
    | ~ sP229(U_2174,U_2175) ),
    inference(clausify,[status(thm)],[f_780_4]) ).

cnf(f_780_7,plain,
    ( U_2174 = hAPP_nat_nat(suc,sK133(U_2175,U_2174))
    | ~ sP229(U_2174,U_2175) ),
    inference(clausify,[status(thm)],[f_780_4]) ).

fof(f_781_1,plain,
    ! [I,K] :
      ( ? [J] :
          ( K = hAPP_nat_nat(suc,J)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) )
      | K = hAPP_nat_nat(suc,I)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K)) ),
    inference(fof_nnf,[status(thm)],[fact_677_lessE]) ).

fof(f_781_2,plain,
    ! [U_2178,U_2177] :
      ( ? [U_2176] :
          ( U_2177 = hAPP_nat_nat(suc,U_2176)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2178),U_2176)) )
      | U_2177 = hAPP_nat_nat(suc,U_2178)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2178),U_2177)) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

fof(f_781_3,plain,
    ! [U_2178,U_2177] :
      ( ( U_2177 = hAPP_nat_nat(suc,sK134(U_2178,U_2177))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2178),sK134(U_2178,U_2177))) )
      | U_2177 = hAPP_nat_nat(suc,U_2178)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2178),U_2177)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_2176,sK134(U_2178,U_2177))],[f_781_2]) ).

fof(f_781_4,plain,
    ( ! [U_2178,U_2177] :
        ( U_2177 = hAPP_nat_nat(suc,sK134(U_2178,U_2177))
        | ~ sP230(U_2178,U_2177) )
    & ! [U_2178,U_2177] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2178),sK134(U_2178,U_2177)))
        | ~ sP230(U_2178,U_2177) )
    & ! [U_2178,U_2177] :
        ( sP230(U_2178,U_2177)
        | U_2177 = hAPP_nat_nat(suc,U_2178)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2178),U_2177)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP230])],[f_781_3]) ).

cnf(f_781_5,plain,
    ( sP230(U_2178,U_2177)
    | U_2177 = hAPP_nat_nat(suc,U_2178)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2178),U_2177)) ),
    inference(clausify,[status(thm)],[f_781_4]) ).

cnf(f_781_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2178),sK134(U_2178,U_2177)))
    | ~ sP230(U_2178,U_2177) ),
    inference(clausify,[status(thm)],[f_781_4]) ).

cnf(f_781_7,plain,
    ( U_2177 = hAPP_nat_nat(suc,sK134(U_2178,U_2177))
    | ~ sP230(U_2178,U_2177) ),
    inference(clausify,[status(thm)],[f_781_4]) ).

fof(f_782_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    inference(fof_nnf,[status(thm)],[fact_678_less__zeroE]) ).

fof(f_782_2,plain,
    ! [U_2179] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2179),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

fof(f_782_3,plain,
    ! [U_2179] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2179),zero_zero_nat)),
    inference(definitional_conversion,[status(esa)],[f_782_2]) ).

cnf(f_782_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2179),zero_zero_nat)),
    inference(clausify,[status(thm)],[f_782_3]) ).

fof(f_783_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)),
    inference(fof_nnf,[status(thm)],[fact_679_le0]) ).

fof(f_783_2,plain,
    ! [U_2180] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2180)),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

fof(f_783_3,plain,
    ! [U_2180] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2180)),
    inference(definitional_conversion,[status(esa)],[f_783_2]) ).

cnf(f_783_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2180)),
    inference(clausify,[status(thm)],[f_783_3]) ).

fof(f_784_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_680_zero__less__Suc]) ).

fof(f_784_2,plain,
    ! [U_2181] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,U_2181))),
    inference(variable_rename,[status(thm)],[f_784_1]) ).

fof(f_784_3,plain,
    ! [U_2181] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,U_2181))),
    inference(definitional_conversion,[status(esa)],[f_784_2]) ).

cnf(f_784_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,U_2181))),
    inference(clausify,[status(thm)],[f_784_3]) ).

fof(f_785_1,plain,
    ! [M_1,Na] :
      ( ( hAPP_nat_nat(plus_plus_nat(M_1),Na) = hAPP_nat_nat(suc,zero_zero_nat)
        | ( ( Na != hAPP_nat_nat(suc,zero_zero_nat)
            | M_1 != zero_zero_nat )
          & ( Na != zero_zero_nat
            | M_1 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_1 = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M_1 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(plus_plus_nat(M_1),Na) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_681_add__is__1]) ).

fof(f_785_2,plain,
    ! [U_2183,U_2182] :
      ( ( hAPP_nat_nat(plus_plus_nat(U_2183),U_2182) = hAPP_nat_nat(suc,zero_zero_nat)
        | ( ( U_2182 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_2183 != zero_zero_nat )
          & ( U_2182 != zero_zero_nat
            | U_2183 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( U_2182 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_2183 = zero_zero_nat )
        | ( U_2182 = zero_zero_nat
          & U_2183 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(plus_plus_nat(U_2183),U_2182) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

fof(f_785_3,plain,
    ( ! [U_2187,U_2185] :
        ( hAPP_nat_nat(plus_plus_nat(U_2187),U_2185) = hAPP_nat_nat(suc,zero_zero_nat)
        | ( ( U_2185 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_2187 != zero_zero_nat )
          & ( U_2185 != zero_zero_nat
            | U_2187 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
    & ! [U_2186,U_2184] :
        ( ( U_2184 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_2186 = zero_zero_nat )
        | ( U_2184 = zero_zero_nat
          & U_2186 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(plus_plus_nat(U_2186),U_2184) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(miniscope,[status(thm)],[f_785_2]) ).

fof(f_785_4,plain,
    ( ! [U_2187,U_2185] :
        ( U_2185 != hAPP_nat_nat(suc,zero_zero_nat)
        | U_2187 != zero_zero_nat
        | ~ sP233(U_2187,U_2185) )
    & ! [U_2187,U_2185] :
        ( U_2185 != zero_zero_nat
        | U_2187 != hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP233(U_2187,U_2185) )
    & ! [U_2186,U_2184] :
        ( U_2184 = hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP232(U_2186,U_2184) )
    & ! [U_2186,U_2184] :
        ( U_2186 = zero_zero_nat
        | ~ sP232(U_2186,U_2184) )
    & ! [U_2186,U_2184] :
        ( U_2184 = zero_zero_nat
        | ~ sP231(U_2186,U_2184) )
    & ! [U_2186,U_2184] :
        ( U_2186 = hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP231(U_2186,U_2184) )
    & ! [U_2187,U_2185] :
        ( hAPP_nat_nat(plus_plus_nat(U_2187),U_2185) = hAPP_nat_nat(suc,zero_zero_nat)
        | sP233(U_2187,U_2185) )
    & ! [U_2186,U_2184] :
        ( sP232(U_2186,U_2184)
        | sP231(U_2186,U_2184)
        | hAPP_nat_nat(plus_plus_nat(U_2186),U_2184) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231,sP232,sP233])],[f_785_3]) ).

cnf(f_785_5,plain,
    ( sP232(U_2186,U_2184)
    | sP231(U_2186,U_2184)
    | hAPP_nat_nat(plus_plus_nat(U_2186),U_2184) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_785_4]) ).

cnf(f_785_6,plain,
    ( hAPP_nat_nat(plus_plus_nat(U_2187),U_2185) = hAPP_nat_nat(suc,zero_zero_nat)
    | sP233(U_2187,U_2185) ),
    inference(clausify,[status(thm)],[f_785_4]) ).

cnf(f_785_7,plain,
    ( U_2186 = hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP231(U_2186,U_2184) ),
    inference(clausify,[status(thm)],[f_785_4]) ).

cnf(f_785_8,plain,
    ( U_2184 = zero_zero_nat
    | ~ sP231(U_2186,U_2184) ),
    inference(clausify,[status(thm)],[f_785_4]) ).

cnf(f_785_9,plain,
    ( U_2186 = zero_zero_nat
    | ~ sP232(U_2186,U_2184) ),
    inference(clausify,[status(thm)],[f_785_4]) ).

cnf(f_785_10,plain,
    ( U_2184 = hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP232(U_2186,U_2184) ),
    inference(clausify,[status(thm)],[f_785_4]) ).

cnf(f_785_11,plain,
    ( U_2185 != zero_zero_nat
    | U_2187 != hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP233(U_2187,U_2185) ),
    inference(clausify,[status(thm)],[f_785_4]) ).

cnf(f_785_12,plain,
    ( U_2185 != hAPP_nat_nat(suc,zero_zero_nat)
    | U_2187 != zero_zero_nat
    | ~ sP233(U_2187,U_2185) ),
    inference(clausify,[status(thm)],[f_785_4]) ).

fof(f_786_1,plain,
    ! [M_1,Na] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(M_1),Na)
        | ( ( Na != hAPP_nat_nat(suc,zero_zero_nat)
            | M_1 != zero_zero_nat )
          & ( Na != zero_zero_nat
            | M_1 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M_1 = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M_1 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(plus_plus_nat(M_1),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_682_one__is__add]) ).

fof(f_786_2,plain,
    ! [U_2189,U_2188] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(U_2189),U_2188)
        | ( ( U_2188 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_2189 != zero_zero_nat )
          & ( U_2188 != zero_zero_nat
            | U_2189 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( U_2188 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_2189 = zero_zero_nat )
        | ( U_2188 = zero_zero_nat
          & U_2189 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(plus_plus_nat(U_2189),U_2188) ) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

fof(f_786_3,plain,
    ( ! [U_2193,U_2191] :
        ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(U_2193),U_2191)
        | ( ( U_2191 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_2193 != zero_zero_nat )
          & ( U_2191 != zero_zero_nat
            | U_2193 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
    & ! [U_2192,U_2190] :
        ( ( U_2190 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_2192 = zero_zero_nat )
        | ( U_2190 = zero_zero_nat
          & U_2192 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(plus_plus_nat(U_2192),U_2190) ) ),
    inference(miniscope,[status(thm)],[f_786_2]) ).

fof(f_786_4,plain,
    ( ! [U_2191,U_2193] :
        ( U_2191 != hAPP_nat_nat(suc,zero_zero_nat)
        | U_2193 != zero_zero_nat
        | ~ sP236(U_2191,U_2193) )
    & ! [U_2191,U_2193] :
        ( U_2191 != zero_zero_nat
        | U_2193 != hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP236(U_2191,U_2193) )
    & ! [U_2190,U_2192] :
        ( U_2190 = hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP235(U_2190,U_2192) )
    & ! [U_2190,U_2192] :
        ( U_2192 = zero_zero_nat
        | ~ sP235(U_2190,U_2192) )
    & ! [U_2190,U_2192] :
        ( U_2190 = zero_zero_nat
        | ~ sP234(U_2190,U_2192) )
    & ! [U_2190,U_2192] :
        ( U_2192 = hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP234(U_2190,U_2192) )
    & ! [U_2191,U_2193] :
        ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(U_2193),U_2191)
        | sP236(U_2191,U_2193) )
    & ! [U_2190,U_2192] :
        ( sP235(U_2190,U_2192)
        | sP234(U_2190,U_2192)
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(plus_plus_nat(U_2192),U_2190) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234,sP235,sP236])],[f_786_3]) ).

cnf(f_786_5,plain,
    ( sP235(U_2190,U_2192)
    | sP234(U_2190,U_2192)
    | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(plus_plus_nat(U_2192),U_2190) ),
    inference(clausify,[status(thm)],[f_786_4]) ).

cnf(f_786_6,plain,
    ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(U_2193),U_2191)
    | sP236(U_2191,U_2193) ),
    inference(clausify,[status(thm)],[f_786_4]) ).

cnf(f_786_7,plain,
    ( U_2192 = hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP234(U_2190,U_2192) ),
    inference(clausify,[status(thm)],[f_786_4]) ).

cnf(f_786_8,plain,
    ( U_2190 = zero_zero_nat
    | ~ sP234(U_2190,U_2192) ),
    inference(clausify,[status(thm)],[f_786_4]) ).

cnf(f_786_9,plain,
    ( U_2192 = zero_zero_nat
    | ~ sP235(U_2190,U_2192) ),
    inference(clausify,[status(thm)],[f_786_4]) ).

cnf(f_786_10,plain,
    ( U_2190 = hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP235(U_2190,U_2192) ),
    inference(clausify,[status(thm)],[f_786_4]) ).

cnf(f_786_11,plain,
    ( U_2191 != zero_zero_nat
    | U_2193 != hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP236(U_2191,U_2193) ),
    inference(clausify,[status(thm)],[f_786_4]) ).

cnf(f_786_12,plain,
    ( U_2191 != hAPP_nat_nat(suc,zero_zero_nat)
    | U_2193 != zero_zero_nat
    | ~ sP236(U_2191,U_2193) ),
    inference(clausify,[status(thm)],[f_786_4]) ).

fof(f_787_1,plain,
    ! [N,M] : hAPP_nat_nat(minus_minus_nat(N),hAPP_nat_nat(plus_plus_nat(N),M)) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_683_diff__add__0]) ).

fof(f_787_2,plain,
    ! [U_2195,U_2194] : hAPP_nat_nat(minus_minus_nat(U_2195),hAPP_nat_nat(plus_plus_nat(U_2195),U_2194)) = zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_787_1]) ).

fof(f_787_3,plain,
    ! [U_2194,U_2195] : hAPP_nat_nat(minus_minus_nat(U_2195),hAPP_nat_nat(plus_plus_nat(U_2195),U_2194)) = zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_787_2]) ).

cnf(f_787_4,plain,
    hAPP_nat_nat(minus_minus_nat(U_2195),hAPP_nat_nat(plus_plus_nat(U_2195),U_2194)) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_787_3]) ).

fof(f_788_1,plain,
    ! [M,N] :
      ( hAPP_nat_nat(minus_minus_nat(M),N) = zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_684_diff__is__0__eq_H]) ).

fof(f_788_2,plain,
    ! [U_2197,U_2196] :
      ( hAPP_nat_nat(minus_minus_nat(U_2197),U_2196) = zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2197),U_2196)) ),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

fof(f_788_3,plain,
    ! [U_2197,U_2196] :
      ( hAPP_nat_nat(minus_minus_nat(U_2197),U_2196) = zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2197),U_2196)) ),
    inference(definitional_conversion,[status(esa)],[f_788_2]) ).

cnf(f_788_4,plain,
    ( hAPP_nat_nat(minus_minus_nat(U_2197),U_2196) = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2197),U_2196)) ),
    inference(clausify,[status(thm)],[f_788_3]) ).

fof(f_789_1,plain,
    ! [M_1,Na] :
      ( ( hAPP_nat_nat(minus_minus_nat(M_1),Na) = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | hAPP_nat_nat(minus_minus_nat(M_1),Na) != zero_zero_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_685_diff__is__0__eq]) ).

fof(f_789_2,plain,
    ! [U_2199,U_2198] :
      ( ( hAPP_nat_nat(minus_minus_nat(U_2199),U_2198) = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2199),U_2198)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2199),U_2198))
        | hAPP_nat_nat(minus_minus_nat(U_2199),U_2198) != zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

fof(f_789_3,plain,
    ( ! [U_2203,U_2201] :
        ( hAPP_nat_nat(minus_minus_nat(U_2203),U_2201) = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2203),U_2201)) )
    & ! [U_2202,U_2200] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2202),U_2200))
        | hAPP_nat_nat(minus_minus_nat(U_2202),U_2200) != zero_zero_nat ) ),
    inference(miniscope,[status(thm)],[f_789_2]) ).

fof(f_789_4,plain,
    ( ! [U_2201,U_2203] :
        ( hAPP_nat_nat(minus_minus_nat(U_2203),U_2201) = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2203),U_2201)) )
    & ! [U_2200,U_2202] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2202),U_2200))
        | hAPP_nat_nat(minus_minus_nat(U_2202),U_2200) != zero_zero_nat ) ),
    inference(definitional_conversion,[status(esa)],[f_789_3]) ).

cnf(f_789_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2202),U_2200))
    | hAPP_nat_nat(minus_minus_nat(U_2202),U_2200) != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_789_4]) ).

cnf(f_789_6,plain,
    ( hAPP_nat_nat(minus_minus_nat(U_2203),U_2201) = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2203),U_2201)) ),
    inference(clausify,[status(thm)],[f_789_4]) ).

fof(f_790_1,plain,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    inference(fof_nnf,[status(thm)],[fact_686_One__nat__def]) ).

fof(f_790_2,plain,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    inference(definitional_conversion,[status(esa)],[f_790_1]) ).

cnf(f_790_3,plain,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    inference(clausify,[status(thm)],[f_790_2]) ).

fof(f_791_1,plain,
    ! [M,N] :
      ( M = N
      | hAPP_nat_nat(minus_minus_nat(N),M) != zero_zero_nat
      | hAPP_nat_nat(minus_minus_nat(M),N) != zero_zero_nat ),
    inference(fof_nnf,[status(thm)],[fact_687_diffs0__imp__equal]) ).

fof(f_791_2,plain,
    ! [U_2205,U_2204] :
      ( U_2205 = U_2204
      | hAPP_nat_nat(minus_minus_nat(U_2204),U_2205) != zero_zero_nat
      | hAPP_nat_nat(minus_minus_nat(U_2205),U_2204) != zero_zero_nat ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

fof(f_791_3,plain,
    ! [U_2204,U_2205] :
      ( U_2205 = U_2204
      | hAPP_nat_nat(minus_minus_nat(U_2204),U_2205) != zero_zero_nat
      | hAPP_nat_nat(minus_minus_nat(U_2205),U_2204) != zero_zero_nat ),
    inference(definitional_conversion,[status(esa)],[f_791_2]) ).

cnf(f_791_4,plain,
    ( U_2205 = U_2204
    | hAPP_nat_nat(minus_minus_nat(U_2204),U_2205) != zero_zero_nat
    | hAPP_nat_nat(minus_minus_nat(U_2205),U_2204) != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_791_3]) ).

fof(f_792_1,plain,
    ! [M] : hAPP_nat_nat(minus_minus_nat(M),M) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_688_diff__self__eq__0]) ).

fof(f_792_2,plain,
    ! [U_2206] : hAPP_nat_nat(minus_minus_nat(U_2206),U_2206) = zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_792_1]) ).

fof(f_792_3,plain,
    ! [U_2206] : hAPP_nat_nat(minus_minus_nat(U_2206),U_2206) = zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_792_2]) ).

cnf(f_792_4,plain,
    hAPP_nat_nat(minus_minus_nat(U_2206),U_2206) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_792_3]) ).

fof(f_793_1,plain,
    ! [M] : hAPP_nat_nat(minus_minus_nat(M),zero_zero_nat) = M,
    inference(fof_nnf,[status(thm)],[fact_689_minus__nat_Odiff__0]) ).

fof(f_793_2,plain,
    ! [U_2207] : hAPP_nat_nat(minus_minus_nat(U_2207),zero_zero_nat) = U_2207,
    inference(variable_rename,[status(thm)],[f_793_1]) ).

fof(f_793_3,plain,
    ! [U_2207] : hAPP_nat_nat(minus_minus_nat(U_2207),zero_zero_nat) = U_2207,
    inference(definitional_conversion,[status(esa)],[f_793_2]) ).

cnf(f_793_4,plain,
    hAPP_nat_nat(minus_minus_nat(U_2207),zero_zero_nat) = U_2207,
    inference(clausify,[status(thm)],[f_793_3]) ).

fof(f_794_1,plain,
    ! [N] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),N) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_690_diff__0__eq__0]) ).

fof(f_794_2,plain,
    ! [U_2208] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),U_2208) = zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_794_1]) ).

fof(f_794_3,plain,
    ! [U_2208] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),U_2208) = zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_794_2]) ).

cnf(f_794_4,plain,
    hAPP_nat_nat(minus_minus_nat(zero_zero_nat),U_2208) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_794_3]) ).

fof(f_795_1,plain,
    ! [M] : hAPP_nat_nat(suc,M) != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_691_Suc__neq__Zero]) ).

fof(f_795_2,plain,
    ! [U_2209] : hAPP_nat_nat(suc,U_2209) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_795_1]) ).

fof(f_795_3,plain,
    ! [U_2209] : hAPP_nat_nat(suc,U_2209) != zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_795_2]) ).

cnf(f_795_4,plain,
    hAPP_nat_nat(suc,U_2209) != zero_zero_nat,
    inference(clausify,[status(thm)],[f_795_3]) ).

fof(f_796_1,plain,
    ! [M] : zero_zero_nat != hAPP_nat_nat(suc,M),
    inference(fof_nnf,[status(thm)],[fact_692_Zero__neq__Suc]) ).

fof(f_796_2,plain,
    ! [U_2210] : zero_zero_nat != hAPP_nat_nat(suc,U_2210),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

fof(f_796_3,plain,
    ! [U_2210] : zero_zero_nat != hAPP_nat_nat(suc,U_2210),
    inference(definitional_conversion,[status(esa)],[f_796_2]) ).

cnf(f_796_4,plain,
    zero_zero_nat != hAPP_nat_nat(suc,U_2210),
    inference(clausify,[status(thm)],[f_796_3]) ).

fof(f_797_1,plain,
    ! [Nat_1] : hAPP_nat_nat(suc,Nat_1) != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_693_nat_Osimps_I3_J]) ).

fof(f_797_2,plain,
    ! [U_2211] : hAPP_nat_nat(suc,U_2211) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_797_1]) ).

fof(f_797_3,plain,
    ! [U_2211] : hAPP_nat_nat(suc,U_2211) != zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_797_2]) ).

cnf(f_797_4,plain,
    hAPP_nat_nat(suc,U_2211) != zero_zero_nat,
    inference(clausify,[status(thm)],[f_797_3]) ).

fof(f_798_1,plain,
    ! [M] : hAPP_nat_nat(suc,M) != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_694_Suc__not__Zero]) ).

fof(f_798_2,plain,
    ! [U_2212] : hAPP_nat_nat(suc,U_2212) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_798_1]) ).

fof(f_798_3,plain,
    ! [U_2212] : hAPP_nat_nat(suc,U_2212) != zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_798_2]) ).

cnf(f_798_4,plain,
    hAPP_nat_nat(suc,U_2212) != zero_zero_nat,
    inference(clausify,[status(thm)],[f_798_3]) ).

fof(f_799_1,plain,
    ! [Nat] : zero_zero_nat != hAPP_nat_nat(suc,Nat),
    inference(fof_nnf,[status(thm)],[fact_695_nat_Osimps_I2_J]) ).

fof(f_799_2,plain,
    ! [U_2213] : zero_zero_nat != hAPP_nat_nat(suc,U_2213),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

fof(f_799_3,plain,
    ! [U_2213] : zero_zero_nat != hAPP_nat_nat(suc,U_2213),
    inference(definitional_conversion,[status(esa)],[f_799_2]) ).

cnf(f_799_4,plain,
    zero_zero_nat != hAPP_nat_nat(suc,U_2213),
    inference(clausify,[status(thm)],[f_799_3]) ).

fof(f_800_1,plain,
    ! [M] : zero_zero_nat != hAPP_nat_nat(suc,M),
    inference(fof_nnf,[status(thm)],[fact_696_Zero__not__Suc]) ).

fof(f_800_2,plain,
    ! [U_2214] : zero_zero_nat != hAPP_nat_nat(suc,U_2214),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

fof(f_800_3,plain,
    ! [U_2214] : zero_zero_nat != hAPP_nat_nat(suc,U_2214),
    inference(definitional_conversion,[status(esa)],[f_800_2]) ).

cnf(f_800_4,plain,
    zero_zero_nat != hAPP_nat_nat(suc,U_2214),
    inference(clausify,[status(thm)],[f_800_3]) ).

fof(f_801_1,plain,
    bot_bot_nat = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_697_bot__nat__def]) ).

fof(f_801_2,plain,
    bot_bot_nat = zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_801_1]) ).

cnf(f_801_3,plain,
    bot_bot_nat = zero_zero_nat,
    inference(clausify,[status(thm)],[f_801_2]) ).

fof(f_802_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_698_le__0__eq]) ).

fof(f_802_2,plain,
    ! [U_2215] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2215),zero_zero_nat))
        | U_2215 != zero_zero_nat )
      & ( U_2215 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2215),zero_zero_nat)) ) ),
    inference(variable_rename,[status(thm)],[f_802_1]) ).

fof(f_802_3,plain,
    ( ! [U_2217] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2217),zero_zero_nat))
        | U_2217 != zero_zero_nat )
    & ! [U_2216] :
        ( U_2216 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2216),zero_zero_nat)) ) ),
    inference(miniscope,[status(thm)],[f_802_2]) ).

fof(f_802_4,plain,
    ( ! [U_2217] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2217),zero_zero_nat))
        | U_2217 != zero_zero_nat )
    & ! [U_2216] :
        ( U_2216 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2216),zero_zero_nat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_802_3]) ).

cnf(f_802_5,plain,
    ( U_2216 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2216),zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_802_4]) ).

cnf(f_802_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2217),zero_zero_nat))
    | U_2217 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_802_4]) ).

fof(f_803_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)),
    inference(fof_nnf,[status(thm)],[fact_699_less__eq__nat_Osimps_I1_J]) ).

fof(f_803_2,plain,
    ! [U_2218] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2218)),
    inference(variable_rename,[status(thm)],[f_803_1]) ).

fof(f_803_3,plain,
    ! [U_2218] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2218)),
    inference(definitional_conversion,[status(esa)],[f_803_2]) ).

cnf(f_803_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2218)),
    inference(clausify,[status(thm)],[f_803_3]) ).

fof(f_804_1,plain,
    ! [P] :
      ( ~ hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(fNot,P)) ),
    inference(fof_nnf,[status(thm)],[help_fNot_1_1_U]) ).

fof(f_804_2,plain,
    ! [U_2219] :
      ( ~ hBOOL(U_2219)
      | ~ hBOOL(hAPP_bool_bool(fNot,U_2219)) ),
    inference(variable_rename,[status(thm)],[f_804_1]) ).

fof(f_804_3,plain,
    ! [U_2219] :
      ( ~ hBOOL(U_2219)
      | ~ hBOOL(hAPP_bool_bool(fNot,U_2219)) ),
    inference(definitional_conversion,[status(esa)],[f_804_2]) ).

cnf(f_804_4,plain,
    ( ~ hBOOL(U_2219)
    | ~ hBOOL(hAPP_bool_bool(fNot,U_2219)) ),
    inference(clausify,[status(thm)],[f_804_3]) ).

fof(f_805_1,plain,
    ! [P] :
      ( hBOOL(hAPP_bool_bool(fNot,P))
      | hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fNot_2_1_U]) ).

fof(f_805_2,plain,
    ! [U_2220] :
      ( hBOOL(hAPP_bool_bool(fNot,U_2220))
      | hBOOL(U_2220) ),
    inference(variable_rename,[status(thm)],[f_805_1]) ).

fof(f_805_3,plain,
    ! [U_2220] :
      ( hBOOL(hAPP_bool_bool(fNot,U_2220))
      | hBOOL(U_2220) ),
    inference(definitional_conversion,[status(esa)],[f_805_2]) ).

cnf(f_805_4,plain,
    ( hBOOL(hAPP_bool_bool(fNot,U_2220))
    | hBOOL(U_2220) ),
    inference(clausify,[status(thm)],[f_805_3]) ).

fof(f_806_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_806_2,plain,
    ! [U_2222,U_2221] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2221),U_2222))
      | ~ hBOOL(U_2222)
      | ~ hBOOL(U_2221) ),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

fof(f_806_3,plain,
    ! [U_2222] :
      ( ! [U_2221] :
          ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2221),U_2222))
          | ~ hBOOL(U_2221) )
      | ~ hBOOL(U_2222) ),
    inference(miniscope,[status(thm)],[f_806_2]) ).

fof(f_806_4,plain,
    ! [U_2221,U_2222] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2221),U_2222))
      | ~ hBOOL(U_2221)
      | ~ hBOOL(U_2222) ),
    inference(definitional_conversion,[status(esa)],[f_806_3]) ).

cnf(f_806_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2221),U_2222))
    | ~ hBOOL(U_2221)
    | ~ hBOOL(U_2222) ),
    inference(clausify,[status(thm)],[f_806_4]) ).

fof(f_807_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_807_2,plain,
    ! [U_2224,U_2223] :
      ( hBOOL(U_2224)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2224),U_2223)) ),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

fof(f_807_3,plain,
    ! [U_2224] :
      ( ! [U_2223] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2224),U_2223))
      | hBOOL(U_2224) ),
    inference(miniscope,[status(thm)],[f_807_2]) ).

fof(f_807_4,plain,
    ! [U_2224,U_2223] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2224),U_2223))
      | hBOOL(U_2224) ),
    inference(definitional_conversion,[status(esa)],[f_807_3]) ).

cnf(f_807_5,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2224),U_2223))
    | hBOOL(U_2224) ),
    inference(clausify,[status(thm)],[f_807_4]) ).

fof(f_808_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_808_2,plain,
    ! [U_2226,U_2225] :
      ( hBOOL(U_2225)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2226),U_2225)) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

fof(f_808_3,plain,
    ! [U_2225,U_2226] :
      ( hBOOL(U_2225)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2226),U_2225)) ),
    inference(definitional_conversion,[status(esa)],[f_808_2]) ).

cnf(f_808_4,plain,
    ( hBOOL(U_2225)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_2226),U_2225)) ),
    inference(clausify,[status(thm)],[f_808_3]) ).

fof(f_809_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_809_2,plain,
    ! [U_2228,U_2227] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_2227),U_2228))
      | ~ hBOOL(U_2227) ),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

fof(f_809_3,plain,
    ! [U_2227,U_2228] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_2227),U_2228))
      | ~ hBOOL(U_2227) ),
    inference(definitional_conversion,[status(esa)],[f_809_2]) ).

cnf(f_809_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_2227),U_2228))
    | ~ hBOOL(U_2227) ),
    inference(clausify,[status(thm)],[f_809_3]) ).

fof(f_810_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_810_2,plain,
    ! [U_2230,U_2229] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_2230),U_2229))
      | ~ hBOOL(U_2229) ),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

fof(f_810_3,plain,
    ! [U_2229,U_2230] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_2230),U_2229))
      | ~ hBOOL(U_2229) ),
    inference(definitional_conversion,[status(esa)],[f_810_2]) ).

cnf(f_810_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_2230),U_2229))
    | ~ hBOOL(U_2229) ),
    inference(clausify,[status(thm)],[f_810_3]) ).

fof(f_811_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_811_2,plain,
    ! [U_2232,U_2231] :
      ( hBOOL(U_2231)
      | hBOOL(U_2232)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_2232),U_2231)) ),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

fof(f_811_3,plain,
    ! [U_2232] :
      ( ! [U_2231] :
          ( hBOOL(U_2231)
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_2232),U_2231)) )
      | hBOOL(U_2232) ),
    inference(miniscope,[status(thm)],[f_811_2]) ).

fof(f_811_4,plain,
    ! [U_2231,U_2232] :
      ( hBOOL(U_2231)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_2232),U_2231))
      | hBOOL(U_2232) ),
    inference(definitional_conversion,[status(esa)],[f_811_3]) ).

cnf(f_811_5,plain,
    ( hBOOL(U_2231)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_2232),U_2231))
    | hBOOL(U_2232) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

fof(f_812_1,plain,
    ~ hBOOL(fFalse),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_U]) ).

fof(f_812_2,plain,
    ~ hBOOL(fFalse),
    inference(definitional_conversion,[status(esa)],[f_812_1]) ).

cnf(f_812_3,plain,
    ~ hBOOL(fFalse),
    inference(clausify,[status(thm)],[f_812_2]) ).

fof(f_813_1,plain,
    ! [P] :
      ( P = fFalse
      | P = fTrue
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T]) ).

fof(f_813_2,plain,
    ! [U_2233] :
      ( U_2233 = fFalse
      | U_2233 = fTrue
      | ~ is_bool(U_2233) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

fof(f_813_3,plain,
    ! [U_2233] :
      ( U_2233 = fFalse
      | U_2233 = fTrue
      | ~ is_bool(U_2233) ),
    inference(definitional_conversion,[status(esa)],[f_813_2]) ).

cnf(f_813_4,plain,
    ( U_2233 = fFalse
    | U_2233 = fTrue
    | ~ is_bool(U_2233) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

fof(f_814_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_814_2,plain,
    ! [U_2235,U_2234] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_2234),U_2235))
      | hBOOL(U_2234) ),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

fof(f_814_3,plain,
    ! [U_2234,U_2235] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_2234),U_2235))
      | hBOOL(U_2234) ),
    inference(definitional_conversion,[status(esa)],[f_814_2]) ).

cnf(f_814_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_2234),U_2235))
    | hBOOL(U_2234) ),
    inference(clausify,[status(thm)],[f_814_3]) ).

fof(f_815_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_815_2,plain,
    ! [U_2237,U_2236] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_2237),U_2236))
      | ~ hBOOL(U_2236) ),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

fof(f_815_3,plain,
    ! [U_2236,U_2237] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_2237),U_2236))
      | ~ hBOOL(U_2236) ),
    inference(definitional_conversion,[status(esa)],[f_815_2]) ).

cnf(f_815_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_2237),U_2236))
    | ~ hBOOL(U_2236) ),
    inference(clausify,[status(thm)],[f_815_3]) ).

fof(f_816_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_816_2,plain,
    ! [U_2239,U_2238] :
      ( hBOOL(U_2238)
      | ~ hBOOL(U_2239)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_2239),U_2238)) ),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

fof(f_816_3,plain,
    ! [U_2239] :
      ( ! [U_2238] :
          ( hBOOL(U_2238)
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_2239),U_2238)) )
      | ~ hBOOL(U_2239) ),
    inference(miniscope,[status(thm)],[f_816_2]) ).

fof(f_816_4,plain,
    ! [U_2238,U_2239] :
      ( hBOOL(U_2238)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_2239),U_2238))
      | ~ hBOOL(U_2239) ),
    inference(definitional_conversion,[status(esa)],[f_816_3]) ).

cnf(f_816_5,plain,
    ( hBOOL(U_2238)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_2239),U_2238))
    | ~ hBOOL(U_2239) ),
    inference(clausify,[status(thm)],[f_816_4]) ).

fof(f_817_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_817_2,plain,
    ! [U_2241,U_2240] :
      ( U_2241 = U_2240
      | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_2241),U_2240))
      | ~ is_a(U_2240)
      | ~ is_a(U_2241) ),
    inference(variable_rename,[status(thm)],[f_817_1]) ).

fof(f_817_3,plain,
    ! [U_2240,U_2241] :
      ( U_2241 = U_2240
      | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_2241),U_2240))
      | ~ is_a(U_2240)
      | ~ is_a(U_2241) ),
    inference(definitional_conversion,[status(esa)],[f_817_2]) ).

cnf(f_817_4,plain,
    ( U_2241 = U_2240
    | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_2241),U_2240))
    | ~ is_a(U_2240)
    | ~ is_a(U_2241) ),
    inference(clausify,[status(thm)],[f_817_3]) ).

fof(f_818_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_818_2,plain,
    ! [U_2243,U_2242] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_2243),U_2242))
      | U_2243 != U_2242 ),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

fof(f_818_3,plain,
    ! [U_2243,U_2242] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_2243),U_2242))
      | U_2243 != U_2242 ),
    inference(definitional_conversion,[status(esa)],[f_818_2]) ).

cnf(f_818_4,plain,
    ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_2243),U_2242))
    | U_2243 != U_2242 ),
    inference(clausify,[status(thm)],[f_818_3]) ).

fof(f_819_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_819_2,plain,
    ! [U_2245,U_2244] :
      ( U_2245 = U_2244
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_2245),U_2244)) ),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

fof(f_819_3,plain,
    ! [U_2244,U_2245] :
      ( U_2245 = U_2244
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_2245),U_2244)) ),
    inference(definitional_conversion,[status(esa)],[f_819_2]) ).

cnf(f_819_4,plain,
    ( U_2245 = U_2244
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_2245),U_2244)) ),
    inference(clausify,[status(thm)],[f_819_3]) ).

fof(f_820_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_820_2,plain,
    ! [U_2247,U_2246] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_2247),U_2246))
      | U_2247 != U_2246 ),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

fof(f_820_3,plain,
    ! [U_2246,U_2247] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_2247),U_2246))
      | U_2247 != U_2246 ),
    inference(definitional_conversion,[status(esa)],[f_820_2]) ).

cnf(f_820_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_2247),U_2246))
    | U_2247 != U_2246 ),
    inference(clausify,[status(thm)],[f_820_3]) ).

fof(f_821_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_821_2,plain,
    ! [U_2249,U_2248] :
      ( U_2249 = U_2248
      | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_2249),U_2248))
      | ~ is_pname(U_2248)
      | ~ is_pname(U_2249) ),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

fof(f_821_3,plain,
    ! [U_2248,U_2249] :
      ( U_2249 = U_2248
      | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_2249),U_2248))
      | ~ is_pname(U_2248)
      | ~ is_pname(U_2249) ),
    inference(definitional_conversion,[status(esa)],[f_821_2]) ).

cnf(f_821_4,plain,
    ( U_2249 = U_2248
    | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_2249),U_2248))
    | ~ is_pname(U_2248)
    | ~ is_pname(U_2249) ),
    inference(clausify,[status(thm)],[f_821_3]) ).

fof(f_822_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_822_2,plain,
    ! [U_2251,U_2250] :
      ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_2251),U_2250))
      | U_2251 != U_2250 ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

fof(f_822_3,plain,
    ! [U_2251,U_2250] :
      ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_2251),U_2250))
      | U_2251 != U_2250 ),
    inference(definitional_conversion,[status(esa)],[f_822_2]) ).

cnf(f_822_4,plain,
    ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_2251),U_2250))
    | U_2251 != U_2250 ),
    inference(clausify,[status(thm)],[f_822_3]) ).

fof(f_823_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_823_2,plain,
    ! [U_2253,U_2252] :
      ( hAPP_a_bool(cOMBK_bool_a(U_2253),U_2252) = U_2253
      | ~ is_bool(U_2253) ),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

fof(f_823_3,plain,
    ! [U_2253] :
      ( ! [U_2252] : hAPP_a_bool(cOMBK_bool_a(U_2253),U_2252) = U_2253
      | ~ is_bool(U_2253) ),
    inference(miniscope,[status(thm)],[f_823_2]) ).

fof(f_823_4,plain,
    ! [U_2252,U_2253] :
      ( hAPP_a_bool(cOMBK_bool_a(U_2253),U_2252) = U_2253
      | ~ is_bool(U_2253) ),
    inference(definitional_conversion,[status(esa)],[f_823_3]) ).

cnf(f_823_5,plain,
    ( hAPP_a_bool(cOMBK_bool_a(U_2253),U_2252) = U_2253
    | ~ is_bool(U_2253) ),
    inference(clausify,[status(thm)],[f_823_4]) ).

fof(f_824_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_824_2,plain,
    ! [U_2255,U_2254] :
      ( hAPP_pname_a(cOMBK_a_pname(U_2255),U_2254) = U_2255
      | ~ is_a(U_2255) ),
    inference(variable_rename,[status(thm)],[f_824_1]) ).

fof(f_824_3,plain,
    ! [U_2255] :
      ( ! [U_2254] : hAPP_pname_a(cOMBK_a_pname(U_2255),U_2254) = U_2255
      | ~ is_a(U_2255) ),
    inference(miniscope,[status(thm)],[f_824_2]) ).

fof(f_824_4,plain,
    ! [U_2254,U_2255] :
      ( hAPP_pname_a(cOMBK_a_pname(U_2255),U_2254) = U_2255
      | ~ is_a(U_2255) ),
    inference(definitional_conversion,[status(esa)],[f_824_3]) ).

cnf(f_824_5,plain,
    ( hAPP_pname_a(cOMBK_a_pname(U_2255),U_2254) = U_2255
    | ~ is_a(U_2255) ),
    inference(clausify,[status(thm)],[f_824_4]) ).

fof(f_825_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_825_2,plain,
    ! [U_2258,U_2257,U_2256] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(U_2258),U_2257),U_2256) = hAPP_a_bool(hAPP_a_fun_a_bool(U_2258,U_2256),U_2257),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

fof(f_825_3,plain,
    ! [U_2256,U_2257,U_2258] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(U_2258),U_2257),U_2256) = hAPP_a_bool(hAPP_a_fun_a_bool(U_2258,U_2256),U_2257),
    inference(definitional_conversion,[status(esa)],[f_825_2]) ).

cnf(f_825_4,plain,
    hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(U_2258),U_2257),U_2256) = hAPP_a_bool(hAPP_a_fun_a_bool(U_2258,U_2256),U_2257),
    inference(clausify,[status(thm)],[f_825_3]) ).

fof(f_826_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_826_2,plain,
    ! [U_2260,U_2259] :
      ( hAPP_nat_bool(cOMBK_bool_nat(U_2260),U_2259) = U_2260
      | ~ is_bool(U_2260) ),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

fof(f_826_3,plain,
    ! [U_2260] :
      ( ! [U_2259] : hAPP_nat_bool(cOMBK_bool_nat(U_2260),U_2259) = U_2260
      | ~ is_bool(U_2260) ),
    inference(miniscope,[status(thm)],[f_826_2]) ).

fof(f_826_4,plain,
    ! [U_2259,U_2260] :
      ( hAPP_nat_bool(cOMBK_bool_nat(U_2260),U_2259) = U_2260
      | ~ is_bool(U_2260) ),
    inference(definitional_conversion,[status(esa)],[f_826_3]) ).

cnf(f_826_5,plain,
    ( hAPP_nat_bool(cOMBK_bool_nat(U_2260),U_2259) = U_2260
    | ~ is_bool(U_2260) ),
    inference(clausify,[status(thm)],[f_826_4]) ).

fof(f_827_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_827_2,plain,
    ! [U_2262,U_2261] :
      ( U_2262 = U_2261
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_2262),U_2261))
      | ~ is_fun_a_bool(U_2261)
      | ~ is_fun_a_bool(U_2262) ),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

fof(f_827_3,plain,
    ! [U_2261,U_2262] :
      ( U_2262 = U_2261
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_2262),U_2261))
      | ~ is_fun_a_bool(U_2261)
      | ~ is_fun_a_bool(U_2262) ),
    inference(definitional_conversion,[status(esa)],[f_827_2]) ).

cnf(f_827_4,plain,
    ( U_2262 = U_2261
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_2262),U_2261))
    | ~ is_fun_a_bool(U_2261)
    | ~ is_fun_a_bool(U_2262) ),
    inference(clausify,[status(thm)],[f_827_3]) ).

fof(f_828_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_828_2,plain,
    ! [U_2264,U_2263] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_2264),U_2263))
      | U_2264 != U_2263 ),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

fof(f_828_3,plain,
    ! [U_2263,U_2264] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_2264),U_2263))
      | U_2264 != U_2263 ),
    inference(definitional_conversion,[status(esa)],[f_828_2]) ).

cnf(f_828_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_2264),U_2263))
    | U_2264 != U_2263 ),
    inference(clausify,[status(thm)],[f_828_3]) ).

fof(f_829_1,plain,
    ! [P,Q] :
      ( hAPP_pname_bool(cOMBK_bool_pname(P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U]) ).

fof(f_829_2,plain,
    ! [U_2266,U_2265] :
      ( hAPP_pname_bool(cOMBK_bool_pname(U_2266),U_2265) = U_2266
      | ~ is_bool(U_2266) ),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

fof(f_829_3,plain,
    ! [U_2266] :
      ( ! [U_2265] : hAPP_pname_bool(cOMBK_bool_pname(U_2266),U_2265) = U_2266
      | ~ is_bool(U_2266) ),
    inference(miniscope,[status(thm)],[f_829_2]) ).

fof(f_829_4,plain,
    ! [U_2266,U_2265] :
      ( hAPP_pname_bool(cOMBK_bool_pname(U_2266),U_2265) = U_2266
      | ~ is_bool(U_2266) ),
    inference(definitional_conversion,[status(esa)],[f_829_3]) ).

cnf(f_829_5,plain,
    ( hAPP_pname_bool(cOMBK_bool_pname(U_2266),U_2265) = U_2266
    | ~ is_bool(U_2266) ),
    inference(clausify,[status(thm)],[f_829_4]) ).

fof(f_830_1,plain,
    ! [P,Q,R] : hAPP_a_bool(hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_a_fun_nat_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000tc__Nat__Onat_000tc__HOL__Obool_U]) ).

fof(f_830_2,plain,
    ! [U_2269,U_2268,U_2267] : hAPP_a_bool(hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(U_2269),U_2268),U_2267) = hAPP_nat_bool(hAPP_a_fun_nat_bool(U_2269,U_2267),U_2268),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

fof(f_830_3,plain,
    ! [U_2267,U_2268,U_2269] : hAPP_a_bool(hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(U_2269),U_2268),U_2267) = hAPP_nat_bool(hAPP_a_fun_nat_bool(U_2269,U_2267),U_2268),
    inference(definitional_conversion,[status(esa)],[f_830_2]) ).

cnf(f_830_4,plain,
    hAPP_a_bool(hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(U_2269),U_2268),U_2267) = hAPP_nat_bool(hAPP_a_fun_nat_bool(U_2269,U_2267),U_2268),
    inference(clausify,[status(thm)],[f_830_3]) ).

fof(f_831_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(P),Q),R) = hAPP_a_bool(hAPP_nat_fun_a_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000t__a_000tc__HOL__Obool_U]) ).

fof(f_831_2,plain,
    ! [U_2272,U_2271,U_2270] : hAPP_nat_bool(hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(U_2272),U_2271),U_2270) = hAPP_a_bool(hAPP_nat_fun_a_bool(U_2272,U_2270),U_2271),
    inference(variable_rename,[status(thm)],[f_831_1]) ).

fof(f_831_3,plain,
    ! [U_2270,U_2271,U_2272] : hAPP_nat_bool(hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(U_2272),U_2271),U_2270) = hAPP_a_bool(hAPP_nat_fun_a_bool(U_2272,U_2270),U_2271),
    inference(definitional_conversion,[status(esa)],[f_831_2]) ).

cnf(f_831_4,plain,
    hAPP_nat_bool(hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(U_2272),U_2271),U_2270) = hAPP_a_bool(hAPP_nat_fun_a_bool(U_2272,U_2270),U_2271),
    inference(clausify,[status(thm)],[f_831_3]) ).

fof(f_832_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_832_2,plain,
    ! [U_2275,U_2274,U_2273] : hAPP_a_bool(cOMBB_bool_bool_a(U_2275,U_2274),U_2273) = hAPP_bool_bool(U_2275,hAPP_a_bool(U_2274,U_2273)),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

fof(f_832_3,plain,
    ! [U_2273,U_2274,U_2275] : hAPP_a_bool(cOMBB_bool_bool_a(U_2275,U_2274),U_2273) = hAPP_bool_bool(U_2275,hAPP_a_bool(U_2274,U_2273)),
    inference(definitional_conversion,[status(esa)],[f_832_2]) ).

cnf(f_832_4,plain,
    hAPP_a_bool(cOMBB_bool_bool_a(U_2275,U_2274),U_2273) = hAPP_bool_bool(U_2275,hAPP_a_bool(U_2274,U_2273)),
    inference(clausify,[status(thm)],[f_832_3]) ).

fof(f_833_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_833_2,plain,
    ! [U_2278,U_2277,U_2276] : hAPP_a_bool(cOMBS_a_bool_bool(U_2278,U_2277),U_2276) = hAPP_bool_bool(hAPP_a_fun_bool_bool(U_2278,U_2276),hAPP_a_bool(U_2277,U_2276)),
    inference(variable_rename,[status(thm)],[f_833_1]) ).

fof(f_833_3,plain,
    ! [U_2276,U_2277,U_2278] : hAPP_a_bool(cOMBS_a_bool_bool(U_2278,U_2277),U_2276) = hAPP_bool_bool(hAPP_a_fun_bool_bool(U_2278,U_2276),hAPP_a_bool(U_2277,U_2276)),
    inference(definitional_conversion,[status(esa)],[f_833_2]) ).

cnf(f_833_4,plain,
    hAPP_a_bool(cOMBS_a_bool_bool(U_2278,U_2277),U_2276) = hAPP_bool_bool(hAPP_a_fun_bool_bool(U_2278,U_2276),hAPP_a_bool(U_2277,U_2276)),
    inference(clausify,[status(thm)],[f_833_3]) ).

fof(f_834_1,plain,
    ! [P,Q,R] : hAPP_a_bool(hAPP_p1534023578a_bool(cOMBC_a_pname_bool(P),Q),R) = hAPP_pname_bool(hAPP_a93125764e_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U]) ).

fof(f_834_2,plain,
    ! [U_2281,U_2280,U_2279] : hAPP_a_bool(hAPP_p1534023578a_bool(cOMBC_a_pname_bool(U_2281),U_2280),U_2279) = hAPP_pname_bool(hAPP_a93125764e_bool(U_2281,U_2279),U_2280),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

fof(f_834_3,plain,
    ! [U_2279,U_2280,U_2281] : hAPP_a_bool(hAPP_p1534023578a_bool(cOMBC_a_pname_bool(U_2281),U_2280),U_2279) = hAPP_pname_bool(hAPP_a93125764e_bool(U_2281,U_2279),U_2280),
    inference(definitional_conversion,[status(esa)],[f_834_2]) ).

cnf(f_834_4,plain,
    hAPP_a_bool(hAPP_p1534023578a_bool(cOMBC_a_pname_bool(U_2281),U_2280),U_2279) = hAPP_pname_bool(hAPP_a93125764e_bool(U_2281,U_2279),U_2280),
    inference(clausify,[status(thm)],[f_834_3]) ).

fof(f_835_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_835_2,plain,
    ! [U_2284,U_2283,U_2282] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(U_2284),U_2283),U_2282) = hAPP_a_bool(hAPP_p1534023578a_bool(U_2284,U_2282),U_2283),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

fof(f_835_3,plain,
    ! [U_2282,U_2283,U_2284] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(U_2284),U_2283),U_2282) = hAPP_a_bool(hAPP_p1534023578a_bool(U_2284,U_2282),U_2283),
    inference(definitional_conversion,[status(esa)],[f_835_2]) ).

cnf(f_835_4,plain,
    hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(U_2284),U_2283),U_2282) = hAPP_a_bool(hAPP_p1534023578a_bool(U_2284,U_2282),U_2283),
    inference(clausify,[status(thm)],[f_835_3]) ).

fof(f_836_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_836_2,plain,
    ! [U_2286,U_2285] :
      ( U_2286 = U_2285
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_2286),U_2285)) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

fof(f_836_3,plain,
    ! [U_2285,U_2286] :
      ( U_2286 = U_2285
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_2286),U_2285)) ),
    inference(definitional_conversion,[status(esa)],[f_836_2]) ).

cnf(f_836_4,plain,
    ( U_2286 = U_2285
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_2286),U_2285)) ),
    inference(clausify,[status(thm)],[f_836_3]) ).

fof(f_837_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_837_2,plain,
    ! [U_2288,U_2287] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_2288),U_2287))
      | U_2288 != U_2287 ),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

fof(f_837_3,plain,
    ! [U_2287,U_2288] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_2288),U_2287))
      | U_2288 != U_2287 ),
    inference(definitional_conversion,[status(esa)],[f_837_2]) ).

cnf(f_837_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_2288),U_2287))
    | U_2288 != U_2287 ),
    inference(clausify,[status(thm)],[f_837_3]) ).

fof(f_838_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_838_2,plain,
    ! [U_2290,U_2289] :
      ( U_2290 = U_2289
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_2290),U_2289))
      | ~ is_fun_pname_bool(U_2289)
      | ~ is_fun_pname_bool(U_2290) ),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

fof(f_838_3,plain,
    ! [U_2289,U_2290] :
      ( U_2290 = U_2289
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_2290),U_2289))
      | ~ is_fun_pname_bool(U_2289)
      | ~ is_fun_pname_bool(U_2290) ),
    inference(definitional_conversion,[status(esa)],[f_838_2]) ).

cnf(f_838_4,plain,
    ( U_2290 = U_2289
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_2290),U_2289))
    | ~ is_fun_pname_bool(U_2289)
    | ~ is_fun_pname_bool(U_2290) ),
    inference(clausify,[status(thm)],[f_838_3]) ).

fof(f_839_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_839_2,plain,
    ! [U_2292,U_2291] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_2292),U_2291))
      | U_2292 != U_2291 ),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

fof(f_839_3,plain,
    ! [U_2291,U_2292] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_2292),U_2291))
      | U_2292 != U_2291 ),
    inference(definitional_conversion,[status(esa)],[f_839_2]) ).

cnf(f_839_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_2292),U_2291))
    | U_2292 != U_2291 ),
    inference(clausify,[status(thm)],[f_839_3]) ).

fof(f_840_1,plain,
    ! [P,Q,R] : hAPP_a_fun_a_bool(cOMBB_a_fun_a_bool_a(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_a_a(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a_U]) ).

fof(f_840_2,plain,
    ! [U_2295,U_2294,U_2293] : hAPP_a_fun_a_bool(cOMBB_a_fun_a_bool_a(U_2295,U_2294),U_2293) = hAPP_a_fun_a_bool(U_2295,hAPP_a_a(U_2294,U_2293)),
    inference(variable_rename,[status(thm)],[f_840_1]) ).

fof(f_840_3,plain,
    ! [U_2293,U_2294,U_2295] : hAPP_a_fun_a_bool(cOMBB_a_fun_a_bool_a(U_2295,U_2294),U_2293) = hAPP_a_fun_a_bool(U_2295,hAPP_a_a(U_2294,U_2293)),
    inference(definitional_conversion,[status(esa)],[f_840_2]) ).

cnf(f_840_4,plain,
    hAPP_a_fun_a_bool(cOMBB_a_fun_a_bool_a(U_2295,U_2294),U_2293) = hAPP_a_fun_a_bool(U_2295,hAPP_a_a(U_2294,U_2293)),
    inference(clausify,[status(thm)],[f_840_3]) ).

fof(f_841_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_841_2,plain,
    ! [U_2298,U_2297,U_2296] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(U_2298),U_2297),U_2296) = hAPP_nat_bool(hAPP_n1699378549t_bool(U_2298,U_2296),U_2297),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

fof(f_841_3,plain,
    ! [U_2296,U_2297,U_2298] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(U_2298),U_2297),U_2296) = hAPP_nat_bool(hAPP_n1699378549t_bool(U_2298,U_2296),U_2297),
    inference(definitional_conversion,[status(esa)],[f_841_2]) ).

cnf(f_841_4,plain,
    hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(U_2298),U_2297),U_2296) = hAPP_nat_bool(hAPP_n1699378549t_bool(U_2298,U_2296),U_2297),
    inference(clausify,[status(thm)],[f_841_3]) ).

fof(f_842_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_842_2,plain,
    ! [U_2301,U_2300,U_2299] : hAPP_nat_bool(cOMBB_bool_bool_nat(U_2301,U_2300),U_2299) = hAPP_bool_bool(U_2301,hAPP_nat_bool(U_2300,U_2299)),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

fof(f_842_3,plain,
    ! [U_2299,U_2300,U_2301] : hAPP_nat_bool(cOMBB_bool_bool_nat(U_2301,U_2300),U_2299) = hAPP_bool_bool(U_2301,hAPP_nat_bool(U_2300,U_2299)),
    inference(definitional_conversion,[status(esa)],[f_842_2]) ).

cnf(f_842_4,plain,
    hAPP_nat_bool(cOMBB_bool_bool_nat(U_2301,U_2300),U_2299) = hAPP_bool_bool(U_2301,hAPP_nat_bool(U_2300,U_2299)),
    inference(clausify,[status(thm)],[f_842_3]) ).

fof(f_843_1,plain,
    ! [P,Q] :
      ( hAPP_fun_a_bool_bool(cOMBK_324466864a_bool(P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U]) ).

fof(f_843_2,plain,
    ! [U_2303,U_2302] :
      ( hAPP_fun_a_bool_bool(cOMBK_324466864a_bool(U_2303),U_2302) = U_2303
      | ~ is_bool(U_2303) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

fof(f_843_3,plain,
    ! [U_2303] :
      ( ! [U_2302] : hAPP_fun_a_bool_bool(cOMBK_324466864a_bool(U_2303),U_2302) = U_2303
      | ~ is_bool(U_2303) ),
    inference(miniscope,[status(thm)],[f_843_2]) ).

fof(f_843_4,plain,
    ! [U_2303,U_2302] :
      ( hAPP_fun_a_bool_bool(cOMBK_324466864a_bool(U_2303),U_2302) = U_2303
      | ~ is_bool(U_2303) ),
    inference(definitional_conversion,[status(esa)],[f_843_3]) ).

cnf(f_843_5,plain,
    ( hAPP_fun_a_bool_bool(cOMBK_324466864a_bool(U_2303),U_2302) = U_2303
    | ~ is_bool(U_2303) ),
    inference(clausify,[status(thm)],[f_843_4]) ).

fof(f_844_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_844_2,plain,
    ! [U_2306,U_2305,U_2304] : hAPP_nat_bool(cOMBS_nat_bool_bool(U_2306,U_2305),U_2304) = hAPP_bool_bool(hAPP_n1006566506l_bool(U_2306,U_2304),hAPP_nat_bool(U_2305,U_2304)),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

fof(f_844_3,plain,
    ! [U_2304,U_2305,U_2306] : hAPP_nat_bool(cOMBS_nat_bool_bool(U_2306,U_2305),U_2304) = hAPP_bool_bool(hAPP_n1006566506l_bool(U_2306,U_2304),hAPP_nat_bool(U_2305,U_2304)),
    inference(definitional_conversion,[status(esa)],[f_844_2]) ).

cnf(f_844_4,plain,
    hAPP_nat_bool(cOMBS_nat_bool_bool(U_2306,U_2305),U_2304) = hAPP_bool_bool(hAPP_n1006566506l_bool(U_2306,U_2304),hAPP_nat_bool(U_2305,U_2304)),
    inference(clausify,[status(thm)],[f_844_3]) ).

fof(f_845_1,plain,
    ! [P,Q,R] : hAPP_pname_bool(hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_p1499970991t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U]) ).

fof(f_845_2,plain,
    ! [U_2309,U_2308,U_2307] : hAPP_pname_bool(hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(U_2309),U_2308),U_2307) = hAPP_nat_bool(hAPP_p1499970991t_bool(U_2309,U_2307),U_2308),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

fof(f_845_3,plain,
    ! [U_2307,U_2308,U_2309] : hAPP_pname_bool(hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(U_2309),U_2308),U_2307) = hAPP_nat_bool(hAPP_p1499970991t_bool(U_2309,U_2307),U_2308),
    inference(definitional_conversion,[status(esa)],[f_845_2]) ).

cnf(f_845_4,plain,
    hAPP_pname_bool(hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(U_2309),U_2308),U_2307) = hAPP_nat_bool(hAPP_p1499970991t_bool(U_2309,U_2307),U_2308),
    inference(clausify,[status(thm)],[f_845_3]) ).

fof(f_846_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(P),Q),R) = hAPP_pname_bool(hAPP_n1025906991e_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U]) ).

fof(f_846_2,plain,
    ! [U_2312,U_2311,U_2310] : hAPP_nat_bool(hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(U_2312),U_2311),U_2310) = hAPP_pname_bool(hAPP_n1025906991e_bool(U_2312,U_2310),U_2311),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

fof(f_846_3,plain,
    ! [U_2310,U_2311,U_2312] : hAPP_nat_bool(hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(U_2312),U_2311),U_2310) = hAPP_pname_bool(hAPP_n1025906991e_bool(U_2312,U_2310),U_2311),
    inference(definitional_conversion,[status(esa)],[f_846_2]) ).

cnf(f_846_4,plain,
    hAPP_nat_bool(hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(U_2312),U_2311),U_2310) = hAPP_pname_bool(hAPP_n1025906991e_bool(U_2312,U_2310),U_2311),
    inference(clausify,[status(thm)],[f_846_3]) ).

fof(f_847_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_847_2,plain,
    ! [U_2315,U_2314,U_2313] : hAPP_pname_bool(cOMBB_647938656_pname(U_2315,U_2314),U_2313) = hAPP_bool_bool(U_2315,hAPP_pname_bool(U_2314,U_2313)),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

fof(f_847_3,plain,
    ! [U_2313,U_2314,U_2315] : hAPP_pname_bool(cOMBB_647938656_pname(U_2315,U_2314),U_2313) = hAPP_bool_bool(U_2315,hAPP_pname_bool(U_2314,U_2313)),
    inference(definitional_conversion,[status(esa)],[f_847_2]) ).

cnf(f_847_4,plain,
    hAPP_pname_bool(cOMBB_647938656_pname(U_2315,U_2314),U_2313) = hAPP_bool_bool(U_2315,hAPP_pname_bool(U_2314,U_2313)),
    inference(clausify,[status(thm)],[f_847_3]) ).

fof(f_848_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_848_2,plain,
    ! [U_2318,U_2317,U_2316] : hAPP_pname_bool(cOMBS_568398431l_bool(U_2318,U_2317),U_2316) = hAPP_bool_bool(hAPP_p393069232l_bool(U_2318,U_2316),hAPP_pname_bool(U_2317,U_2316)),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

fof(f_848_3,plain,
    ! [U_2316,U_2317,U_2318] : hAPP_pname_bool(cOMBS_568398431l_bool(U_2318,U_2317),U_2316) = hAPP_bool_bool(hAPP_p393069232l_bool(U_2318,U_2316),hAPP_pname_bool(U_2317,U_2316)),
    inference(definitional_conversion,[status(esa)],[f_848_2]) ).

cnf(f_848_4,plain,
    hAPP_pname_bool(cOMBS_568398431l_bool(U_2318,U_2317),U_2316) = hAPP_bool_bool(hAPP_p393069232l_bool(U_2318,U_2316),hAPP_pname_bool(U_2317,U_2316)),
    inference(clausify,[status(thm)],[f_848_3]) ).

fof(f_849_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_849_2,plain,
    ! [U_2321,U_2320,U_2319] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(U_2321),U_2320),U_2319) = hAPP_pname_bool(hAPP_p61793385e_bool(U_2321,U_2319),U_2320),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

fof(f_849_3,plain,
    ! [U_2319,U_2320,U_2321] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(U_2321),U_2320),U_2319) = hAPP_pname_bool(hAPP_p61793385e_bool(U_2321,U_2319),U_2320),
    inference(definitional_conversion,[status(esa)],[f_849_2]) ).

cnf(f_849_4,plain,
    hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(U_2321),U_2320),U_2319) = hAPP_pname_bool(hAPP_p61793385e_bool(U_2321,U_2319),U_2320),
    inference(clausify,[status(thm)],[f_849_3]) ).

fof(f_850_1,plain,
    ! [P,Q,R] : hAPP_nat_fun_a_bool(cOMBB_1885489796ol_nat(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_nat_a(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat]) ).

fof(f_850_2,plain,
    ! [U_2324,U_2323,U_2322] : hAPP_nat_fun_a_bool(cOMBB_1885489796ol_nat(U_2324,U_2323),U_2322) = hAPP_a_fun_a_bool(U_2324,hAPP_nat_a(U_2323,U_2322)),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

fof(f_850_3,plain,
    ! [U_2322,U_2323,U_2324] : hAPP_nat_fun_a_bool(cOMBB_1885489796ol_nat(U_2324,U_2323),U_2322) = hAPP_a_fun_a_bool(U_2324,hAPP_nat_a(U_2323,U_2322)),
    inference(definitional_conversion,[status(esa)],[f_850_2]) ).

cnf(f_850_4,plain,
    hAPP_nat_fun_a_bool(cOMBB_1885489796ol_nat(U_2324,U_2323),U_2322) = hAPP_a_fun_a_bool(U_2324,hAPP_nat_a(U_2323,U_2322)),
    inference(clausify,[status(thm)],[f_850_3]) ).

fof(f_851_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_851_2,plain,
    ! [U_2327,U_2326,U_2325] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(U_2327),U_2326),U_2325) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(U_2327,U_2325),U_2326),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

fof(f_851_3,plain,
    ! [U_2325,U_2326,U_2327] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(U_2327),U_2326),U_2325) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(U_2327,U_2325),U_2326),
    inference(definitional_conversion,[status(esa)],[f_851_2]) ).

cnf(f_851_4,plain,
    hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(U_2327),U_2326),U_2325) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(U_2327,U_2325),U_2326),
    inference(clausify,[status(thm)],[f_851_3]) ).

fof(f_852_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_852_2,plain,
    ! [U_2330,U_2329,U_2328] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(U_2330,U_2329),U_2328) = hAPP_a_fun_a_bool(U_2330,hAPP_pname_a(U_2329,U_2328)),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

fof(f_852_3,plain,
    ! [U_2328,U_2329,U_2330] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(U_2330,U_2329),U_2328) = hAPP_a_fun_a_bool(U_2330,hAPP_pname_a(U_2329,U_2328)),
    inference(definitional_conversion,[status(esa)],[f_852_2]) ).

cnf(f_852_4,plain,
    hAPP_p1534023578a_bool(cOMBB_1897541054_pname(U_2330,U_2329),U_2328) = hAPP_a_fun_a_bool(U_2330,hAPP_pname_a(U_2329,U_2328)),
    inference(clausify,[status(thm)],[f_852_3]) ).

fof(f_853_1,plain,
    ! [P,Q] :
      ( hAPP_f54304608l_bool(cOMBK_1994329625t_bool(P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool]) ).

fof(f_853_2,plain,
    ! [U_2332,U_2331] :
      ( hAPP_f54304608l_bool(cOMBK_1994329625t_bool(U_2332),U_2331) = U_2332
      | ~ is_bool(U_2332) ),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

fof(f_853_3,plain,
    ! [U_2332] :
      ( ! [U_2331] : hAPP_f54304608l_bool(cOMBK_1994329625t_bool(U_2332),U_2331) = U_2332
      | ~ is_bool(U_2332) ),
    inference(miniscope,[status(thm)],[f_853_2]) ).

fof(f_853_4,plain,
    ! [U_2332,U_2331] :
      ( hAPP_f54304608l_bool(cOMBK_1994329625t_bool(U_2332),U_2331) = U_2332
      | ~ is_bool(U_2332) ),
    inference(definitional_conversion,[status(esa)],[f_853_3]) ).

cnf(f_853_5,plain,
    ( hAPP_f54304608l_bool(cOMBK_1994329625t_bool(U_2332),U_2331) = U_2332
    | ~ is_bool(U_2332) ),
    inference(clausify,[status(thm)],[f_853_4]) ).

fof(f_854_1,plain,
    ! [P,Q] :
      ( hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo]) ).

fof(f_854_2,plain,
    ! [U_2334,U_2333] :
      ( hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(U_2334),U_2333) = U_2334
      | ~ is_bool(U_2334) ),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

fof(f_854_3,plain,
    ! [U_2334] :
      ( ! [U_2333] : hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(U_2334),U_2333) = U_2334
      | ~ is_bool(U_2334) ),
    inference(miniscope,[status(thm)],[f_854_2]) ).

fof(f_854_4,plain,
    ! [U_2333,U_2334] :
      ( hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(U_2334),U_2333) = U_2334
      | ~ is_bool(U_2334) ),
    inference(definitional_conversion,[status(esa)],[f_854_3]) ).

cnf(f_854_5,plain,
    ( hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(U_2334),U_2333) = U_2334
    | ~ is_bool(U_2334) ),
    inference(clausify,[status(thm)],[f_854_4]) ).

fof(f_855_1,plain,
    ! [P,Q,R] : hAPP_a_fun_nat_bool(cOMBB_1321347587bool_a(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_a_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_855_2,plain,
    ! [U_2337,U_2336,U_2335] : hAPP_a_fun_nat_bool(cOMBB_1321347587bool_a(U_2337,U_2336),U_2335) = hAPP_n1699378549t_bool(U_2337,hAPP_a_nat(U_2336,U_2335)),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

fof(f_855_3,plain,
    ! [U_2335,U_2336,U_2337] : hAPP_a_fun_nat_bool(cOMBB_1321347587bool_a(U_2337,U_2336),U_2335) = hAPP_n1699378549t_bool(U_2337,hAPP_a_nat(U_2336,U_2335)),
    inference(definitional_conversion,[status(esa)],[f_855_2]) ).

cnf(f_855_4,plain,
    hAPP_a_fun_nat_bool(cOMBB_1321347587bool_a(U_2337,U_2336),U_2335) = hAPP_n1699378549t_bool(U_2337,hAPP_a_nat(U_2336,U_2335)),
    inference(clausify,[status(thm)],[f_855_3]) ).

fof(f_856_1,plain,
    ! [P,Q,R] : hAPP_a_bool(hAPP_f1549043526a_bool(cOMBC_777206479l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_a1392362872l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__]) ).

fof(f_856_2,plain,
    ! [U_2340,U_2339,U_2338] : hAPP_a_bool(hAPP_f1549043526a_bool(cOMBC_777206479l_bool(U_2340),U_2339),U_2338) = hAPP_f54304608l_bool(hAPP_a1392362872l_bool(U_2340,U_2338),U_2339),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

fof(f_856_3,plain,
    ! [U_2338,U_2339,U_2340] : hAPP_a_bool(hAPP_f1549043526a_bool(cOMBC_777206479l_bool(U_2340),U_2339),U_2338) = hAPP_f54304608l_bool(hAPP_a1392362872l_bool(U_2340,U_2338),U_2339),
    inference(definitional_conversion,[status(esa)],[f_856_2]) ).

cnf(f_856_4,plain,
    hAPP_a_bool(hAPP_f1549043526a_bool(cOMBC_777206479l_bool(U_2340),U_2339),U_2338) = hAPP_f54304608l_bool(hAPP_a1392362872l_bool(U_2340,U_2338),U_2339),
    inference(clausify,[status(thm)],[f_856_3]) ).

fof(f_857_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_857_2,plain,
    ! [U_2343,U_2342,U_2341] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(U_2343),U_2342),U_2341) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(U_2343,U_2341),U_2342),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

fof(f_857_3,plain,
    ! [U_2341,U_2342,U_2343] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(U_2343),U_2342),U_2341) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(U_2343,U_2341),U_2342),
    inference(definitional_conversion,[status(esa)],[f_857_2]) ).

cnf(f_857_4,plain,
    hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(U_2343),U_2342),U_2341) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(U_2343,U_2341),U_2342),
    inference(clausify,[status(thm)],[f_857_3]) ).

fof(f_858_1,plain,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(cOMBC_619334683t_bool(P),Q),R) = hAPP_nat_bool(hAPP_f282463732t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat_000tc__]) ).

fof(f_858_2,plain,
    ! [U_2346,U_2345,U_2344] : hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(cOMBC_619334683t_bool(U_2346),U_2345),U_2344) = hAPP_nat_bool(hAPP_f282463732t_bool(U_2346,U_2344),U_2345),
    inference(variable_rename,[status(thm)],[f_858_1]) ).

fof(f_858_3,plain,
    ! [U_2344,U_2345,U_2346] : hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(cOMBC_619334683t_bool(U_2346),U_2345),U_2344) = hAPP_nat_bool(hAPP_f282463732t_bool(U_2346,U_2344),U_2345),
    inference(definitional_conversion,[status(esa)],[f_858_2]) ).

cnf(f_858_4,plain,
    hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(cOMBC_619334683t_bool(U_2346),U_2345),U_2344) = hAPP_nat_bool(hAPP_f282463732t_bool(U_2346,U_2344),U_2345),
    inference(clausify,[status(thm)],[f_858_3]) ).

fof(f_859_1,plain,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_fun_a_bool_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H]) ).

fof(f_859_2,plain,
    ! [U_2349,U_2348,U_2347] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(U_2349,U_2348),U_2347) = hAPP_bool_bool(U_2349,hAPP_fun_a_bool_bool(U_2348,U_2347)),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

fof(f_859_3,plain,
    ! [U_2347,U_2348,U_2349] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(U_2349,U_2348),U_2347) = hAPP_bool_bool(U_2349,hAPP_fun_a_bool_bool(U_2348,U_2347)),
    inference(definitional_conversion,[status(esa)],[f_859_2]) ).

cnf(f_859_4,plain,
    hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(U_2349,U_2348),U_2347) = hAPP_bool_bool(U_2349,hAPP_fun_a_bool_bool(U_2348,U_2347)),
    inference(clausify,[status(thm)],[f_859_3]) ).

fof(f_860_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_860_2,plain,
    ! [U_2352,U_2351,U_2350] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(U_2352,U_2351),U_2350) = hAPP_b589554111l_bool(U_2352,hAPP_a_bool(U_2351,U_2350)),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

fof(f_860_3,plain,
    ! [U_2350,U_2351,U_2352] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(U_2352,U_2351),U_2350) = hAPP_b589554111l_bool(U_2352,hAPP_a_bool(U_2351,U_2350)),
    inference(definitional_conversion,[status(esa)],[f_860_2]) ).

cnf(f_860_4,plain,
    hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(U_2352,U_2351),U_2350) = hAPP_b589554111l_bool(U_2352,hAPP_a_bool(U_2351,U_2350)),
    inference(clausify,[status(thm)],[f_860_3]) ).

fof(f_861_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_861_2,plain,
    ! [U_2355,U_2354,U_2353] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(U_2355,U_2354),U_2353) = hAPP_bool_bool(hAPP_f198738859l_bool(U_2355,U_2353),hAPP_fun_a_bool_bool(U_2354,U_2353)),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

fof(f_861_3,plain,
    ! [U_2353,U_2354,U_2355] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(U_2355,U_2354),U_2353) = hAPP_bool_bool(hAPP_f198738859l_bool(U_2355,U_2353),hAPP_fun_a_bool_bool(U_2354,U_2353)),
    inference(definitional_conversion,[status(esa)],[f_861_2]) ).

cnf(f_861_4,plain,
    hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(U_2355,U_2354),U_2353) = hAPP_bool_bool(hAPP_f198738859l_bool(U_2355,U_2353),hAPP_fun_a_bool_bool(U_2354,U_2353)),
    inference(clausify,[status(thm)],[f_861_3]) ).

fof(f_862_1,plain,
    ! [P,Q,R] : hAPP_a_bool(hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_a217006258l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc]) ).

fof(f_862_2,plain,
    ! [U_2358,U_2357,U_2356] : hAPP_a_bool(hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(U_2358),U_2357),U_2356) = hAPP_f1664156314l_bool(hAPP_a217006258l_bool(U_2358,U_2356),U_2357),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

fof(f_862_3,plain,
    ! [U_2356,U_2357,U_2358] : hAPP_a_bool(hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(U_2358),U_2357),U_2356) = hAPP_f1664156314l_bool(hAPP_a217006258l_bool(U_2358,U_2356),U_2357),
    inference(definitional_conversion,[status(esa)],[f_862_2]) ).

cnf(f_862_4,plain,
    hAPP_a_bool(hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(U_2358),U_2357),U_2356) = hAPP_f1664156314l_bool(hAPP_a217006258l_bool(U_2358,U_2356),U_2357),
    inference(clausify,[status(thm)],[f_862_3]) ).

fof(f_863_1,plain,
    ! [P,Q,R] : hAPP_pname_bool(hAPP_f1794073134e_bool(cOMBC_445755039l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc]) ).

fof(f_863_2,plain,
    ! [U_2361,U_2360,U_2359] : hAPP_pname_bool(hAPP_f1794073134e_bool(cOMBC_445755039l_bool(U_2361),U_2360),U_2359) = hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(U_2361,U_2359),U_2360),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

fof(f_863_3,plain,
    ! [U_2359,U_2360,U_2361] : hAPP_pname_bool(hAPP_f1794073134e_bool(cOMBC_445755039l_bool(U_2361),U_2360),U_2359) = hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(U_2361,U_2359),U_2360),
    inference(definitional_conversion,[status(esa)],[f_863_2]) ).

cnf(f_863_4,plain,
    hAPP_pname_bool(hAPP_f1794073134e_bool(cOMBC_445755039l_bool(U_2361),U_2360),U_2359) = hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(U_2361,U_2359),U_2360),
    inference(clausify,[status(thm)],[f_863_3]) ).

fof(f_864_1,plain,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(P),Q),R) = hAPP_pname_bool(hAPP_f1794073134e_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname_000tc]) ).

fof(f_864_2,plain,
    ! [U_2364,U_2363,U_2362] : hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(U_2364),U_2363),U_2362) = hAPP_pname_bool(hAPP_f1794073134e_bool(U_2364,U_2362),U_2363),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

fof(f_864_3,plain,
    ! [U_2362,U_2363,U_2364] : hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(U_2364),U_2363),U_2362) = hAPP_pname_bool(hAPP_f1794073134e_bool(U_2364,U_2362),U_2363),
    inference(definitional_conversion,[status(esa)],[f_864_2]) ).

cnf(f_864_4,plain,
    hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(U_2364),U_2363),U_2362) = hAPP_pname_bool(hAPP_f1794073134e_bool(U_2364,U_2362),U_2363),
    inference(clausify,[status(thm)],[f_864_3]) ).

fof(f_865_1,plain,
    ! [P,Q,R] : hAPP_a93125764e_bool(cOMBB_610033911bool_a(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_a_pname(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob]) ).

fof(f_865_2,plain,
    ! [U_2367,U_2366,U_2365] : hAPP_a93125764e_bool(cOMBB_610033911bool_a(U_2367,U_2366),U_2365) = hAPP_p61793385e_bool(U_2367,hAPP_a_pname(U_2366,U_2365)),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

fof(f_865_3,plain,
    ! [U_2365,U_2366,U_2367] : hAPP_a93125764e_bool(cOMBB_610033911bool_a(U_2367,U_2366),U_2365) = hAPP_p61793385e_bool(U_2367,hAPP_a_pname(U_2366,U_2365)),
    inference(definitional_conversion,[status(esa)],[f_865_2]) ).

cnf(f_865_4,plain,
    hAPP_a93125764e_bool(cOMBB_610033911bool_a(U_2367,U_2366),U_2365) = hAPP_p61793385e_bool(U_2367,hAPP_a_pname(U_2366,U_2365)),
    inference(clausify,[status(thm)],[f_865_3]) ).

fof(f_866_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__003]) ).

fof(f_866_2,plain,
    ! [U_2370,U_2369,U_2368] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(U_2370,U_2369),U_2368) = hAPP_n1699378549t_bool(U_2370,hAPP_nat_nat(U_2369,U_2368)),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

fof(f_866_3,plain,
    ! [U_2368,U_2369,U_2370] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(U_2370,U_2369),U_2368) = hAPP_n1699378549t_bool(U_2370,hAPP_nat_nat(U_2369,U_2368)),
    inference(definitional_conversion,[status(esa)],[f_866_2]) ).

cnf(f_866_4,plain,
    hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(U_2370,U_2369),U_2368) = hAPP_n1699378549t_bool(U_2370,hAPP_nat_nat(U_2369,U_2368)),
    inference(clausify,[status(thm)],[f_866_3]) ).

fof(f_867_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_867_2,plain,
    ! [U_2373,U_2372,U_2371] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(U_2373),U_2372),U_2371) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(U_2373,U_2371),U_2372),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

fof(f_867_3,plain,
    ! [U_2371,U_2372,U_2373] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(U_2373),U_2372),U_2371) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(U_2373,U_2371),U_2372),
    inference(definitional_conversion,[status(esa)],[f_867_2]) ).

cnf(f_867_4,plain,
    hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(U_2373),U_2372),U_2371) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(U_2373,U_2371),U_2372),
    inference(clausify,[status(thm)],[f_867_3]) ).

fof(f_868_1,plain,
    ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_n215258509l_bool(cOMBC_385542954t_bool(P),Q),R) = hAPP_nat_bool(hAPP_f800510211t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona]) ).

fof(f_868_2,plain,
    ! [U_2376,U_2375,U_2374] : hAPP_f54304608l_bool(hAPP_n215258509l_bool(cOMBC_385542954t_bool(U_2376),U_2375),U_2374) = hAPP_nat_bool(hAPP_f800510211t_bool(U_2376,U_2374),U_2375),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

fof(f_868_3,plain,
    ! [U_2374,U_2375,U_2376] : hAPP_f54304608l_bool(hAPP_n215258509l_bool(cOMBC_385542954t_bool(U_2376),U_2375),U_2374) = hAPP_nat_bool(hAPP_f800510211t_bool(U_2376,U_2374),U_2375),
    inference(definitional_conversion,[status(esa)],[f_868_2]) ).

cnf(f_868_4,plain,
    hAPP_f54304608l_bool(hAPP_n215258509l_bool(cOMBC_385542954t_bool(U_2376),U_2375),U_2374) = hAPP_nat_bool(hAPP_f800510211t_bool(U_2376,U_2374),U_2375),
    inference(clausify,[status(thm)],[f_868_3]) ).

fof(f_869_1,plain,
    ! [P,Q,R] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f54304608l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On]) ).

fof(f_869_2,plain,
    ! [U_2379,U_2378,U_2377] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(U_2379,U_2378),U_2377) = hAPP_bool_bool(U_2379,hAPP_f54304608l_bool(U_2378,U_2377)),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

fof(f_869_3,plain,
    ! [U_2377,U_2378,U_2379] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(U_2379,U_2378),U_2377) = hAPP_bool_bool(U_2379,hAPP_f54304608l_bool(U_2378,U_2377)),
    inference(definitional_conversion,[status(esa)],[f_869_2]) ).

cnf(f_869_4,plain,
    hAPP_f54304608l_bool(cOMBB_238756964t_bool(U_2379,U_2378),U_2377) = hAPP_bool_bool(U_2379,hAPP_f54304608l_bool(U_2378,U_2377)),
    inference(clausify,[status(thm)],[f_869_3]) ).

fof(f_870_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_870_2,plain,
    ! [U_2382,U_2381,U_2380] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(U_2382,U_2381),U_2380) = hAPP_b589554111l_bool(U_2382,hAPP_nat_bool(U_2381,U_2380)),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

fof(f_870_3,plain,
    ! [U_2380,U_2381,U_2382] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(U_2382,U_2381),U_2380) = hAPP_b589554111l_bool(U_2382,hAPP_nat_bool(U_2381,U_2380)),
    inference(definitional_conversion,[status(esa)],[f_870_2]) ).

cnf(f_870_4,plain,
    hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(U_2382,U_2381),U_2380) = hAPP_b589554111l_bool(U_2382,hAPP_nat_bool(U_2381,U_2380)),
    inference(clausify,[status(thm)],[f_870_3]) ).

fof(f_871_1,plain,
    ! [P,Q,R] : hAPP_p1499970991t_bool(cOMBB_523834888_pname(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_pname_nat(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__005]) ).

fof(f_871_2,plain,
    ! [U_2385,U_2384,U_2383] : hAPP_p1499970991t_bool(cOMBB_523834888_pname(U_2385,U_2384),U_2383) = hAPP_n1699378549t_bool(U_2385,hAPP_pname_nat(U_2384,U_2383)),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

fof(f_871_3,plain,
    ! [U_2383,U_2384,U_2385] : hAPP_p1499970991t_bool(cOMBB_523834888_pname(U_2385,U_2384),U_2383) = hAPP_n1699378549t_bool(U_2385,hAPP_pname_nat(U_2384,U_2383)),
    inference(definitional_conversion,[status(esa)],[f_871_2]) ).

cnf(f_871_4,plain,
    hAPP_p1499970991t_bool(cOMBB_523834888_pname(U_2385,U_2384),U_2383) = hAPP_n1699378549t_bool(U_2385,hAPP_pname_nat(U_2384,U_2383)),
    inference(clausify,[status(thm)],[f_871_3]) ).

fof(f_872_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_872_2,plain,
    ! [U_2388,U_2387,U_2386] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(U_2388,U_2387),U_2386) = hAPP_bool_bool(hAPP_f1748468828l_bool(U_2388,U_2386),hAPP_f54304608l_bool(U_2387,U_2386)),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

fof(f_872_3,plain,
    ! [U_2386,U_2387,U_2388] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(U_2388,U_2387),U_2386) = hAPP_bool_bool(hAPP_f1748468828l_bool(U_2388,U_2386),hAPP_f54304608l_bool(U_2387,U_2386)),
    inference(definitional_conversion,[status(esa)],[f_872_2]) ).

cnf(f_872_4,plain,
    hAPP_f54304608l_bool(cOMBS_1187019125l_bool(U_2388,U_2387),U_2386) = hAPP_bool_bool(hAPP_f1748468828l_bool(U_2388,U_2386),hAPP_f54304608l_bool(U_2387,U_2386)),
    inference(clausify,[status(thm)],[f_872_3]) ).

fof(f_873_1,plain,
    ! [P,Q,R] : hAPP_pname_bool(hAPP_f654413245e_bool(cOMBC_267053842l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_p130839763l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo]) ).

fof(f_873_2,plain,
    ! [U_2391,U_2390,U_2389] : hAPP_pname_bool(hAPP_f654413245e_bool(cOMBC_267053842l_bool(U_2391),U_2390),U_2389) = hAPP_f54304608l_bool(hAPP_p130839763l_bool(U_2391,U_2389),U_2390),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

fof(f_873_3,plain,
    ! [U_2389,U_2390,U_2391] : hAPP_pname_bool(hAPP_f654413245e_bool(cOMBC_267053842l_bool(U_2391),U_2390),U_2389) = hAPP_f54304608l_bool(hAPP_p130839763l_bool(U_2391,U_2389),U_2390),
    inference(definitional_conversion,[status(esa)],[f_873_2]) ).

cnf(f_873_4,plain,
    hAPP_pname_bool(hAPP_f654413245e_bool(cOMBC_267053842l_bool(U_2391),U_2390),U_2389) = hAPP_f54304608l_bool(hAPP_p130839763l_bool(U_2391,U_2389),U_2390),
    inference(clausify,[status(thm)],[f_873_3]) ).

fof(f_874_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_874_2,plain,
    ! [U_2394,U_2393,U_2392] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(U_2394),U_2393),U_2392) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(U_2394,U_2392),U_2393),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

fof(f_874_3,plain,
    ! [U_2392,U_2393,U_2394] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(U_2394),U_2393),U_2392) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(U_2394,U_2392),U_2393),
    inference(definitional_conversion,[status(esa)],[f_874_2]) ).

cnf(f_874_4,plain,
    hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(U_2394),U_2393),U_2392) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(U_2394,U_2392),U_2393),
    inference(clausify,[status(thm)],[f_874_3]) ).

fof(f_875_1,plain,
    ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_n850744903l_bool(cOMBC_1666426608t_bool(P),Q),R) = hAPP_nat_bool(hAPP_f1066163005t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Nat__O]) ).

fof(f_875_2,plain,
    ! [U_2397,U_2396,U_2395] : hAPP_f1664156314l_bool(hAPP_n850744903l_bool(cOMBC_1666426608t_bool(U_2397),U_2396),U_2395) = hAPP_nat_bool(hAPP_f1066163005t_bool(U_2397,U_2395),U_2396),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

fof(f_875_3,plain,
    ! [U_2395,U_2396,U_2397] : hAPP_f1664156314l_bool(hAPP_n850744903l_bool(cOMBC_1666426608t_bool(U_2397),U_2396),U_2395) = hAPP_nat_bool(hAPP_f1066163005t_bool(U_2397,U_2395),U_2396),
    inference(definitional_conversion,[status(esa)],[f_875_2]) ).

cnf(f_875_4,plain,
    hAPP_f1664156314l_bool(hAPP_n850744903l_bool(cOMBC_1666426608t_bool(U_2397),U_2396),U_2395) = hAPP_nat_bool(hAPP_f1066163005t_bool(U_2397,U_2395),U_2396),
    inference(clausify,[status(thm)],[f_875_3]) ).

fof(f_876_1,plain,
    ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_p130839763l_bool(cOMBC_615407716e_bool(P),Q),R) = hAPP_pname_bool(hAPP_f654413245e_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn]) ).

fof(f_876_2,plain,
    ! [U_2400,U_2399,U_2398] : hAPP_f54304608l_bool(hAPP_p130839763l_bool(cOMBC_615407716e_bool(U_2400),U_2399),U_2398) = hAPP_pname_bool(hAPP_f654413245e_bool(U_2400,U_2398),U_2399),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

fof(f_876_3,plain,
    ! [U_2398,U_2399,U_2400] : hAPP_f54304608l_bool(hAPP_p130839763l_bool(cOMBC_615407716e_bool(U_2400),U_2399),U_2398) = hAPP_pname_bool(hAPP_f654413245e_bool(U_2400,U_2398),U_2399),
    inference(definitional_conversion,[status(esa)],[f_876_2]) ).

cnf(f_876_4,plain,
    hAPP_f54304608l_bool(hAPP_p130839763l_bool(cOMBC_615407716e_bool(U_2400),U_2399),U_2398) = hAPP_pname_bool(hAPP_f654413245e_bool(U_2400,U_2398),U_2399),
    inference(clausify,[status(thm)],[f_876_3]) ).

fof(f_877_1,plain,
    ! [P,Q,R] : hAPP_n1025906991e_bool(cOMBB_1212655066ol_nat(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_nat_pname(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_006]) ).

fof(f_877_2,plain,
    ! [U_2403,U_2402,U_2401] : hAPP_n1025906991e_bool(cOMBB_1212655066ol_nat(U_2403,U_2402),U_2401) = hAPP_p61793385e_bool(U_2403,hAPP_nat_pname(U_2402,U_2401)),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

fof(f_877_3,plain,
    ! [U_2401,U_2402,U_2403] : hAPP_n1025906991e_bool(cOMBB_1212655066ol_nat(U_2403,U_2402),U_2401) = hAPP_p61793385e_bool(U_2403,hAPP_nat_pname(U_2402,U_2401)),
    inference(definitional_conversion,[status(esa)],[f_877_2]) ).

cnf(f_877_4,plain,
    hAPP_n1025906991e_bool(cOMBB_1212655066ol_nat(U_2403,U_2402),U_2401) = hAPP_p61793385e_bool(U_2403,hAPP_nat_pname(U_2402,U_2401)),
    inference(clausify,[status(thm)],[f_877_3]) ).

fof(f_878_1,plain,
    ! [P,Q,R] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f1664156314l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op]) ).

fof(f_878_2,plain,
    ! [U_2406,U_2405,U_2404] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(U_2406,U_2405),U_2404) = hAPP_bool_bool(U_2406,hAPP_f1664156314l_bool(U_2405,U_2404)),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

fof(f_878_3,plain,
    ! [U_2404,U_2405,U_2406] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(U_2406,U_2405),U_2404) = hAPP_bool_bool(U_2406,hAPP_f1664156314l_bool(U_2405,U_2404)),
    inference(definitional_conversion,[status(esa)],[f_878_2]) ).

cnf(f_878_4,plain,
    hAPP_f1664156314l_bool(cOMBB_307249310e_bool(U_2406,U_2405),U_2404) = hAPP_bool_bool(U_2406,hAPP_f1664156314l_bool(U_2405,U_2404)),
    inference(clausify,[status(thm)],[f_878_3]) ).

fof(f_879_1,plain,
    ! [P,Q,R] : hAPP_p393069232l_bool(cOMBB_675860798_pname(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_pname_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007]) ).

fof(f_879_2,plain,
    ! [U_2409,U_2408,U_2407] : hAPP_p393069232l_bool(cOMBB_675860798_pname(U_2409,U_2408),U_2407) = hAPP_b589554111l_bool(U_2409,hAPP_pname_bool(U_2408,U_2407)),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

fof(f_879_3,plain,
    ! [U_2407,U_2408,U_2409] : hAPP_p393069232l_bool(cOMBB_675860798_pname(U_2409,U_2408),U_2407) = hAPP_b589554111l_bool(U_2409,hAPP_pname_bool(U_2408,U_2407)),
    inference(definitional_conversion,[status(esa)],[f_879_2]) ).

cnf(f_879_4,plain,
    hAPP_p393069232l_bool(cOMBB_675860798_pname(U_2409,U_2408),U_2407) = hAPP_b589554111l_bool(U_2409,hAPP_pname_bool(U_2408,U_2407)),
    inference(clausify,[status(thm)],[f_879_3]) ).

fof(f_880_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_880_2,plain,
    ! [U_2412,U_2411,U_2410] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(U_2412,U_2411),U_2410) = hAPP_bool_bool(hAPP_f1476298914l_bool(U_2412,U_2410),hAPP_f1664156314l_bool(U_2411,U_2410)),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

fof(f_880_3,plain,
    ! [U_2410,U_2411,U_2412] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(U_2412,U_2411),U_2410) = hAPP_bool_bool(hAPP_f1476298914l_bool(U_2412,U_2410),hAPP_f1664156314l_bool(U_2411,U_2410)),
    inference(definitional_conversion,[status(esa)],[f_880_2]) ).

cnf(f_880_4,plain,
    hAPP_f1664156314l_bool(cOMBS_350070575l_bool(U_2412,U_2411),U_2410) = hAPP_bool_bool(hAPP_f1476298914l_bool(U_2412,U_2410),hAPP_f1664156314l_bool(U_2411,U_2410)),
    inference(clausify,[status(thm)],[f_880_3]) ).

fof(f_881_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_881_2,plain,
    ! [U_2415,U_2414,U_2413] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(U_2415),U_2414),U_2413) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(U_2415,U_2413),U_2414),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

fof(f_881_3,plain,
    ! [U_2413,U_2414,U_2415] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(U_2415),U_2414),U_2413) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(U_2415,U_2413),U_2414),
    inference(definitional_conversion,[status(esa)],[f_881_2]) ).

cnf(f_881_4,plain,
    hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(U_2415),U_2414),U_2413) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(U_2415,U_2413),U_2414),
    inference(clausify,[status(thm)],[f_881_3]) ).

fof(f_882_1,plain,
    ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_p338031245l_bool(cOMBC_1004116266e_bool(P),Q),R) = hAPP_pname_bool(hAPP_f759274231e_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O]) ).

fof(f_882_2,plain,
    ! [U_2418,U_2417,U_2416] : hAPP_f1664156314l_bool(hAPP_p338031245l_bool(cOMBC_1004116266e_bool(U_2418),U_2417),U_2416) = hAPP_pname_bool(hAPP_f759274231e_bool(U_2418,U_2416),U_2417),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

fof(f_882_3,plain,
    ! [U_2416,U_2417,U_2418] : hAPP_f1664156314l_bool(hAPP_p338031245l_bool(cOMBC_1004116266e_bool(U_2418),U_2417),U_2416) = hAPP_pname_bool(hAPP_f759274231e_bool(U_2418,U_2416),U_2417),
    inference(definitional_conversion,[status(esa)],[f_882_2]) ).

cnf(f_882_4,plain,
    hAPP_f1664156314l_bool(hAPP_p338031245l_bool(cOMBC_1004116266e_bool(U_2418),U_2417),U_2416) = hAPP_pname_bool(hAPP_f759274231e_bool(U_2418,U_2416),U_2417),
    inference(clausify,[status(thm)],[f_882_3]) ).

fof(f_883_1,plain,
    ! [P,Q,R] : hAPP_p61793385e_bool(cOMBB_542850580_pname(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_pname_pname(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_008]) ).

fof(f_883_2,plain,
    ! [U_2421,U_2420,U_2419] : hAPP_p61793385e_bool(cOMBB_542850580_pname(U_2421,U_2420),U_2419) = hAPP_p61793385e_bool(U_2421,hAPP_pname_pname(U_2420,U_2419)),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

fof(f_883_3,plain,
    ! [U_2419,U_2420,U_2421] : hAPP_p61793385e_bool(cOMBB_542850580_pname(U_2421,U_2420),U_2419) = hAPP_p61793385e_bool(U_2421,hAPP_pname_pname(U_2420,U_2419)),
    inference(definitional_conversion,[status(esa)],[f_883_2]) ).

cnf(f_883_4,plain,
    hAPP_p61793385e_bool(cOMBB_542850580_pname(U_2421,U_2420),U_2419) = hAPP_p61793385e_bool(U_2421,hAPP_pname_pname(U_2420,U_2419)),
    inference(clausify,[status(thm)],[f_883_3]) ).

fof(f_884_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_884_2,plain,
    ! [U_2424,U_2423,U_2422] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(U_2424),U_2423),U_2422) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(U_2424,U_2422),U_2423),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

fof(f_884_3,plain,
    ! [U_2422,U_2423,U_2424] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(U_2424),U_2423),U_2422) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(U_2424,U_2422),U_2423),
    inference(definitional_conversion,[status(esa)],[f_884_2]) ).

cnf(f_884_4,plain,
    hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(U_2424),U_2423),U_2422) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(U_2424,U_2422),U_2423),
    inference(clausify,[status(thm)],[f_884_3]) ).

fof(f_885_1,plain,
    ! [P,Q,R] : hAPP_f282463732t_bool(cOMBB_164527437a_bool(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_fun_a_bool_nat(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__009]) ).

fof(f_885_2,plain,
    ! [U_2427,U_2426,U_2425] : hAPP_f282463732t_bool(cOMBB_164527437a_bool(U_2427,U_2426),U_2425) = hAPP_n1699378549t_bool(U_2427,hAPP_fun_a_bool_nat(U_2426,U_2425)),
    inference(variable_rename,[status(thm)],[f_885_1]) ).

fof(f_885_3,plain,
    ! [U_2425,U_2426,U_2427] : hAPP_f282463732t_bool(cOMBB_164527437a_bool(U_2427,U_2426),U_2425) = hAPP_n1699378549t_bool(U_2427,hAPP_fun_a_bool_nat(U_2426,U_2425)),
    inference(definitional_conversion,[status(esa)],[f_885_2]) ).

cnf(f_885_4,plain,
    hAPP_f282463732t_bool(cOMBB_164527437a_bool(U_2427,U_2426),U_2425) = hAPP_n1699378549t_bool(U_2427,hAPP_fun_a_bool_nat(U_2426,U_2425)),
    inference(clausify,[status(thm)],[f_885_3]) ).

fof(f_886_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_010]) ).

fof(f_886_2,plain,
    ! [U_2430,U_2429,U_2428] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(U_2430,U_2429),U_2428) = hAPP_b589554111l_bool(U_2430,hAPP_fun_a_bool_bool(U_2429,U_2428)),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

fof(f_886_3,plain,
    ! [U_2428,U_2429,U_2430] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(U_2430,U_2429),U_2428) = hAPP_b589554111l_bool(U_2430,hAPP_fun_a_bool_bool(U_2429,U_2428)),
    inference(definitional_conversion,[status(esa)],[f_886_2]) ).

cnf(f_886_4,plain,
    hAPP_f198738859l_bool(cOMBB_338059395a_bool(U_2430,U_2429),U_2428) = hAPP_b589554111l_bool(U_2430,hAPP_fun_a_bool_bool(U_2429,U_2428)),
    inference(clausify,[status(thm)],[f_886_3]) ).

fof(f_887_1,plain,
    ! [P,Q,R] : hAPP_f1794073134e_bool(cOMBB_1693087065a_bool(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_f1128469712_pname(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_011]) ).

fof(f_887_2,plain,
    ! [U_2433,U_2432,U_2431] : hAPP_f1794073134e_bool(cOMBB_1693087065a_bool(U_2433,U_2432),U_2431) = hAPP_p61793385e_bool(U_2433,hAPP_f1128469712_pname(U_2432,U_2431)),
    inference(variable_rename,[status(thm)],[f_887_1]) ).

fof(f_887_3,plain,
    ! [U_2431,U_2432,U_2433] : hAPP_f1794073134e_bool(cOMBB_1693087065a_bool(U_2433,U_2432),U_2431) = hAPP_p61793385e_bool(U_2433,hAPP_f1128469712_pname(U_2432,U_2431)),
    inference(definitional_conversion,[status(esa)],[f_887_2]) ).

cnf(f_887_4,plain,
    hAPP_f1794073134e_bool(cOMBB_1693087065a_bool(U_2433,U_2432),U_2431) = hAPP_p61793385e_bool(U_2433,hAPP_f1128469712_pname(U_2432,U_2431)),
    inference(clausify,[status(thm)],[f_887_3]) ).

fof(f_888_1,plain,
    ! [P,Q,R] : hAPP_f800510211t_bool(cOMBB_1250273980t_bool(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_f22106695ol_nat(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__012]) ).

fof(f_888_2,plain,
    ! [U_2436,U_2435,U_2434] : hAPP_f800510211t_bool(cOMBB_1250273980t_bool(U_2436,U_2435),U_2434) = hAPP_n1699378549t_bool(U_2436,hAPP_f22106695ol_nat(U_2435,U_2434)),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

fof(f_888_3,plain,
    ! [U_2434,U_2435,U_2436] : hAPP_f800510211t_bool(cOMBB_1250273980t_bool(U_2436,U_2435),U_2434) = hAPP_n1699378549t_bool(U_2436,hAPP_f22106695ol_nat(U_2435,U_2434)),
    inference(definitional_conversion,[status(esa)],[f_888_2]) ).

cnf(f_888_4,plain,
    hAPP_f800510211t_bool(cOMBB_1250273980t_bool(U_2436,U_2435),U_2434) = hAPP_n1699378549t_bool(U_2436,hAPP_f22106695ol_nat(U_2435,U_2434)),
    inference(clausify,[status(thm)],[f_888_3]) ).

fof(f_889_1,plain,
    ! [P,Q,R] : hAPP_a85458249l_bool(cOMBB_472261505bool_a(P,Q),R) = hAPP_f1631501043l_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__fun_Itc__fun_It__]) ).

fof(f_889_2,plain,
    ! [U_2439,U_2438,U_2437] : hAPP_a85458249l_bool(cOMBB_472261505bool_a(U_2439,U_2438),U_2437) = hAPP_f1631501043l_bool(U_2439,hAPP_a_fun_a_bool(U_2438,U_2437)),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

fof(f_889_3,plain,
    ! [U_2437,U_2438,U_2439] : hAPP_a85458249l_bool(cOMBB_472261505bool_a(U_2439,U_2438),U_2437) = hAPP_f1631501043l_bool(U_2439,hAPP_a_fun_a_bool(U_2438,U_2437)),
    inference(definitional_conversion,[status(esa)],[f_889_2]) ).

cnf(f_889_4,plain,
    hAPP_a85458249l_bool(cOMBB_472261505bool_a(U_2439,U_2438),U_2437) = hAPP_f1631501043l_bool(U_2439,hAPP_a_fun_a_bool(U_2438,U_2437)),
    inference(clausify,[status(thm)],[f_889_3]) ).

fof(f_890_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_890_2,plain,
    ! [U_2442,U_2441,U_2440] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(U_2442),U_2441),U_2440) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(U_2442,U_2440),U_2441),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

fof(f_890_3,plain,
    ! [U_2440,U_2441,U_2442] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(U_2442),U_2441),U_2440) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(U_2442,U_2440),U_2441),
    inference(definitional_conversion,[status(esa)],[f_890_2]) ).

cnf(f_890_4,plain,
    hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(U_2442),U_2441),U_2440) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(U_2442,U_2440),U_2441),
    inference(clausify,[status(thm)],[f_890_3]) ).

fof(f_891_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_013]) ).

fof(f_891_2,plain,
    ! [U_2445,U_2444,U_2443] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(U_2445,U_2444),U_2443) = hAPP_b589554111l_bool(U_2445,hAPP_f54304608l_bool(U_2444,U_2443)),
    inference(variable_rename,[status(thm)],[f_891_1]) ).

fof(f_891_3,plain,
    ! [U_2443,U_2444,U_2445] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(U_2445,U_2444),U_2443) = hAPP_b589554111l_bool(U_2445,hAPP_f54304608l_bool(U_2444,U_2443)),
    inference(definitional_conversion,[status(esa)],[f_891_2]) ).

cnf(f_891_4,plain,
    hAPP_f1748468828l_bool(cOMBB_444170502t_bool(U_2445,U_2444),U_2443) = hAPP_b589554111l_bool(U_2445,hAPP_f54304608l_bool(U_2444,U_2443)),
    inference(clausify,[status(thm)],[f_891_3]) ).

fof(f_892_1,plain,
    ! [P,Q,R] : hAPP_f1066163005t_bool(cOMBB_1896684278e_bool(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_f921600141ol_nat(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__014]) ).

fof(f_892_2,plain,
    ! [U_2448,U_2447,U_2446] : hAPP_f1066163005t_bool(cOMBB_1896684278e_bool(U_2448,U_2447),U_2446) = hAPP_n1699378549t_bool(U_2448,hAPP_f921600141ol_nat(U_2447,U_2446)),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

fof(f_892_3,plain,
    ! [U_2446,U_2447,U_2448] : hAPP_f1066163005t_bool(cOMBB_1896684278e_bool(U_2448,U_2447),U_2446) = hAPP_n1699378549t_bool(U_2448,hAPP_f921600141ol_nat(U_2447,U_2446)),
    inference(definitional_conversion,[status(esa)],[f_892_2]) ).

cnf(f_892_4,plain,
    hAPP_f1066163005t_bool(cOMBB_1896684278e_bool(U_2448,U_2447),U_2446) = hAPP_n1699378549t_bool(U_2448,hAPP_f921600141ol_nat(U_2447,U_2446)),
    inference(clausify,[status(thm)],[f_892_3]) ).

fof(f_893_1,plain,
    ! [P,Q,R] : hAPP_f654413245e_bool(cOMBB_141086128t_bool(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_f1291551745_pname(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_015]) ).

fof(f_893_2,plain,
    ! [U_2451,U_2450,U_2449] : hAPP_f654413245e_bool(cOMBB_141086128t_bool(U_2451,U_2450),U_2449) = hAPP_p61793385e_bool(U_2451,hAPP_f1291551745_pname(U_2450,U_2449)),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

fof(f_893_3,plain,
    ! [U_2449,U_2450,U_2451] : hAPP_f654413245e_bool(cOMBB_141086128t_bool(U_2451,U_2450),U_2449) = hAPP_p61793385e_bool(U_2451,hAPP_f1291551745_pname(U_2450,U_2449)),
    inference(definitional_conversion,[status(esa)],[f_893_2]) ).

cnf(f_893_4,plain,
    hAPP_f654413245e_bool(cOMBB_141086128t_bool(U_2451,U_2450),U_2449) = hAPP_p61793385e_bool(U_2451,hAPP_f1291551745_pname(U_2450,U_2449)),
    inference(clausify,[status(thm)],[f_893_3]) ).

fof(f_894_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_016]) ).

fof(f_894_2,plain,
    ! [U_2454,U_2453,U_2452] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(U_2454,U_2453),U_2452) = hAPP_b589554111l_bool(U_2454,hAPP_f1664156314l_bool(U_2453,U_2452)),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

fof(f_894_3,plain,
    ! [U_2452,U_2453,U_2454] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(U_2454,U_2453),U_2452) = hAPP_b589554111l_bool(U_2454,hAPP_f1664156314l_bool(U_2453,U_2452)),
    inference(definitional_conversion,[status(esa)],[f_894_2]) ).

cnf(f_894_4,plain,
    hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(U_2454,U_2453),U_2452) = hAPP_b589554111l_bool(U_2454,hAPP_f1664156314l_bool(U_2453,U_2452)),
    inference(clausify,[status(thm)],[f_894_3]) ).

fof(f_895_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_895_2,plain,
    ! [U_2457,U_2456,U_2455] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(U_2457),U_2456),U_2455) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(U_2457,U_2455),U_2456),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

fof(f_895_3,plain,
    ! [U_2455,U_2456,U_2457] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(U_2457),U_2456),U_2455) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(U_2457,U_2455),U_2456),
    inference(definitional_conversion,[status(esa)],[f_895_2]) ).

cnf(f_895_4,plain,
    hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(U_2457),U_2456),U_2455) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(U_2457,U_2455),U_2456),
    inference(clausify,[status(thm)],[f_895_3]) ).

fof(f_896_1,plain,
    ! [P,Q,R] : hAPP_f759274231e_bool(cOMBB_598082538e_bool(P,Q),R) = hAPP_p61793385e_bool(P,hAPP_f1297739591_pname(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_017]) ).

fof(f_896_2,plain,
    ! [U_2460,U_2459,U_2458] : hAPP_f759274231e_bool(cOMBB_598082538e_bool(U_2460,U_2459),U_2458) = hAPP_p61793385e_bool(U_2460,hAPP_f1297739591_pname(U_2459,U_2458)),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

fof(f_896_3,plain,
    ! [U_2458,U_2459,U_2460] : hAPP_f759274231e_bool(cOMBB_598082538e_bool(U_2460,U_2459),U_2458) = hAPP_p61793385e_bool(U_2460,hAPP_f1297739591_pname(U_2459,U_2458)),
    inference(definitional_conversion,[status(esa)],[f_896_2]) ).

cnf(f_896_4,plain,
    hAPP_f759274231e_bool(cOMBB_598082538e_bool(U_2460,U_2459),U_2458) = hAPP_p61793385e_bool(U_2460,hAPP_f1297739591_pname(U_2459,U_2458)),
    inference(clausify,[status(thm)],[f_896_3]) ).

fof(f_897_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___018]) ).

fof(f_897_2,plain,
    ! [U_2463,U_2462,U_2461] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(U_2463,U_2462),U_2461) = hAPP_f1631501043l_bool(U_2463,hAPP_nat_fun_a_bool(U_2462,U_2461)),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

fof(f_897_3,plain,
    ! [U_2461,U_2462,U_2463] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(U_2463,U_2462),U_2461) = hAPP_f1631501043l_bool(U_2463,hAPP_nat_fun_a_bool(U_2462,U_2461)),
    inference(definitional_conversion,[status(esa)],[f_897_2]) ).

cnf(f_897_4,plain,
    hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(U_2463,U_2462),U_2461) = hAPP_f1631501043l_bool(U_2463,hAPP_nat_fun_a_bool(U_2462,U_2461)),
    inference(clausify,[status(thm)],[f_897_3]) ).

fof(f_898_1,plain,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(P),Q),R) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__]) ).

fof(f_898_2,plain,
    ! [U_2466,U_2465,U_2464] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(U_2466),U_2465),U_2464) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(U_2466,U_2464),U_2465),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

fof(f_898_3,plain,
    ! [U_2464,U_2465,U_2466] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(U_2466),U_2465),U_2464) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(U_2466,U_2464),U_2465),
    inference(definitional_conversion,[status(esa)],[f_898_2]) ).

cnf(f_898_4,plain,
    hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(U_2466),U_2465),U_2464) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(U_2466,U_2464),U_2465),
    inference(clausify,[status(thm)],[f_898_3]) ).

fof(f_899_1,plain,
    ! [P,Q,R] : hAPP_p1824510254l_bool(cOMBB_392435466_pname(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_p1534023578a_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___019]) ).

fof(f_899_2,plain,
    ! [U_2469,U_2468,U_2467] : hAPP_p1824510254l_bool(cOMBB_392435466_pname(U_2469,U_2468),U_2467) = hAPP_f1631501043l_bool(U_2469,hAPP_p1534023578a_bool(U_2468,U_2467)),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

fof(f_899_3,plain,
    ! [U_2467,U_2468,U_2469] : hAPP_p1824510254l_bool(cOMBB_392435466_pname(U_2469,U_2468),U_2467) = hAPP_f1631501043l_bool(U_2469,hAPP_p1534023578a_bool(U_2468,U_2467)),
    inference(definitional_conversion,[status(esa)],[f_899_2]) ).

cnf(f_899_4,plain,
    hAPP_p1824510254l_bool(cOMBB_392435466_pname(U_2469,U_2468),U_2467) = hAPP_f1631501043l_bool(U_2469,hAPP_p1534023578a_bool(U_2468,U_2467)),
    inference(clausify,[status(thm)],[f_899_3]) ).

fof(f_900_1,plain,
    ! [P,Q,R] : hAPP_a1392362872l_bool(cOMBB_743407885bool_a(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_a_fun_nat_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_900_2,plain,
    ! [U_2472,U_2471,U_2470] : hAPP_a1392362872l_bool(cOMBB_743407885bool_a(U_2472,U_2471),U_2470) = hAPP_f103356543l_bool(U_2472,hAPP_a_fun_nat_bool(U_2471,U_2470)),
    inference(variable_rename,[status(thm)],[f_900_1]) ).

fof(f_900_3,plain,
    ! [U_2470,U_2471,U_2472] : hAPP_a1392362872l_bool(cOMBB_743407885bool_a(U_2472,U_2471),U_2470) = hAPP_f103356543l_bool(U_2472,hAPP_a_fun_nat_bool(U_2471,U_2470)),
    inference(definitional_conversion,[status(esa)],[f_900_2]) ).

cnf(f_900_4,plain,
    hAPP_a1392362872l_bool(cOMBB_743407885bool_a(U_2472,U_2471),U_2470) = hAPP_f103356543l_bool(U_2472,hAPP_a_fun_nat_bool(U_2471,U_2470)),
    inference(clausify,[status(thm)],[f_900_3]) ).

fof(f_901_1,plain,
    ! [P,Q,R] : hAPP_a217006258l_bool(cOMBB_1137537805bool_a(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_a93125764e_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_901_2,plain,
    ! [U_2475,U_2474,U_2473] : hAPP_a217006258l_bool(cOMBB_1137537805bool_a(U_2475,U_2474),U_2473) = hAPP_f434788991l_bool(U_2475,hAPP_a93125764e_bool(U_2474,U_2473)),
    inference(variable_rename,[status(thm)],[f_901_1]) ).

fof(f_901_3,plain,
    ! [U_2473,U_2474,U_2475] : hAPP_a217006258l_bool(cOMBB_1137537805bool_a(U_2475,U_2474),U_2473) = hAPP_f434788991l_bool(U_2475,hAPP_a93125764e_bool(U_2474,U_2473)),
    inference(definitional_conversion,[status(esa)],[f_901_2]) ).

cnf(f_901_4,plain,
    hAPP_a217006258l_bool(cOMBB_1137537805bool_a(U_2475,U_2474),U_2473) = hAPP_f434788991l_bool(U_2475,hAPP_a93125764e_bool(U_2474,U_2473)),
    inference(clausify,[status(thm)],[f_901_3]) ).

fof(f_902_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__020]) ).

fof(f_902_2,plain,
    ! [U_2478,U_2477,U_2476] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(U_2478,U_2477),U_2476) = hAPP_f103356543l_bool(U_2478,hAPP_n1699378549t_bool(U_2477,U_2476)),
    inference(variable_rename,[status(thm)],[f_902_1]) ).

fof(f_902_3,plain,
    ! [U_2476,U_2477,U_2478] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(U_2478,U_2477),U_2476) = hAPP_f103356543l_bool(U_2478,hAPP_n1699378549t_bool(U_2477,U_2476)),
    inference(definitional_conversion,[status(esa)],[f_902_2]) ).

cnf(f_902_4,plain,
    hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(U_2478,U_2477),U_2476) = hAPP_f103356543l_bool(U_2478,hAPP_n1699378549t_bool(U_2477,U_2476)),
    inference(clausify,[status(thm)],[f_902_3]) ).

fof(f_903_1,plain,
    ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__021]) ).

fof(f_903_2,plain,
    ! [U_2481,U_2480,U_2479] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(U_2481),U_2480),U_2479) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(U_2481,U_2479),U_2480),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

fof(f_903_3,plain,
    ! [U_2479,U_2480,U_2481] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(U_2481),U_2480),U_2479) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(U_2481,U_2479),U_2480),
    inference(definitional_conversion,[status(esa)],[f_903_2]) ).

cnf(f_903_4,plain,
    hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(U_2481),U_2480),U_2479) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(U_2481,U_2479),U_2480),
    inference(clausify,[status(thm)],[f_903_3]) ).

fof(f_904_1,plain,
    ! [P,Q,R] : hAPP_p130839763l_bool(cOMBB_928955006_pname(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_p1499970991t_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__022]) ).

fof(f_904_2,plain,
    ! [U_2484,U_2483,U_2482] : hAPP_p130839763l_bool(cOMBB_928955006_pname(U_2484,U_2483),U_2482) = hAPP_f103356543l_bool(U_2484,hAPP_p1499970991t_bool(U_2483,U_2482)),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

fof(f_904_3,plain,
    ! [U_2482,U_2483,U_2484] : hAPP_p130839763l_bool(cOMBB_928955006_pname(U_2484,U_2483),U_2482) = hAPP_f103356543l_bool(U_2484,hAPP_p1499970991t_bool(U_2483,U_2482)),
    inference(definitional_conversion,[status(esa)],[f_904_2]) ).

cnf(f_904_4,plain,
    hAPP_p130839763l_bool(cOMBB_928955006_pname(U_2484,U_2483),U_2482) = hAPP_f103356543l_bool(U_2484,hAPP_p1499970991t_bool(U_2483,U_2482)),
    inference(clausify,[status(thm)],[f_904_3]) ).

fof(f_905_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_023]) ).

fof(f_905_2,plain,
    ! [U_2487,U_2486,U_2485] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(U_2487,U_2486),U_2485) = hAPP_f434788991l_bool(U_2487,hAPP_n1025906991e_bool(U_2486,U_2485)),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

fof(f_905_3,plain,
    ! [U_2485,U_2486,U_2487] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(U_2487,U_2486),U_2485) = hAPP_f434788991l_bool(U_2487,hAPP_n1025906991e_bool(U_2486,U_2485)),
    inference(definitional_conversion,[status(esa)],[f_905_2]) ).

cnf(f_905_4,plain,
    hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(U_2487,U_2486),U_2485) = hAPP_f434788991l_bool(U_2487,hAPP_n1025906991e_bool(U_2486,U_2485)),
    inference(clausify,[status(thm)],[f_905_3]) ).

fof(f_906_1,plain,
    ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_024]) ).

fof(f_906_2,plain,
    ! [U_2490,U_2489,U_2488] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(U_2490),U_2489),U_2488) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(U_2490,U_2488),U_2489),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

fof(f_906_3,plain,
    ! [U_2488,U_2489,U_2490] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(U_2490),U_2489),U_2488) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(U_2490,U_2488),U_2489),
    inference(definitional_conversion,[status(esa)],[f_906_2]) ).

cnf(f_906_4,plain,
    hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(U_2490),U_2489),U_2488) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(U_2490,U_2488),U_2489),
    inference(clausify,[status(thm)],[f_906_3]) ).

fof(f_907_1,plain,
    ! [P,Q,R] : hAPP_p338031245l_bool(cOMBB_408569982_pname(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_p61793385e_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_025]) ).

fof(f_907_2,plain,
    ! [U_2493,U_2492,U_2491] : hAPP_p338031245l_bool(cOMBB_408569982_pname(U_2493,U_2492),U_2491) = hAPP_f434788991l_bool(U_2493,hAPP_p61793385e_bool(U_2492,U_2491)),
    inference(variable_rename,[status(thm)],[f_907_1]) ).

fof(f_907_3,plain,
    ! [U_2491,U_2492,U_2493] : hAPP_p338031245l_bool(cOMBB_408569982_pname(U_2493,U_2492),U_2491) = hAPP_f434788991l_bool(U_2493,hAPP_p61793385e_bool(U_2492,U_2491)),
    inference(definitional_conversion,[status(esa)],[f_907_2]) ).

cnf(f_907_4,plain,
    hAPP_p338031245l_bool(cOMBB_408569982_pname(U_2493,U_2492),U_2491) = hAPP_f434788991l_bool(U_2493,hAPP_p61793385e_bool(U_2492,U_2491)),
    inference(clausify,[status(thm)],[f_907_3]) ).

fof(f_908_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_908_2,plain,
    ! [U_2496,U_2495,U_2494] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(U_2496),U_2495),U_2494) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(U_2496,U_2494),U_2495),
    inference(variable_rename,[status(thm)],[f_908_1]) ).

fof(f_908_3,plain,
    ! [U_2494,U_2495,U_2496] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(U_2496),U_2495),U_2494) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(U_2496,U_2494),U_2495),
    inference(definitional_conversion,[status(esa)],[f_908_2]) ).

cnf(f_908_4,plain,
    hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(U_2496),U_2495),U_2494) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(U_2496,U_2494),U_2495),
    inference(clausify,[status(thm)],[f_908_3]) ).

fof(f_909_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_909_2,plain,
    ! [U_2499,U_2498,U_2497] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(U_2499),U_2498),U_2497) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(U_2499,U_2497),U_2498),
    inference(variable_rename,[status(thm)],[f_909_1]) ).

fof(f_909_3,plain,
    ! [U_2497,U_2498,U_2499] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(U_2499),U_2498),U_2497) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(U_2499,U_2497),U_2498),
    inference(definitional_conversion,[status(esa)],[f_909_2]) ).

cnf(f_909_4,plain,
    hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(U_2499),U_2498),U_2497) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(U_2499,U_2497),U_2498),
    inference(clausify,[status(thm)],[f_909_3]) ).

fof(f_910_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_910_2,plain,
    ! [U_2502,U_2501,U_2500] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(U_2502),U_2501),U_2500) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(U_2502,U_2500),U_2501),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

fof(f_910_3,plain,
    ! [U_2500,U_2501,U_2502] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(U_2502),U_2501),U_2500) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(U_2502,U_2500),U_2501),
    inference(definitional_conversion,[status(esa)],[f_910_2]) ).

cnf(f_910_4,plain,
    hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(U_2502),U_2501),U_2500) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(U_2502,U_2500),U_2501),
    inference(clausify,[status(thm)],[f_910_3]) ).

fof(f_911_1,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

fof(f_911_2,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
    inference(definitional_conversion,[status(esa)],[f_911_1]) ).

cnf(f_911_3,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
    inference(clausify,[status(thm)],[f_911_2]) ).

fof(f_912_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_912_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_912_1]) ).

cnf(f_912_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_912_2]) ).

fof(f_913_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_913_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_913_1]) ).

cnf(f_913_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_913_2]) ).

fof(f_914_1,plain,
    hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
    inference(fof_nnf,[status(thm)],[conj_3]) ).

fof(f_914_2,plain,
    hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
    inference(definitional_conversion,[status(esa)],[f_914_1]) ).

cnf(f_914_3,plain,
    hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
    inference(clausify,[status(thm)],[f_914_2]) ).

fof(f_915_1,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(fof_nnf,[status(thm)],[conj_4]) ).

fof(f_915_2,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(definitional_conversion,[status(esa)],[f_915_1]) ).

cnf(f_915_3,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(clausify,[status(thm)],[f_915_2]) ).

fof(f_916_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_916_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_916_1]) ).

cnf(f_916_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_916_2]) ).

fof(f_917_1,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(negate,[status(cth)],[conj_6]) ).

fof(f_917_2,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(definitional_conversion,[status(esa)],[f_917_1]) ).

cnf(f_917_3,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(clausify,[status(thm)],[f_917_2]) ).

cnf(equality_1,axiom,
    Eq_x_0 = Eq_x_0,
    theory(equality,[reflexivity]) ).

cnf(equality_2,axiom,
    ( Eq_x_1 = Eq_x_0
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[symmetry]) ).

cnf(equality_3,axiom,
    ( Eq_x_0 = Eq_x_2
    | Eq_x_1 != Eq_x_2
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[transitivity]) ).

cnf(equality_4,axiom,
    ( cOMBB_bool_bool_a(Eq_x_0,Eq_x_1) = cOMBB_bool_bool_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_5,axiom,
    ( cOMBB_647938656_pname(Eq_x_0,Eq_x_1) = cOMBB_647938656_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_6,axiom,
    ( cOMBB_2140588453a_bool(Eq_x_0,Eq_x_1) = cOMBB_2140588453a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_7,axiom,
    ( cOMBB_307249310e_bool(Eq_x_0,Eq_x_1) = cOMBB_307249310e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_8,axiom,
    ( cOMBK_bool_a(Eq_x_0) = cOMBK_bool_a(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_9,axiom,
    ( cOMBK_bool_pname(Eq_x_0) = cOMBK_bool_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_10,axiom,
    ( cOMBK_324466864a_bool(Eq_x_0) = cOMBK_324466864a_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_11,axiom,
    ( cOMBK_1857069011e_bool(Eq_x_0) = cOMBK_1857069011e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_12,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_13,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_14,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_15,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_16,axiom,
    ( undefined_a(Eq_x_0) = undefined_a(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_17,axiom,
    ( undefined_pname(Eq_x_0) = undefined_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,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_19,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_20,axiom,
    ( undefi17486888e_bool(Eq_x_0) = undefi17486888e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( undefi1699038445l_bool(Eq_x_0) = undefi1699038445l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_22,axiom,
    ( undefi64961550l_bool(Eq_x_0) = undefi64961550l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_23,axiom,
    ( collect_a(Eq_x_0) = collect_a(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_24,axiom,
    ( collect_pname(Eq_x_0) = collect_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,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_26,axiom,
    ( collec1974731493e_bool(Eq_x_0) = collec1974731493e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,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_28,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_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,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_42,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_43,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_44,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_45,axiom,
    ( insert_a(Eq_x_0,Eq_x_1) = insert_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_46,axiom,
    ( insert_pname(Eq_x_0,Eq_x_1) = insert_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_47,axiom,
    ( insert_fun_a_bool(Eq_x_0,Eq_x_1) = insert_fun_a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_48,axiom,
    ( insert1325755072e_bool(Eq_x_0,Eq_x_1) = insert1325755072e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_49,axiom,
    ( hAPP_a_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_50,axiom,
    ( hAPP_a_pname(Eq_x_0,Eq_x_1) = hAPP_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_51,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_52,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_53,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_54,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_55,axiom,
    ( hAPP_a217006258l_bool(Eq_x_0,Eq_x_1) = hAPP_a217006258l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_56,axiom,
    ( hAPP_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_57,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_58,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_59,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_60,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_61,axiom,
    ( hAPP_p1824510254l_bool(Eq_x_0,Eq_x_1) = hAPP_p1824510254l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_62,axiom,
    ( hAPP_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_63,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_64,axiom,
    ( hAPP_nat_a(Eq_x_0,Eq_x_1) = hAPP_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_65,axiom,
    ( hAPP_nat_pname(Eq_x_0,Eq_x_1) = hAPP_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_66,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_67,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_68,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_69,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_70,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_71,axiom,
    ( hAPP_f1128469712_pname(Eq_x_0,Eq_x_1) = hAPP_f1128469712_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_72,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_73,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_74,axiom,
    ( hAPP_f1794073134e_bool(Eq_x_0,Eq_x_1) = hAPP_f1794073134e_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_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_76,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_77,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_78,axiom,
    ( hAPP_f1051908748a_bool(Eq_x_0,Eq_x_1) = hAPP_f1051908748a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_79,axiom,
    ( hAPP_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_80,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_81,axiom,
    ( hAPP_f1291551745_pname(Eq_x_0,Eq_x_1) = hAPP_f1291551745_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_82,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_83,axiom,
    ( hAPP_f1549043526a_bool(Eq_x_0,Eq_x_1) = hAPP_f1549043526a_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_f654413245e_bool(Eq_x_0,Eq_x_1) = hAPP_f654413245e_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_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_86,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_87,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_88,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_89,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_90,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_91,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_92,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_93,axiom,
    ( p(Eq_x_0) = p(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_94,axiom,
    ( mgt(Eq_x_0) = mgt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_95,axiom,
    ( wt(Eq_x_0) = wt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_96,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_97,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_98,axiom,
    ( collec1015864663l_bool(Eq_x_0) = collec1015864663l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_99,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_100,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_101,axiom,
    ( collec1613912337l_bool(Eq_x_0) = collec1613912337l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_102,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_103,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_104,axiom,
    ( collec707592106l_bool(Eq_x_0) = collec707592106l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_105,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_106,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_107,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_108,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_109,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_110,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_111,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_112,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_113,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_114,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_115,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_116,axiom,
    ( insert_fun_nat_bool(Eq_x_0,Eq_x_1) = insert_fun_nat_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_117,axiom,
    ( insert_nat(Eq_x_0,Eq_x_1) = insert_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_118,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_119,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_120,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_121,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_122,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_123,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_124,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_125,axiom,
    ( hAPP_f22106695ol_nat(Eq_x_0,Eq_x_1) = hAPP_f22106695ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_126,axiom,
    ( hAPP_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_127,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_128,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_129,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_130,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_131,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_132,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_133,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_134,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_135,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_136,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_137,axiom,
    ( collect_nat(Eq_x_0) = collect_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_138,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_139,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_140,axiom,
    ( minus_minus_nat(Eq_x_0) = minus_minus_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_141,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_142,axiom,
    ( image_nat_nat(Eq_x_0,Eq_x_1) = image_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_143,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_144,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_145,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_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,
    ( cOMBB_1212655066ol_nat(Eq_x_0,Eq_x_1) = cOMBB_1212655066ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_148,axiom,
    ( cOMBC_nat_pname_bool(Eq_x_0) = cOMBC_nat_pname_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_149,axiom,
    ( hAPP_p1499970991t_bool(Eq_x_0,Eq_x_1) = hAPP_p1499970991t_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,
    ( cOMBC_1355376034l_bool(Eq_x_0) = cOMBC_1355376034l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_151,axiom,
    ( cOMBB_610033911bool_a(Eq_x_0,Eq_x_1) = cOMBB_610033911bool_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_152,axiom,
    ( cOMBC_a_pname_bool(Eq_x_0) = cOMBC_a_pname_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_153,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_154,axiom,
    ( cOMBB_542850580_pname(Eq_x_0,Eq_x_1) = cOMBB_542850580_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_155,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_156,axiom,
    ( cOMBC_1245412066l_bool(Eq_x_0) = cOMBC_1245412066l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_157,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_158,axiom,
    ( cOMBB_141086128t_bool(Eq_x_0,Eq_x_1) = cOMBB_141086128t_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_159,axiom,
    ( cOMBC_615407716e_bool(Eq_x_0) = cOMBC_615407716e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_160,axiom,
    ( hAPP_p130839763l_bool(Eq_x_0,Eq_x_1) = hAPP_p130839763l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_161,axiom,
    ( cOMBC_1988546018l_bool(Eq_x_0) = cOMBC_1988546018l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_162,axiom,
    ( cOMBB_598082538e_bool(Eq_x_0,Eq_x_1) = cOMBB_598082538e_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_163,axiom,
    ( cOMBC_1004116266e_bool(Eq_x_0) = cOMBC_1004116266e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_164,axiom,
    ( cOMBC_1880041174l_bool(Eq_x_0) = cOMBC_1880041174l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_165,axiom,
    ( cOMBB_1693087065a_bool(Eq_x_0,Eq_x_1) = cOMBB_1693087065a_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,
    ( cOMBC_1738168533e_bool(Eq_x_0) = cOMBC_1738168533e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_167,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_168,axiom,
    ( cOMBB_1321347587bool_a(Eq_x_0,Eq_x_1) = cOMBB_1321347587bool_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,
    ( cOMBC_a_nat_bool(Eq_x_0) = cOMBC_a_nat_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_170,axiom,
    ( hAPP_a_nat(Eq_x_0,Eq_x_1) = hAPP_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_171,axiom,
    ( cOMBB_523834888_pname(Eq_x_0,Eq_x_1) = cOMBB_523834888_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_172,axiom,
    ( cOMBC_pname_nat_bool(Eq_x_0) = cOMBC_pname_nat_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_173,axiom,
    ( hAPP_pname_nat(Eq_x_0,Eq_x_1) = hAPP_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_174,axiom,
    ( cOMBB_1250273980t_bool(Eq_x_0,Eq_x_1) = cOMBB_1250273980t_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,
    ( cOMBC_385542954t_bool(Eq_x_0) = cOMBC_385542954t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_176,axiom,
    ( cOMBB_1896684278e_bool(Eq_x_0,Eq_x_1) = cOMBB_1896684278e_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_177,axiom,
    ( cOMBC_1666426608t_bool(Eq_x_0) = cOMBC_1666426608t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_178,axiom,
    ( cOMBB_164527437a_bool(Eq_x_0,Eq_x_1) = cOMBB_164527437a_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,
    ( cOMBC_619334683t_bool(Eq_x_0) = cOMBC_619334683t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_180,axiom,
    ( cOMBB_1885489796ol_nat(Eq_x_0,Eq_x_1) = cOMBB_1885489796ol_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_181,axiom,
    ( cOMBC_nat_a_bool(Eq_x_0) = cOMBC_nat_a_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_182,axiom,
    ( hAPP_a_fun_nat_bool(Eq_x_0,Eq_x_1) = hAPP_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_183,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_184,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_185,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_186,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_187,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_188,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_189,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_190,axiom,
    ( cOMBB_928955006_pname(Eq_x_0,Eq_x_1) = cOMBB_928955006_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_191,axiom,
    ( cOMBC_267053842l_bool(Eq_x_0) = cOMBC_267053842l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_192,axiom,
    ( cOMBB_408569982_pname(Eq_x_0,Eq_x_1) = cOMBB_408569982_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_193,axiom,
    ( cOMBB_392435466_pname(Eq_x_0,Eq_x_1) = cOMBB_392435466_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_194,axiom,
    ( cOMBC_445755039l_bool(Eq_x_0) = cOMBC_445755039l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_195,axiom,
    ( cOMBB_a_fun_a_bool_a(Eq_x_0,Eq_x_1) = cOMBB_a_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_196,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_197,axiom,
    ( cOMBB_743407885bool_a(Eq_x_0,Eq_x_1) = cOMBB_743407885bool_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_198,axiom,
    ( cOMBC_777206479l_bool(Eq_x_0) = cOMBC_777206479l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_199,axiom,
    ( cOMBB_1137537805bool_a(Eq_x_0,Eq_x_1) = cOMBB_1137537805bool_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_200,axiom,
    ( cOMBC_1834145417l_bool(Eq_x_0) = cOMBC_1834145417l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_201,axiom,
    ( cOMBB_472261505bool_a(Eq_x_0,Eq_x_1) = cOMBB_472261505bool_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_202,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_203,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_204,axiom,
    ( cOMBB_238756964t_bool(Eq_x_0,Eq_x_1) = cOMBB_238756964t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_205,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_206,axiom,
    ( cOMBK_1994329625t_bool(Eq_x_0) = cOMBK_1994329625t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_207,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_208,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_209,axiom,
    ( body(Eq_x_0) = body(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_210,axiom,
    ( the_com(Eq_x_0) = the_com(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_211,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_212,axiom,
    ( plus_plus_nat(Eq_x_0) = plus_plus_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_213,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_214,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_215,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_216,axiom,
    ( hAPP_a1392362872l_bool(Eq_x_0,Eq_x_1) = hAPP_a1392362872l_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_217,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_218,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_219,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_220,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_221,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_222,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_223,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_224,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_225,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_226,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_227,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_228,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_229,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_230,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_231,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_232,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_233,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_234,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_235,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_236,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_237,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_238,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_239,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_240,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_241,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_242,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_243,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_244,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_245,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_246,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_247,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_248,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_249,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_250,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_251,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_252,axiom,
    ( sK33(Eq_x_0,Eq_x_1) = sK33(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,
    ( sK34(Eq_x_0,Eq_x_1) = sK34(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,
    ( sK35(Eq_x_0,Eq_x_1) = sK35(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_255,axiom,
    ( sK36(Eq_x_0,Eq_x_1) = sK36(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_256,axiom,
    ( sK37(Eq_x_0,Eq_x_1) = sK37(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,
    ( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_258,axiom,
    ( sK39(Eq_x_0,Eq_x_1) = sK39(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_259,axiom,
    ( sK40(Eq_x_0,Eq_x_1) = sK40(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_260,axiom,
    ( sK41(Eq_x_0,Eq_x_1) = sK41(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_261,axiom,
    ( sK42(Eq_x_0,Eq_x_1) = sK42(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,
    ( sK43(Eq_x_0,Eq_x_1) = sK43(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,
    ( sK44(Eq_x_0,Eq_x_1) = sK44(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,
    ( sK45(Eq_x_0,Eq_x_1) = sK45(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,
    ( sK46(Eq_x_0,Eq_x_1) = sK46(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,
    ( sK47(Eq_x_0,Eq_x_1) = sK47(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,
    ( sK48(Eq_x_0,Eq_x_1) = sK48(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,
    ( sK49(Eq_x_0,Eq_x_1) = sK49(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,
    ( sK50(Eq_x_0,Eq_x_1) = sK50(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,
    ( sK51(Eq_x_0,Eq_x_1) = sK51(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,
    ( sK52(Eq_x_0,Eq_x_1) = sK52(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_272,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_273,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_274,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_275,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_276,axiom,
    ( sK57(Eq_x_0,Eq_x_1,Eq_x_2) = sK57(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,
    ( 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_278,axiom,
    ( sK59(Eq_x_0,Eq_x_1,Eq_x_2) = sK59(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,
    ( sK60(Eq_x_0,Eq_x_1,Eq_x_2) = sK60(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,
    ( sK61(Eq_x_0,Eq_x_1,Eq_x_2) = sK61(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,
    ( sK62(Eq_x_0,Eq_x_1,Eq_x_2) = sK62(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,
    ( sK63(Eq_x_0,Eq_x_1,Eq_x_2) = sK63(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,
    ( 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_284,axiom,
    ( sK65(Eq_x_0,Eq_x_1,Eq_x_2) = sK65(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,
    ( 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_286,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_287,axiom,
    ( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(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,
    ( 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_289,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_290,axiom,
    ( sK71(Eq_x_0,Eq_x_1) = sK71(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_291,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_292,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_293,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_294,axiom,
    ( sK75(Eq_x_0,Eq_x_1,Eq_x_2) = sK75(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,
    ( sK76(Eq_x_0,Eq_x_1,Eq_x_2) = sK76(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,
    ( sK77(Eq_x_0,Eq_x_1,Eq_x_2) = sK77(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,
    ( sK78(Eq_x_0,Eq_x_1,Eq_x_2) = sK78(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,
    ( sK79(Eq_x_0) = sK79(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_299,axiom,
    ( sK80(Eq_x_0,Eq_x_1) = sK80(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_300,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_301,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_302,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_303,axiom,
    ( sK84(Eq_x_0,Eq_x_1) = sK84(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_304,axiom,
    ( sK85(Eq_x_0) = sK85(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_305,axiom,
    ( sK86(Eq_x_0) = sK86(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_306,axiom,
    ( sK87(Eq_x_0) = sK87(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_307,axiom,
    ( sK88(Eq_x_0) = sK88(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_308,axiom,
    ( sK89(Eq_x_0) = sK89(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_309,axiom,
    ( sK90(Eq_x_0) = sK90(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_310,axiom,
    ( sK91(Eq_x_0) = sK91(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_311,axiom,
    ( sK92(Eq_x_0) = sK92(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_312,axiom,
    ( sK93(Eq_x_0) = sK93(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_313,axiom,
    ( sK94(Eq_x_0) = sK94(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_314,axiom,
    ( sK95(Eq_x_0) = sK95(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_315,axiom,
    ( sK96(Eq_x_0) = sK96(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_316,axiom,
    ( sK97(Eq_x_0) = sK97(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_317,axiom,
    ( sK98(Eq_x_0) = sK98(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_318,axiom,
    ( sK99(Eq_x_0) = sK99(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_319,axiom,
    ( sK100(Eq_x_0) = sK100(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_320,axiom,
    ( sK101(Eq_x_0) = sK101(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_321,axiom,
    ( sK102(Eq_x_0) = sK102(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_322,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_323,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_324,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_325,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_326,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_327,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_328,axiom,
    ( sK109(Eq_x_0,Eq_x_1,Eq_x_2) = sK109(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_329,axiom,
    ( sK110(Eq_x_0,Eq_x_1,Eq_x_2) = sK110(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_330,axiom,
    ( sK111(Eq_x_0,Eq_x_1,Eq_x_2) = sK111(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_331,axiom,
    ( sK112(Eq_x_0,Eq_x_1,Eq_x_2) = sK112(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_332,axiom,
    ( sK113(Eq_x_0,Eq_x_1,Eq_x_2) = sK113(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_333,axiom,
    ( sK114(Eq_x_0,Eq_x_1,Eq_x_2) = sK114(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_334,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_335,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_336,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_337,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_338,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_339,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_340,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_341,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_342,axiom,
    ( sK123(Eq_x_0) = sK123(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_343,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_344,axiom,
    ( sK125(Eq_x_0,Eq_x_1) = sK125(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_345,axiom,
    ( sK126(Eq_x_0,Eq_x_1,Eq_x_2) = sK126(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_346,axiom,
    ( sK127(Eq_x_0,Eq_x_1,Eq_x_2) = sK127(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_347,axiom,
    ( sK128(Eq_x_0,Eq_x_1,Eq_x_2) = sK128(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_348,axiom,
    ( sK129(Eq_x_0,Eq_x_1) = sK129(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,
    ( sK130(Eq_x_0,Eq_x_1) = sK130(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_350,axiom,
    ( sK131(Eq_x_0,Eq_x_1,Eq_x_2) = sK131(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,
    ( sK132(Eq_x_0,Eq_x_1,Eq_x_2) = sK132(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_352,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_353,axiom,
    ( sK134(Eq_x_0,Eq_x_1) = sK134(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,
    ( 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_355,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_356,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_357,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_358,axiom,
    ( is_bool(Eq_y_0)
    | ~ is_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_359,axiom,
    ( is_a(Eq_y_0)
    | ~ is_a(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_360,axiom,
    ( is_pname(Eq_y_0)
    | ~ is_pname(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_361,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_362,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_363,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_364,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_365,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_366,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_367,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_368,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_369,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_370,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_371,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_372,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_373,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_374,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_375,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_376,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_377,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_378,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_379,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_380,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_381,axiom,
    ( sP19(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP19(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_382,axiom,
    ( sP20(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP20(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_383,axiom,
    ( sP21(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP21(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_384,axiom,
    ( sP22(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP22(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_385,axiom,
    ( sP23(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP23(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_386,axiom,
    ( sP24(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP24(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_387,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_388,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_389,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_390,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_391,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_392,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_393,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_394,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_395,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_396,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_397,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_398,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_399,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_400,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_401,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_402,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_403,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_404,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_405,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_406,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_407,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_408,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_409,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_410,axiom,
    ( sP48(Eq_y_0,Eq_y_1)
    | ~ sP48(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_411,axiom,
    ( sP49(Eq_y_0,Eq_y_1)
    | ~ sP49(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_412,axiom,
    ( sP50(Eq_y_0,Eq_y_1)
    | ~ sP50(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_413,axiom,
    ( sP51(Eq_y_0,Eq_y_1)
    | ~ sP51(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_414,axiom,
    ( sP52(Eq_y_0,Eq_y_1)
    | ~ sP52(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_415,axiom,
    ( sP53(Eq_y_0,Eq_y_1)
    | ~ sP53(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_416,axiom,
    ( sP54(Eq_y_0,Eq_y_1)
    | ~ sP54(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_417,axiom,
    ( sP55(Eq_y_0,Eq_y_1)
    | ~ sP55(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_418,axiom,
    ( sP56(Eq_y_0,Eq_y_1)
    | ~ sP56(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_419,axiom,
    ( sP57(Eq_y_0,Eq_y_1)
    | ~ sP57(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_420,axiom,
    ( sP58(Eq_y_0,Eq_y_1)
    | ~ sP58(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_421,axiom,
    ( sP59(Eq_y_0,Eq_y_1)
    | ~ sP59(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_422,axiom,
    ( sP60(Eq_y_0,Eq_y_1)
    | ~ sP60(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_423,axiom,
    ( sP61(Eq_y_0,Eq_y_1)
    | ~ sP61(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_424,axiom,
    ( sP62(Eq_y_0,Eq_y_1)
    | ~ sP62(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_425,axiom,
    ( sP63(Eq_y_0,Eq_y_1)
    | ~ sP63(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_426,axiom,
    ( sP64(Eq_y_0,Eq_y_1)
    | ~ sP64(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_427,axiom,
    ( sP65(Eq_y_0,Eq_y_1)
    | ~ sP65(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_428,axiom,
    ( sP66(Eq_y_0,Eq_y_1)
    | ~ sP66(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_429,axiom,
    ( sP67(Eq_y_0,Eq_y_1)
    | ~ sP67(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_430,axiom,
    ( sP68(Eq_y_0,Eq_y_1)
    | ~ sP68(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_431,axiom,
    ( sP69(Eq_y_0,Eq_y_1)
    | ~ sP69(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_432,axiom,
    ( sP70(Eq_y_0,Eq_y_1)
    | ~ sP70(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_433,axiom,
    ( sP71(Eq_y_0,Eq_y_1)
    | ~ sP71(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_434,axiom,
    ( sP72(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP72(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_435,axiom,
    ( sP73(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP73(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_436,axiom,
    ( sP74(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP74(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_437,axiom,
    ( sP75(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP75(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_438,axiom,
    ( sP76(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP76(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_439,axiom,
    ( sP77(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP77(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_440,axiom,
    ( sP78(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP78(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_441,axiom,
    ( sP79(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP79(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_442,axiom,
    ( sP80(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP80(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_443,axiom,
    ( sP81(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP81(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_444,axiom,
    ( sP82(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP82(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_445,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_446,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_447,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_448,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_449,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_450,axiom,
    ( sP88(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP88(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_451,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_452,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_453,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_454,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_455,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_456,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_457,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_458,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_459,axiom,
    ( sP97(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP97(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_460,axiom,
    ( sP98(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP98(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_461,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_462,axiom,
    ( sP100(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP100(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_463,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_464,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_465,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_466,axiom,
    ( sP104(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP104(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_467,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_468,axiom,
    ( sP106(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP106(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_469,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_470,axiom,
    ( sP108(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP108(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_471,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_472,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_473,axiom,
    ( sP111(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP111(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_474,axiom,
    ( sP112(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP112(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_475,axiom,
    ( sP113(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP113(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_476,axiom,
    ( sP114(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP114(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_477,axiom,
    ( sP115(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP115(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_478,axiom,
    ( sP116(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP116(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_479,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_480,axiom,
    ( sP118(Eq_y_0,Eq_y_1)
    | ~ sP118(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_481,axiom,
    ( sP119(Eq_y_0,Eq_y_1)
    | ~ sP119(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_482,axiom,
    ( sP120(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP120(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_483,axiom,
    ( sP121(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP121(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_484,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_485,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_486,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_487,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_488,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_489,axiom,
    ( sP127(Eq_y_0,Eq_y_1)
    | ~ sP127(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_490,axiom,
    ( sP128(Eq_y_0,Eq_y_1)
    | ~ sP128(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_491,axiom,
    ( sP129(Eq_y_0,Eq_y_1)
    | ~ sP129(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_492,axiom,
    ( sP130(Eq_y_0,Eq_y_1)
    | ~ sP130(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_493,axiom,
    ( sP131(Eq_y_0)
    | ~ sP131(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_494,axiom,
    ( sP132(Eq_y_0)
    | ~ sP132(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_495,axiom,
    ( sP133(Eq_y_0)
    | ~ sP133(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_496,axiom,
    ( sP134(Eq_y_0)
    | ~ sP134(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_497,axiom,
    ( sP135(Eq_y_0)
    | ~ sP135(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_498,axiom,
    ( sP136(Eq_y_0)
    | ~ sP136(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_499,axiom,
    ( sP137(Eq_y_0)
    | ~ sP137(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_500,axiom,
    ( sP138(Eq_y_0)
    | ~ sP138(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_501,axiom,
    ( sP139(Eq_y_0)
    | ~ sP139(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_502,axiom,
    ( sP140(Eq_y_0,Eq_y_1)
    | ~ sP140(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_503,axiom,
    ( sP141(Eq_y_0)
    | ~ sP141(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_504,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_505,axiom,
    ( sP143(Eq_y_0)
    | ~ sP143(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_506,axiom,
    ( sP144(Eq_y_0,Eq_y_1)
    | ~ sP144(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,
    ( sP145(Eq_y_0)
    | ~ sP145(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_508,axiom,
    ( sP146(Eq_y_0,Eq_y_1)
    | ~ sP146(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,
    ( sP147(Eq_y_0)
    | ~ sP147(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_510,axiom,
    ( sP148(Eq_y_0)
    | ~ sP148(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_511,axiom,
    ( sP149(Eq_y_0)
    | ~ sP149(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_512,axiom,
    ( sP150(Eq_y_0)
    | ~ sP150(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_513,axiom,
    ( sP151(Eq_y_0)
    | ~ sP151(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_514,axiom,
    ( sP152(Eq_y_0)
    | ~ sP152(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_515,axiom,
    ( sP153(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP153(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_516,axiom,
    ( sP154(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP154(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_517,axiom,
    ( sP155(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP155(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_518,axiom,
    ( sP156(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP156(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_519,axiom,
    ( sP157(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP157(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_520,axiom,
    ( sP158(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP158(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_521,axiom,
    ( sP159(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP159(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_522,axiom,
    ( sP160(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP160(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_523,axiom,
    ( sP161(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP161(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_524,axiom,
    ( sP162(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP162(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_525,axiom,
    ( sP163(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP163(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_526,axiom,
    ( sP164(Eq_y_0,Eq_y_1)
    | ~ sP164(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,
    ( sP165(Eq_y_0,Eq_y_1)
    | ~ sP165(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,
    ( sP166(Eq_y_0)
    | ~ sP166(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_529,axiom,
    ( sP167(Eq_y_0)
    | ~ sP167(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_530,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_531,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_532,axiom,
    ( sP170(Eq_y_0,Eq_y_1)
    | ~ sP170(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_533,axiom,
    ( sP171(Eq_y_0,Eq_y_1)
    | ~ sP171(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_534,axiom,
    ( sP172(Eq_y_0,Eq_y_1)
    | ~ sP172(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_535,axiom,
    ( sP173(Eq_y_0,Eq_y_1)
    | ~ sP173(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_536,axiom,
    ( sP174(Eq_y_0,Eq_y_1)
    | ~ sP174(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_537,axiom,
    ( sP175(Eq_y_0,Eq_y_1)
    | ~ sP175(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_538,axiom,
    ( sP176(Eq_y_0,Eq_y_1)
    | ~ sP176(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_539,axiom,
    ( sP177(Eq_y_0,Eq_y_1)
    | ~ sP177(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_540,axiom,
    ( sP178(Eq_y_0,Eq_y_1)
    | ~ sP178(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_541,axiom,
    ( sP179(Eq_y_0,Eq_y_1)
    | ~ sP179(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_542,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_543,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_544,axiom,
    ( sP182(Eq_y_0,Eq_y_1)
    | ~ sP182(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_545,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_546,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_547,axiom,
    ( sP185(Eq_y_0,Eq_y_1)
    | ~ sP185(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_548,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_549,axiom,
    ( sP187(Eq_y_0,Eq_y_1)
    | ~ sP187(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_550,axiom,
    ( sP188(Eq_y_0,Eq_y_1)
    | ~ sP188(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_551,axiom,
    ( sP189(Eq_y_0,Eq_y_1)
    | ~ sP189(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_552,axiom,
    ( sP190(Eq_y_0,Eq_y_1)
    | ~ sP190(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_553,axiom,
    ( sP191(Eq_y_0,Eq_y_1)
    | ~ sP191(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_554,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_555,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_556,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_557,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_558,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_559,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_560,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_561,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_562,axiom,
    ( sP200(Eq_y_0,Eq_y_1)
    | ~ sP200(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_563,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_564,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_565,axiom,
    ( sP203(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP203(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,
    ( 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_567,axiom,
    ( sP205(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP205(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,
    ( 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_569,axiom,
    ( sP207(Eq_y_0,Eq_y_1)
    | ~ sP207(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_570,axiom,
    ( sP208(Eq_y_0,Eq_y_1)
    | ~ sP208(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_571,axiom,
    ( sP209(Eq_y_0,Eq_y_1)
    | ~ sP209(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_572,axiom,
    ( sP210(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP210(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,
    ( 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_574,axiom,
    ( sP212(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP212(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,
    ( sP213(Eq_y_0,Eq_y_1)
    | ~ sP213(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_576,axiom,
    ( sP214(Eq_y_0,Eq_y_1)
    | ~ sP214(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,
    ( sP215(Eq_y_0,Eq_y_1)
    | ~ sP215(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,
    ( sP216(Eq_y_0,Eq_y_1)
    | ~ sP216(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,
    ( sP217(Eq_y_0,Eq_y_1)
    | ~ sP217(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,
    ( sP218(Eq_y_0,Eq_y_1)
    | ~ sP218(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,
    ( 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_582,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_583,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_584,axiom,
    ( sP222(Eq_y_0,Eq_y_1)
    | ~ sP222(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,
    ( sP223(Eq_y_0,Eq_y_1)
    | ~ sP223(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,
    ( sP224(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP224(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_587,axiom,
    ( sP225(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP225(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,
    ( sP226(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP226(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,
    ( sP227(Eq_y_0,Eq_y_1)
    | ~ sP227(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_590,axiom,
    ( sP228(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP228(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,
    ( sP229(Eq_y_0,Eq_y_1)
    | ~ sP229(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_592,axiom,
    ( sP230(Eq_y_0,Eq_y_1)
    | ~ sP230(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,
    ( sP231(Eq_y_0,Eq_y_1)
    | ~ sP231(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,
    ( 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_595,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_596,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_597,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_598,axiom,
    ( sP236(Eq_y_0,Eq_y_1)
    | ~ sP236(Eq_x_0,Eq_x_1)
    | 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+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03  This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04  % Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36  % Computer : n009.cluster.edu
% 0.11/0.36  % Model    : x86_64 x86_64
% 0.11/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36  % Memory   : 8046.5625MB
% 0.11/0.36  % OS       : Linux 6.8.0-71-generic
% 0.11/0.37  % CPULimit : 300
% 0.11/0.37  % WCLimit  : 300
% 0.11/0.37  % DateTime : Sun Sep 20 05:41:12 UTC 2026
% 0.11/0.37  % CPUTime  : 
% 59.17/59.48  % SZS status Theorem for theBenchmark
% 59.17/59.48  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------