ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW474+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n015.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 09:08:03 AM UTC 2026

% Result   : Theorem 150.12s 160.49s
% Output   : Proof 150.40s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
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_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_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_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_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_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_Com_OWT,axiom,
    ! [B_1_1] : is_bool(wt(B_1_1)),
    file('theBenchmark.p',gsy_c_Com_OWT) ).

fof(gsy_c_Com_OWT__bodies,hypothesis,
    is_bool(wT_bodies),
    file('theBenchmark.p',gsy_c_Com_OWT__bodies) ).

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

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_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_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_Hoare__Mirabelle__jfehddehev_Ostate__not__singleton,hypothesis,
    is_bool(hoare_165779456gleton),
    file('theBenchmark.p',gsy_c_Hoare__Mirabelle__jfehddehev_Ostate__not__singleton) ).

fof(gsy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,hypothesis,
    ! [B_1_1] : is_fun_pname_bool(dom_pname_com(B_1_1)),
    file('theBenchmark.p',gsy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom) ).

fof(gsy_c_Map_Odom_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Ocom,axiom,
    ! [B_1_1] : is_fun1661590463l_bool(dom_fu2081503504ol_com(B_1_1)),
    file('theBenchmark.p',gsy_c_Map_Odom_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Ocom) ).

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_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_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_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_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_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__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta,axiom,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_54689091_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta) ).

fof(gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta_001,axiom,
    ! [B_1_1,B_2_1] : is_fun1661590463l_bool(image_2131964411e_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta_001) ).

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__Hoare____Mirabelle____jfehddehev__Otriple_Itc__,axiom,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_187965177_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL,axiom,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_1705983821_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otri,axiom,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_1619336331_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otri) ).

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_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_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_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2_1] :
      ( is_pname(B_2_1)
     => is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom,
    ! [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__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0,axiom,
    ! [B_1_1,B_2_1] : is_pname(hAPP_H1621176307_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0) ).

fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_002,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_H78829294e_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_002) ).

fof(gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_003,axiom,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_H356885323e_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_003) ).

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,axiom,
    ! [B_1_1,B_2_1] :
      ( ( is_fun_pname_bool(B_2_1)
        & is_fun1661590463l_bool(B_1_1) )
     => is_bool(hAPP_f1664156314l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(B_2_1)
     => is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(B_2_1)
     => is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O,axiom,
    ! [B_1_1,B_2_1] : is_pname(hAPP_f560369737_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O_004,hypothesis,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f971112728l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O_004) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo,axiom,
    ! [B_1_1,B_2_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_005,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_005) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f166538662l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It) ).

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__Hoare____Mirabelle____jfehddehev__O,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f468958928l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__O) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f595608956l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfeh,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1022807134l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfeh) ).

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

fof(fact_0_empty,axiom,
    ! [G] : hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),bot_bo620288102e_bool)),
    file('theBenchmark.p',fact_0_empty) ).

fof(fact_1_asm,axiom,
    ! [Ts,G] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,Ts),G))
     => hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts)) ),
    file('theBenchmark.p',fact_1_asm) ).

fof(fact_2_weaken,axiom,
    ! [Ts,G,Ts_1] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts_1))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,Ts),Ts_1))
       => hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts)) ) ),
    file('theBenchmark.p',fact_2_weaken) ).

fof(fact_3_thin,axiom,
    ! [G,G_1,Ts] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G_1),Ts))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,G_1),G))
       => hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts)) ) ),
    file('theBenchmark.p',fact_3_thin) ).

fof(fact_4_cut,axiom,
    ! [G,G_1,Ts] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G_1),Ts))
     => ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),G_1))
       => hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts)) ) ),
    file('theBenchmark.p',fact_4_cut) ).

fof(fact_5_hoare__derivs_Oinsert,axiom,
    ! [Ts,G,T] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(T,bot_bo620288102e_bool)))
     => ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts))
       => hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(T,Ts))) ) ),
    file('theBenchmark.p',fact_5_hoare__derivs_Oinsert) ).

fof(fact_6_derivs__insertD,axiom,
    ! [G,T,Ts] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(T,Ts)))
     => ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts))
        & hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(T,bot_bo620288102e_bool))) ) ),
    file('theBenchmark.p',fact_6_derivs__insertD) ).

fof(fact_7_MGT__BodyN,axiom,
    ! [Pn_1,G] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1)),G)),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),bot_bo620288102e_bool)))
     => hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1)),bot_bo620288102e_bool))) ),
    file('theBenchmark.p',fact_7_MGT__BodyN) ).

fof(fact_8_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A)))) ),
    file('theBenchmark.p',fact_8_finite__Collect__subsets) ).

fof(fact_9_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,A))
     => hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(ord_le1285840794e_bool),A)))) ),
    file('theBenchmark.p',fact_9_finite__Collect__subsets) ).

fof(fact_10_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
     => hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),A)))) ),
    file('theBenchmark.p',fact_10_finite__Collect__subsets) ).

fof(fact_11_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,A))
     => hBOOL(hAPP_f1022807134l_bool(finite34021339l_bool,collec256567069l_bool(hAPP_f667366769l_bool(cOMBC_747715418l_bool(ord_le889598034l_bool),A)))) ),
    file('theBenchmark.p',fact_11_finite__Collect__subsets) ).

fof(fact_12_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A))
     => hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(hAPP_f585161855l_bool(cOMBC_1691491604l_bool(ord_le287025148l_bool),A)))) ),
    file('theBenchmark.p',fact_12_finite__Collect__subsets) ).

fof(fact_13_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A)))) ),
    file('theBenchmark.p',fact_13_finite__Collect__subsets) ).

fof(fact_14_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_2003357581_state(H,Fa))) ),
    file('theBenchmark.p',fact_14_finite__imageI) ).

fof(fact_15_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,Fa))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(H,Fa))) ),
    file('theBenchmark.p',fact_15_finite__imageI) ).

fof(fact_16_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,Fa))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1619336331_pname(H,Fa))) ),
    file('theBenchmark.p',fact_16_finite__imageI) ).

fof(fact_17_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,Fa))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_187965177_pname(H,Fa))) ),
    file('theBenchmark.p',fact_17_finite__imageI) ).

fof(fact_18_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(H,Fa))) ),
    file('theBenchmark.p',fact_18_finite__imageI) ).

fof(fact_19_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,Fa))
     => hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_677922117_state(H,Fa))) ),
    file('theBenchmark.p',fact_19_finite__imageI) ).

fof(fact_20_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,Fa))
     => hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_892968839_state(H,Fa))) ),
    file('theBenchmark.p',fact_20_finite__imageI) ).

fof(fact_21_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,Fa))
     => hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_18964633_state(H,Fa))) ),
    file('theBenchmark.p',fact_21_finite__imageI) ).

fof(fact_22_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
     => hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_516545147_state(H,Fa))) ),
    file('theBenchmark.p',fact_22_finite__imageI) ).

fof(fact_23_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(H,Fa))) ),
    file('theBenchmark.p',fact_23_finite__imageI) ).

fof(fact_24_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,image_288317893l_bool(H,Fa))) ),
    file('theBenchmark.p',fact_24_finite__imageI) ).

fof(fact_25_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,image_70449425e_bool(H,Fa))) ),
    file('theBenchmark.p',fact_25_finite__imageI) ).

fof(fact_26_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(H,Fa))) ),
    file('theBenchmark.p',fact_26_finite__imageI) ).

fof(fact_27_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa))
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1210605179l_bool(H,Fa))) ),
    file('theBenchmark.p',fact_27_finite__imageI) ).

fof(fact_28_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa))
     => hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,image_1761575943l_bool(H,Fa))) ),
    file('theBenchmark.p',fact_28_finite__imageI) ).

fof(fact_29_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa))
     => hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,image_1828608335e_bool(H,Fa))) ),
    file('theBenchmark.p',fact_29_finite__imageI) ).

fof(fact_30_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_2131964411e_bool(H,Fa))) ),
    file('theBenchmark.p',fact_30_finite__imageI) ).

fof(fact_31_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_54689091_pname(H,Fa))) ),
    file('theBenchmark.p',fact_31_finite__imageI) ).

fof(fact_32_finite__imageI,axiom,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(H,Fa))) ),
    file('theBenchmark.p',fact_32_finite__imageI) ).

fof(fact_33_empty__subsetI,axiom,
    ! [A] : hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,bot_bo620288102e_bool),A)),
    file('theBenchmark.p',fact_33_empty__subsetI) ).

fof(fact_34_empty__subsetI,axiom,
    ! [A] : hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,bot_bo1649642514l_bool),A)),
    file('theBenchmark.p',fact_34_empty__subsetI) ).

fof(fact_35_empty__subsetI,axiom,
    ! [A] : hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,bot_bo535777328l_bool),A)),
    file('theBenchmark.p',fact_35_empty__subsetI) ).

fof(fact_36_empty__subsetI,axiom,
    ! [A] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A)),
    file('theBenchmark.p',fact_36_empty__subsetI) ).

fof(fact_37_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,A))
     => hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(A_2,A))) ),
    file('theBenchmark.p',fact_37_finite_OinsertI) ).

fof(fact_38_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_2,A))) ),
    file('theBenchmark.p',fact_38_finite_OinsertI) ).

fof(fact_39_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(A_2,A))) ),
    file('theBenchmark.p',fact_39_finite_OinsertI) ).

fof(fact_40_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,A))
     => hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,insert203537868l_bool(A_2,A))) ),
    file('theBenchmark.p',fact_40_finite_OinsertI) ).

fof(fact_41_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A))
     => hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(A_2,A))) ),
    file('theBenchmark.p',fact_41_finite_OinsertI) ).

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

fof(fact_43_finite_OemptyI,axiom,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    file('theBenchmark.p',fact_43_finite_OemptyI) ).

fof(fact_44_finite_OemptyI,axiom,
    hBOOL(hAPP_f971112728l_bool(finite364844667_state,bot_bo620288102e_bool)),
    file('theBenchmark.p',fact_44_finite_OemptyI) ).

fof(fact_45_finite_OemptyI,axiom,
    hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,bot_bo1537088220l_bool)),
    file('theBenchmark.p',fact_45_finite_OemptyI) ).

fof(fact_46_finite_OemptyI,axiom,
    hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,bot_bo1761158942l_bool)),
    file('theBenchmark.p',fact_46_finite_OemptyI) ).

fof(fact_47_finite_OemptyI,axiom,
    hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,bot_bo535777328l_bool)),
    file('theBenchmark.p',fact_47_finite_OemptyI) ).

fof(fact_48_finite_OemptyI,axiom,
    hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)),
    file('theBenchmark.p',fact_48_finite_OemptyI) ).

fof(fact_49_finite__Collect__conjI,axiom,
    ! [Q_1,P_1] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(P_1))) )
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,P_1),Q_1)))) ),
    file('theBenchmark.p',fact_49_finite__Collect__conjI) ).

fof(fact_50_finite__Collect__conjI,axiom,
    ! [Q_1,P_1] :
      ( ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(Q_1)))
        | hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(P_1))) )
     => hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,P_1),Q_1)))) ),
    file('theBenchmark.p',fact_50_finite__Collect__conjI) ).

fof(fact_51_finite__Collect__conjI,axiom,
    ! [Q_1,P_1] :
      ( ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(Q_1)))
        | hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(P_1))) )
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(cOMBS_811933079l_bool(cOMBB_689948150l_bool(fconj,P_1),Q_1)))) ),
    file('theBenchmark.p',fact_51_finite__Collect__conjI) ).

fof(fact_52_finite__Collect__conjI,axiom,
    ! [Q_1,P_1] :
      ( ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(Q_1)))
        | hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(P_1))) )
     => hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(cOMBS_1358309691l_bool(cOMBB_404111180l_bool(fconj,P_1),Q_1)))) ),
    file('theBenchmark.p',fact_52_finite__Collect__conjI) ).

fof(fact_53_finite__Collect__conjI,axiom,
    ! [Q_1,P_1] :
      ( ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(Q_1)))
        | hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(P_1))) )
     => hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,P_1),Q_1)))) ),
    file('theBenchmark.p',fact_53_finite__Collect__conjI) ).

fof(fact_54_finite__Collect__conjI,axiom,
    ! [Q_1,P_1] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
        | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(P_1))) )
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,P_1),Q_1)))) ),
    file('theBenchmark.p',fact_54_finite__Collect__conjI) ).

fof(fact_55_image__constant__conv,axiom,
    ! [C_1,A] :
      ( is_fun_pname_bool(A)
     => ( ( A != bot_bo844097828e_bool
         => image_2003357581_state(cOMBK_367030522_pname(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool) )
        & ( A = bot_bo844097828e_bool
         => image_2003357581_state(cOMBK_367030522_pname(C_1),A) = bot_bo620288102e_bool ) ) ),
    file('theBenchmark.p',fact_55_image__constant__conv) ).

fof(fact_56_image__constant__conv,axiom,
    ! [C_1,A] :
      ( ( A != bot_bo620288102e_bool
       => image_54689091_pname(cOMBK_168215364_state(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) )
      & ( A = bot_bo620288102e_bool
       => image_54689091_pname(cOMBK_168215364_state(C_1),A) = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_56_image__constant__conv) ).

fof(fact_57_image__constant__conv,axiom,
    ! [C_1,A] :
      ( ( A != bot_bo620288102e_bool
       => image_2131964411e_bool(cOMBK_2035509764_state(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool) )
      & ( A = bot_bo620288102e_bool
       => image_2131964411e_bool(cOMBK_2035509764_state(C_1),A) = bot_bo1649642514l_bool ) ),
    file('theBenchmark.p',fact_57_image__constant__conv) ).

fof(fact_58_image__constant__conv,axiom,
    ! [C_1,A] :
      ( ( A != bot_bo620288102e_bool
       => image_1828608335e_bool(cOMBK_1039769424_state(C_1),A) = insert1556680138e_bool(C_1,bot_bo535777328l_bool) )
      & ( A = bot_bo620288102e_bool
       => image_1828608335e_bool(cOMBK_1039769424_state(C_1),A) = bot_bo535777328l_bool ) ),
    file('theBenchmark.p',fact_58_image__constant__conv) ).

fof(fact_59_image__constant__conv,axiom,
    ! [C_1,A] :
      ( is_fun_pname_bool(A)
     => ( ( A != bot_bo844097828e_bool
         => image_47868345e_bool(cOMBK_37193422_pname(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool) )
        & ( A = bot_bo844097828e_bool
         => image_47868345e_bool(cOMBK_37193422_pname(C_1),A) = bot_bo1649642514l_bool ) ) ),
    file('theBenchmark.p',fact_59_image__constant__conv) ).

fof(fact_60_image__constant__conv,axiom,
    ! [C_1,A] :
      ( is_fun_pname_bool(A)
     => ( ( A != bot_bo844097828e_bool
         => image_70449425e_bool(cOMBK_1706929794_pname(C_1),A) = insert1556680138e_bool(C_1,bot_bo535777328l_bool) )
        & ( A = bot_bo844097828e_bool
         => image_70449425e_bool(cOMBK_1706929794_pname(C_1),A) = bot_bo535777328l_bool ) ) ),
    file('theBenchmark.p',fact_60_image__constant__conv) ).

fof(fact_61_image__constant__conv,axiom,
    ! [C_1,A] :
      ( is_fun_pname_bool(A)
     => ( ( A != bot_bo844097828e_bool
         => image_pname_pname(cOMBK_pname_pname(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) )
        & ( A = bot_bo844097828e_bool
         => image_pname_pname(cOMBK_pname_pname(C_1),A) = bot_bo844097828e_bool ) ) ),
    file('theBenchmark.p',fact_61_image__constant__conv) ).

fof(fact_62_image__constant__conv,axiom,
    ! [C_1,A] :
      ( is_fun1661590463l_bool(A)
     => ( ( A != bot_bo1649642514l_bool
         => image_516545147_state(cOMBK_1503445380e_bool(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool) )
        & ( A = bot_bo1649642514l_bool
         => image_516545147_state(cOMBK_1503445380e_bool(C_1),A) = bot_bo620288102e_bool ) ) ),
    file('theBenchmark.p',fact_62_image__constant__conv) ).

fof(fact_63_image__constant__conv,axiom,
    ! [C_1,A] :
      ( ( A != bot_bo535777328l_bool
       => image_18964633_state(cOMBK_701929478e_bool(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool) )
      & ( A = bot_bo535777328l_bool
       => image_18964633_state(cOMBK_701929478e_bool(C_1),A) = bot_bo620288102e_bool ) ),
    file('theBenchmark.p',fact_63_image__constant__conv) ).

fof(fact_64_image__constant__conv,axiom,
    ! [C_1,A] :
      ( is_fun1661590463l_bool(A)
     => ( ( A != bot_bo1649642514l_bool
         => image_1283814551_pname(cOMBK_948730864e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) )
        & ( A = bot_bo1649642514l_bool
         => image_1283814551_pname(cOMBK_948730864e_bool(C_1),A) = bot_bo844097828e_bool ) ) ),
    file('theBenchmark.p',fact_64_image__constant__conv) ).

fof(fact_65_image__constant__conv,axiom,
    ! [C_1,A] :
      ( ( A != bot_bo535777328l_bool
       => image_187965177_pname(cOMBK_1589414042e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) )
      & ( A = bot_bo535777328l_bool
       => image_187965177_pname(cOMBK_1589414042e_bool(C_1),A) = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_65_image__constant__conv) ).

fof(fact_66_image__constant,axiom,
    ! [C_1,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => image_2003357581_state(cOMBK_367030522_pname(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool) ),
    file('theBenchmark.p',fact_66_image__constant) ).

fof(fact_67_image__constant,axiom,
    ! [C_1,X_2,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
     => image_54689091_pname(cOMBK_168215364_state(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) ),
    file('theBenchmark.p',fact_67_image__constant) ).

fof(fact_68_image__constant,axiom,
    ! [C_1,X_2,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
     => image_2131964411e_bool(cOMBK_2035509764_state(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool) ),
    file('theBenchmark.p',fact_68_image__constant) ).

fof(fact_69_image__constant,axiom,
    ! [C_1,X_2,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
     => image_1828608335e_bool(cOMBK_1039769424_state(C_1),A) = insert1556680138e_bool(C_1,bot_bo535777328l_bool) ),
    file('theBenchmark.p',fact_69_image__constant) ).

fof(fact_70_image__constant,axiom,
    ! [C_1,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => image_47868345e_bool(cOMBK_37193422_pname(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool) ),
    file('theBenchmark.p',fact_70_image__constant) ).

fof(fact_71_image__constant,axiom,
    ! [C_1,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => image_70449425e_bool(cOMBK_1706929794_pname(C_1),A) = insert1556680138e_bool(C_1,bot_bo535777328l_bool) ),
    file('theBenchmark.p',fact_71_image__constant) ).

fof(fact_72_image__constant,axiom,
    ! [C_1,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => image_pname_pname(cOMBK_pname_pname(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) ),
    file('theBenchmark.p',fact_72_image__constant) ).

fof(fact_73_image__constant,axiom,
    ! [C_1,X_2,A] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
     => image_516545147_state(cOMBK_1503445380e_bool(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool) ),
    file('theBenchmark.p',fact_73_image__constant) ).

fof(fact_74_image__constant,axiom,
    ! [C_1,X_2,A] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_2),A))
     => image_18964633_state(cOMBK_701929478e_bool(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool) ),
    file('theBenchmark.p',fact_74_image__constant) ).

fof(fact_75_image__constant,axiom,
    ! [C_1,X_2,A] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
     => image_1283814551_pname(cOMBK_948730864e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) ),
    file('theBenchmark.p',fact_75_image__constant) ).

fof(fact_76_image__constant,axiom,
    ! [C_1,X_2,A] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_2),A))
     => image_187965177_pname(cOMBK_1589414042e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool) ),
    file('theBenchmark.p',fact_76_image__constant) ).

fof(fact_77_insert__dom,axiom,
    ! [F,X_2,Y_2] :
      ( hAPP_p799580910on_com(F,X_2) = some_com(Y_2)
     => insert_pname(X_2,dom_pname_com(F)) = dom_pname_com(F) ),
    file('theBenchmark.p',fact_77_insert__dom) ).

fof(fact_78_insert__dom,axiom,
    ! [F,X_2,Y_2] :
      ( hAPP_f2138803836on_com(F,X_2) = some_com(Y_2)
     => insert1325755072e_bool(X_2,dom_fu2081503504ol_com(F)) = dom_fu2081503504ol_com(F) ),
    file('theBenchmark.p',fact_78_insert__dom) ).

fof(fact_79_insert__dom,axiom,
    ! [F,X_2,Y_2] :
      ( hAPP_f2134636538on_com(F,X_2) = some_com(Y_2)
     => insert1556680138e_bool(X_2,dom_fu1342267980ol_com(F)) = dom_fu1342267980ol_com(F) ),
    file('theBenchmark.p',fact_79_insert__dom) ).

fof(fact_80_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_2003357581_state(F,A)))
       => hBOOL(hAPP_f971112728l_bool(finite364844667_state,B)) ) ),
    file('theBenchmark.p',fact_80_finite__surj) ).

fof(fact_81_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1705983821_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_81_finite__surj) ).

fof(fact_82_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1619336331_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_82_finite__surj) ).

fof(fact_83_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_187965177_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_83_finite__surj) ).

fof(fact_84_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1283814551_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_84_finite__surj) ).

fof(fact_85_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_677922117_state(F,A)))
       => hBOOL(hAPP_f971112728l_bool(finite364844667_state,B)) ) ),
    file('theBenchmark.p',fact_85_finite__surj) ).

fof(fact_86_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,A))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_892968839_state(F,A)))
       => hBOOL(hAPP_f971112728l_bool(finite364844667_state,B)) ) ),
    file('theBenchmark.p',fact_86_finite__surj) ).

fof(fact_87_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_18964633_state(F,A)))
       => hBOOL(hAPP_f971112728l_bool(finite364844667_state,B)) ) ),
    file('theBenchmark.p',fact_87_finite__surj) ).

fof(fact_88_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_516545147_state(F,A)))
       => hBOOL(hAPP_f971112728l_bool(finite364844667_state,B)) ) ),
    file('theBenchmark.p',fact_88_finite__surj) ).

fof(fact_89_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,B),image_1642285373l_bool(F,A)))
       => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,B)) ) ),
    file('theBenchmark.p',fact_89_finite__surj) ).

fof(fact_90_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f468958928l_bool(hAPP_f667366769l_bool(ord_le889598034l_bool,B),image_288317893l_bool(F,A)))
       => hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,B)) ) ),
    file('theBenchmark.p',fact_90_finite__surj) ).

fof(fact_91_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_pname_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_91_finite__surj) ).

fof(fact_92_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,B),image_70449425e_bool(F,A)))
       => hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,B)) ) ),
    file('theBenchmark.p',fact_92_finite__surj) ).

fof(fact_93_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_47868345e_bool(F,A)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ),
    file('theBenchmark.p',fact_93_finite__surj) ).

fof(fact_94_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,A))
     => ( hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,B),image_1210605179l_bool(F,A)))
       => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,B)) ) ),
    file('theBenchmark.p',fact_94_finite__surj) ).

fof(fact_95_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,A))
     => ( hBOOL(hAPP_f468958928l_bool(hAPP_f667366769l_bool(ord_le889598034l_bool,B),image_1761575943l_bool(F,A)))
       => hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,B)) ) ),
    file('theBenchmark.p',fact_95_finite__surj) ).

fof(fact_96_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_54689091_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_96_finite__surj) ).

fof(fact_97_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,A))
     => ( hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,B),image_1828608335e_bool(F,A)))
       => hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,B)) ) ),
    file('theBenchmark.p',fact_97_finite__surj) ).

fof(fact_98_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,A))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_2131964411e_bool(F,A)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ),
    file('theBenchmark.p',fact_98_finite__surj) ).

fof(fact_99_subset__singletonD,axiom,
    ! [A,X_2] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),insert1415133716_state(X_2,bot_bo620288102e_bool)))
     => ( A = insert1415133716_state(X_2,bot_bo620288102e_bool)
        | A = bot_bo620288102e_bool ) ),
    file('theBenchmark.p',fact_99_subset__singletonD) ).

fof(fact_100_subset__singletonD,axiom,
    ! [A,X_2] :
      ( is_fun1661590463l_bool(A)
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),insert1325755072e_bool(X_2,bot_bo1649642514l_bool)))
       => ( A = insert1325755072e_bool(X_2,bot_bo1649642514l_bool)
          | A = bot_bo1649642514l_bool ) ) ),
    file('theBenchmark.p',fact_100_subset__singletonD) ).

fof(fact_101_subset__singletonD,axiom,
    ! [A,X_2] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),insert1556680138e_bool(X_2,bot_bo535777328l_bool)))
     => ( A = insert1556680138e_bool(X_2,bot_bo535777328l_bool)
        | A = bot_bo535777328l_bool ) ),
    file('theBenchmark.p',fact_101_subset__singletonD) ).

fof(fact_102_subset__singletonD,axiom,
    ! [A,X_2] :
      ( is_fun_pname_bool(A)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,bot_bo844097828e_bool)))
       => ( A = insert_pname(X_2,bot_bo844097828e_bool)
          | A = bot_bo844097828e_bool ) ) ),
    file('theBenchmark.p',fact_102_subset__singletonD) ).

fof(fact_103_MGF,axiom,
    ! [C_1] :
      ( hBOOL(hoare_165779456gleton)
     => ( hBOOL(wT_bodies)
       => ( hBOOL(wt(C_1))
         => hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,C_1),bot_bo620288102e_bool))) ) ) ),
    file('theBenchmark.p',fact_103_MGF) ).

fof(fact_104_emptyE,axiom,
    ! [A_2] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),bot_bo620288102e_bool)),
    file('theBenchmark.p',fact_104_emptyE) ).

fof(fact_105_emptyE,axiom,
    ! [A_2] : ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),bot_bo1649642514l_bool)),
    file('theBenchmark.p',fact_105_emptyE) ).

fof(fact_106_emptyE,axiom,
    ! [A_2] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),bot_bo535777328l_bool)),
    file('theBenchmark.p',fact_106_emptyE) ).

fof(fact_107_emptyE,axiom,
    ! [A_2] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),bot_bo844097828e_bool)),
    file('theBenchmark.p',fact_107_emptyE) ).

fof(fact_108_insertCI,axiom,
    ! [B_1,A_2,B] :
      ( ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),B))
       => A_2 = B_1 )
     => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,B))) ),
    file('theBenchmark.p',fact_108_insertCI) ).

fof(fact_109_insertCI,axiom,
    ! [B_1,A_2,B] :
      ( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),B))
       => A_2 = B_1 )
     => hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),insert1325755072e_bool(B_1,B))) ),
    file('theBenchmark.p',fact_109_insertCI) ).

fof(fact_110_insertCI,axiom,
    ! [B_1,A_2,B] :
      ( ( ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),B))
       => A_2 = B_1 )
     => hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),insert1556680138e_bool(B_1,B))) ),
    file('theBenchmark.p',fact_110_insertCI) ).

fof(fact_111_insertCI,axiom,
    ! [B_1,A_2,B] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B))
       => A_2 = B_1 )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,B))) ),
    file('theBenchmark.p',fact_111_insertCI) ).

fof(fact_112_insertE,axiom,
    ! [A_2,B_1,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,A)))
     => ( A_2 != B_1
       => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A)) ) ),
    file('theBenchmark.p',fact_112_insertE) ).

fof(fact_113_insertE,axiom,
    ! [A_2,B_1,A] :
      ( ( is_fun_pname_bool(B_1)
        & is_fun_pname_bool(A_2) )
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),insert1325755072e_bool(B_1,A)))
       => ( A_2 != B_1
         => hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A)) ) ) ),
    file('theBenchmark.p',fact_113_insertE) ).

fof(fact_114_insertE,axiom,
    ! [A_2,B_1,A] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),insert1556680138e_bool(B_1,A)))
     => ( A_2 != B_1
       => hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),A)) ) ),
    file('theBenchmark.p',fact_114_insertE) ).

fof(fact_115_insertE,axiom,
    ! [A_2,B_1,A] :
      ( ( is_pname(B_1)
        & is_pname(A_2) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,A)))
       => ( A_2 != B_1
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)) ) ) ),
    file('theBenchmark.p',fact_115_insertE) ).

fof(fact_116_equalityI,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A))
       => A = B ) ),
    file('theBenchmark.p',fact_116_equalityI) ).

fof(fact_117_equalityI,axiom,
    ! [A,B] :
      ( ( is_fun1661590463l_bool(B)
        & is_fun1661590463l_bool(A) )
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),A))
         => A = B ) ) ),
    file('theBenchmark.p',fact_117_equalityI) ).

fof(fact_118_equalityI,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),B))
     => ( hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,B),A))
       => A = B ) ),
    file('theBenchmark.p',fact_118_equalityI) ).

fof(fact_119_equalityI,axiom,
    ! [A,B] :
      ( ( is_fun_pname_bool(B)
        & is_fun_pname_bool(A) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
         => A = B ) ) ),
    file('theBenchmark.p',fact_119_equalityI) ).

fof(fact_120_subsetD,axiom,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,C_1),A))
       => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,C_1),B)) ) ),
    file('theBenchmark.p',fact_120_subsetD) ).

fof(fact_121_subsetD,axiom,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,C_1),A))
       => hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,C_1),B)) ) ),
    file('theBenchmark.p',fact_121_subsetD) ).

fof(fact_122_subsetD,axiom,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),B))
     => ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,C_1),A))
       => hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,C_1),B)) ) ),
    file('theBenchmark.p',fact_122_subsetD) ).

fof(fact_123_subsetD,axiom,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),B)) ) ),
    file('theBenchmark.p',fact_123_subsetD) ).

fof(fact_124_image__eqI,axiom,
    ! [A,B_1,F,X_2] :
      ( B_1 = hAPP_H356885323e_bool(F,X_2)
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
       => hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,B_1),image_2131964411e_bool(F,A))) ) ),
    file('theBenchmark.p',fact_124_image__eqI) ).

fof(fact_125_image__eqI,axiom,
    ! [A,B_1,F,X_2] :
      ( B_1 = hAPP_H1049623551e_bool(F,X_2)
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
       => hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,B_1),image_1828608335e_bool(F,A))) ) ),
    file('theBenchmark.p',fact_125_image__eqI) ).

fof(fact_126_image__eqI,axiom,
    ! [A,B_1,F,X_2] :
      ( B_1 = hAPP_p61793385e_bool(F,X_2)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
       => hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,B_1),image_47868345e_bool(F,A))) ) ),
    file('theBenchmark.p',fact_126_image__eqI) ).

fof(fact_127_image__eqI,axiom,
    ! [A,B_1,F,X_2] :
      ( B_1 = hAPP_p442853985e_bool(F,X_2)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
       => hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,B_1),image_70449425e_bool(F,A))) ) ),
    file('theBenchmark.p',fact_127_image__eqI) ).

fof(fact_128_image__eqI,axiom,
    ! [A,B_1,F,X_2] :
      ( B_1 = hAPP_f888949707_state(F,X_2)
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
       => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_516545147_state(F,A))) ) ),
    file('theBenchmark.p',fact_128_image__eqI) ).

fof(fact_129_image__eqI,axiom,
    ! [A,B_1,F,X_2] :
      ( B_1 = hAPP_f1387463497_state(F,X_2)
     => ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_2),A))
       => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_18964633_state(F,A))) ) ),
    file('theBenchmark.p',fact_129_image__eqI) ).

fof(fact_130_image__eqI,axiom,
    ! [A,B_1,F,X_2] :
      ( B_1 = hAPP_H1621176307_pname(F,X_2)
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_54689091_pname(F,A))) ) ),
    file('theBenchmark.p',fact_130_image__eqI) ).

fof(fact_131_image__eqI,axiom,
    ! [A,B_1,F,X_2] :
      ( B_1 = hAPP_pname_pname(F,X_2)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_pname_pname(F,A))) ) ),
    file('theBenchmark.p',fact_131_image__eqI) ).

fof(fact_132_image__eqI,axiom,
    ! [A,B_1,F,X_2] :
      ( B_1 = hAPP_f1297739591_pname(F,X_2)
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_1283814551_pname(F,A))) ) ),
    file('theBenchmark.p',fact_132_image__eqI) ).

fof(fact_133_image__eqI,axiom,
    ! [A,B_1,F,X_2] :
      ( B_1 = hAPP_f560369737_pname(F,X_2)
     => ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_2),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_187965177_pname(F,A))) ) ),
    file('theBenchmark.p',fact_133_image__eqI) ).

fof(fact_134_image__eqI,axiom,
    ! [A,B_1,F,X_2] :
      ( B_1 = hAPP_p1422361149_state(F,X_2)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
       => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_2003357581_state(F,A))) ) ),
    file('theBenchmark.p',fact_134_image__eqI) ).

fof(fact_135_equals0D,axiom,
    ! [A_2,A] :
      ( A = bot_bo1649642514l_bool
     => ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A)) ),
    file('theBenchmark.p',fact_135_equals0D) ).

fof(fact_136_equals0D,axiom,
    ! [A_2,A] :
      ( A = bot_bo535777328l_bool
     => ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),A)) ),
    file('theBenchmark.p',fact_136_equals0D) ).

fof(fact_137_equals0D,axiom,
    ! [A_2,A] :
      ( A = bot_bo620288102e_bool
     => ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A)) ),
    file('theBenchmark.p',fact_137_equals0D) ).

fof(fact_138_equals0D,axiom,
    ! [A_2,A] :
      ( A = bot_bo844097828e_bool
     => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)) ),
    file('theBenchmark.p',fact_138_equals0D) ).

fof(fact_139_Collect__empty__eq,axiom,
    ! [P_1] :
      ( collec1613912337l_bool(P_1) = bot_bo1537088220l_bool
    <=> ! [X_1] :
          ( is_fun1661590463l_bool(X_1)
         => ~ hBOOL(hAPP_f1935102916l_bool(P_1,X_1)) ) ),
    file('theBenchmark.p',fact_139_Collect__empty__eq) ).

fof(fact_140_Collect__empty__eq,axiom,
    ! [P_1] :
      ( collec488126193l_bool(P_1) = bot_bo1761158942l_bool
    <=> ! [X_1] : ~ hBOOL(hAPP_f166538662l_bool(P_1,X_1)) ),
    file('theBenchmark.p',fact_140_Collect__empty__eq) ).

fof(fact_141_Collect__empty__eq,axiom,
    ! [P_1] :
      ( collec1823980261e_bool(P_1) = bot_bo535777328l_bool
    <=> ! [X_1] : ~ hBOOL(hAPP_f971112728l_bool(P_1,X_1)) ),
    file('theBenchmark.p',fact_141_Collect__empty__eq) ).

fof(fact_142_Collect__empty__eq,axiom,
    ! [P_1] :
      ( collec1974731493e_bool(P_1) = bot_bo1649642514l_bool
    <=> ! [X_1] :
          ( is_fun_pname_bool(X_1)
         => ~ hBOOL(hAPP_f1664156314l_bool(P_1,X_1)) ) ),
    file('theBenchmark.p',fact_142_Collect__empty__eq) ).

fof(fact_143_Collect__empty__eq,axiom,
    ! [P_1] :
      ( collec307967673_state(P_1) = bot_bo620288102e_bool
    <=> ! [X_1] : ~ hBOOL(hAPP_H78829294e_bool(P_1,X_1)) ),
    file('theBenchmark.p',fact_143_Collect__empty__eq) ).

fof(fact_144_Collect__empty__eq,axiom,
    ! [P_1] :
      ( collect_pname(P_1) = bot_bo844097828e_bool
    <=> ! [X_1] :
          ( is_pname(X_1)
         => ~ hBOOL(hAPP_pname_bool(P_1,X_1)) ) ),
    file('theBenchmark.p',fact_144_Collect__empty__eq) ).

fof(fact_145_empty__iff,axiom,
    ! [C_1] : ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,C_1),bot_bo1649642514l_bool)),
    file('theBenchmark.p',fact_145_empty__iff) ).

fof(fact_146_empty__iff,axiom,
    ! [C_1] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,C_1),bot_bo535777328l_bool)),
    file('theBenchmark.p',fact_146_empty__iff) ).

fof(fact_147_empty__iff,axiom,
    ! [C_1] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,C_1),bot_bo620288102e_bool)),
    file('theBenchmark.p',fact_147_empty__iff) ).

fof(fact_148_empty__iff,axiom,
    ! [C_1] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),bot_bo844097828e_bool)),
    file('theBenchmark.p',fact_148_empty__iff) ).

fof(fact_149_empty__Collect__eq,axiom,
    ! [P_1] :
      ( bot_bo1537088220l_bool = collec1613912337l_bool(P_1)
    <=> ! [X_1] :
          ( is_fun1661590463l_bool(X_1)
         => ~ hBOOL(hAPP_f1935102916l_bool(P_1,X_1)) ) ),
    file('theBenchmark.p',fact_149_empty__Collect__eq) ).

fof(fact_150_empty__Collect__eq,axiom,
    ! [P_1] :
      ( bot_bo1761158942l_bool = collec488126193l_bool(P_1)
    <=> ! [X_1] : ~ hBOOL(hAPP_f166538662l_bool(P_1,X_1)) ),
    file('theBenchmark.p',fact_150_empty__Collect__eq) ).

fof(fact_151_empty__Collect__eq,axiom,
    ! [P_1] :
      ( bot_bo535777328l_bool = collec1823980261e_bool(P_1)
    <=> ! [X_1] : ~ hBOOL(hAPP_f971112728l_bool(P_1,X_1)) ),
    file('theBenchmark.p',fact_151_empty__Collect__eq) ).

fof(fact_152_empty__Collect__eq,axiom,
    ! [P_1] :
      ( bot_bo1649642514l_bool = collec1974731493e_bool(P_1)
    <=> ! [X_1] :
          ( is_fun_pname_bool(X_1)
         => ~ hBOOL(hAPP_f1664156314l_bool(P_1,X_1)) ) ),
    file('theBenchmark.p',fact_152_empty__Collect__eq) ).

fof(fact_153_empty__Collect__eq,axiom,
    ! [P_1] :
      ( bot_bo620288102e_bool = collec307967673_state(P_1)
    <=> ! [X_1] : ~ hBOOL(hAPP_H78829294e_bool(P_1,X_1)) ),
    file('theBenchmark.p',fact_153_empty__Collect__eq) ).

fof(fact_154_empty__Collect__eq,axiom,
    ! [P_1] :
      ( bot_bo844097828e_bool = collect_pname(P_1)
    <=> ! [X_1] :
          ( is_pname(X_1)
         => ~ hBOOL(hAPP_pname_bool(P_1,X_1)) ) ),
    file('theBenchmark.p',fact_154_empty__Collect__eq) ).

fof(fact_155_ex__in__conv,axiom,
    ! [A] :
      ( is_fun1661590463l_bool(A)
     => ( ? [X_1] :
            ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
            & is_fun_pname_bool(X_1) )
      <=> A != bot_bo1649642514l_bool ) ),
    file('theBenchmark.p',fact_155_ex__in__conv) ).

fof(fact_156_ex__in__conv,axiom,
    ! [A] :
      ( ? [X_1] : hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_1),A))
    <=> A != bot_bo535777328l_bool ),
    file('theBenchmark.p',fact_156_ex__in__conv) ).

fof(fact_157_ex__in__conv,axiom,
    ! [A] :
      ( ? [X_1] : hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),A))
    <=> A != bot_bo620288102e_bool ),
    file('theBenchmark.p',fact_157_ex__in__conv) ).

fof(fact_158_ex__in__conv,axiom,
    ! [A] :
      ( is_fun_pname_bool(A)
     => ( ? [X_1] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
            & is_pname(X_1) )
      <=> A != bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_158_ex__in__conv) ).

fof(fact_159_all__not__in__conv,axiom,
    ! [A] :
      ( is_fun1661590463l_bool(A)
     => ( ! [X_1] :
            ( is_fun_pname_bool(X_1)
           => ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)) )
      <=> A = bot_bo1649642514l_bool ) ),
    file('theBenchmark.p',fact_159_all__not__in__conv) ).

fof(fact_160_all__not__in__conv,axiom,
    ! [A] :
      ( ! [X_1] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_1),A))
    <=> A = bot_bo535777328l_bool ),
    file('theBenchmark.p',fact_160_all__not__in__conv) ).

fof(fact_161_all__not__in__conv,axiom,
    ! [A] :
      ( ! [X_1] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),A))
    <=> A = bot_bo620288102e_bool ),
    file('theBenchmark.p',fact_161_all__not__in__conv) ).

fof(fact_162_all__not__in__conv,axiom,
    ! [A] :
      ( is_fun_pname_bool(A)
     => ( ! [X_1] :
            ( is_pname(X_1)
           => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) )
      <=> A = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_162_all__not__in__conv) ).

fof(fact_163_empty__def,axiom,
    bot_bo1761158942l_bool = collec488126193l_bool(cOMBK_482404831l_bool(fFalse)),
    file('theBenchmark.p',fact_163_empty__def) ).

fof(fact_164_empty__def,axiom,
    bot_bo535777328l_bool = collec1823980261e_bool(cOMBK_129401207e_bool(fFalse)),
    file('theBenchmark.p',fact_164_empty__def) ).

fof(fact_165_empty__def,axiom,
    bot_bo1649642514l_bool = collec1974731493e_bool(cOMBK_1857069011e_bool(fFalse)),
    file('theBenchmark.p',fact_165_empty__def) ).

fof(fact_166_empty__def,axiom,
    bot_bo620288102e_bool = collec307967673_state(cOMBK_659609255_state(fFalse)),
    file('theBenchmark.p',fact_166_empty__def) ).

fof(fact_167_empty__def,axiom,
    bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)),
    file('theBenchmark.p',fact_167_empty__def) ).

fof(fact_168_insert__absorb,axiom,
    ! [A_2,A] :
      ( is_fun_pname_bool(A)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
       => insert_pname(A_2,A) = A ) ),
    file('theBenchmark.p',fact_168_insert__absorb) ).

fof(fact_169_insert__absorb,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A))
     => insert1415133716_state(A_2,A) = A ),
    file('theBenchmark.p',fact_169_insert__absorb) ).

fof(fact_170_insertI2,axiom,
    ! [B_1,A_2,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,B))) ),
    file('theBenchmark.p',fact_170_insertI2) ).

fof(fact_171_insertI2,axiom,
    ! [B_1,A_2,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),B))
     => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,B))) ),
    file('theBenchmark.p',fact_171_insertI2) ).

fof(fact_172_insert__ident,axiom,
    ! [B,X_2,A] :
      ( ( is_fun_pname_bool(A)
        & is_fun_pname_bool(B) )
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
       => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
         => ( insert_pname(X_2,A) = insert_pname(X_2,B)
          <=> A = B ) ) ) ),
    file('theBenchmark.p',fact_172_insert__ident) ).

fof(fact_173_insert__ident,axiom,
    ! [B,X_2,A] :
      ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
     => ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B))
       => ( insert1415133716_state(X_2,A) = insert1415133716_state(X_2,B)
        <=> A = B ) ) ),
    file('theBenchmark.p',fact_173_insert__ident) ).

fof(fact_174_insert__code,axiom,
    ! [Y_2,A,X_2] :
      ( ( is_pname(X_2)
        & is_pname(Y_2) )
     => ( hBOOL(hAPP_pname_bool(insert_pname(Y_2,A),X_2))
      <=> ( hBOOL(hAPP_pname_bool(A,X_2))
          | Y_2 = X_2 ) ) ),
    file('theBenchmark.p',fact_174_insert__code) ).

fof(fact_175_insert__code,axiom,
    ! [Y_2,A,X_2] :
      ( hBOOL(hAPP_H78829294e_bool(insert1415133716_state(Y_2,A),X_2))
    <=> ( hBOOL(hAPP_H78829294e_bool(A,X_2))
        | Y_2 = X_2 ) ),
    file('theBenchmark.p',fact_175_insert__code) ).

fof(fact_176_insert__iff,axiom,
    ! [A_2,B_1,A] :
      ( ( is_pname(B_1)
        & is_pname(A_2) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,A)))
      <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
          | A_2 = B_1 ) ) ),
    file('theBenchmark.p',fact_176_insert__iff) ).

fof(fact_177_insert__iff,axiom,
    ! [A_2,B_1,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,A)))
    <=> ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A))
        | A_2 = B_1 ) ),
    file('theBenchmark.p',fact_177_insert__iff) ).

fof(fact_178_insert__commute,axiom,
    ! [X_2,Y_2,A] : insert_pname(X_2,insert_pname(Y_2,A)) = insert_pname(Y_2,insert_pname(X_2,A)),
    file('theBenchmark.p',fact_178_insert__commute) ).

fof(fact_179_insert__commute,axiom,
    ! [X_2,Y_2,A] : insert1415133716_state(X_2,insert1415133716_state(Y_2,A)) = insert1415133716_state(Y_2,insert1415133716_state(X_2,A)),
    file('theBenchmark.p',fact_179_insert__commute) ).

fof(fact_180_insert__absorb2,axiom,
    ! [X_2,A] : insert_pname(X_2,insert_pname(X_2,A)) = insert_pname(X_2,A),
    file('theBenchmark.p',fact_180_insert__absorb2) ).

fof(fact_181_insert__absorb2,axiom,
    ! [X_2,A] : insert1415133716_state(X_2,insert1415133716_state(X_2,A)) = insert1415133716_state(X_2,A),
    file('theBenchmark.p',fact_181_insert__absorb2) ).

fof(fact_182_insert__Collect,axiom,
    ! [A_2,P_1] : insert_pname(A_2,collect_pname(P_1)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2))),P_1)),
    file('theBenchmark.p',fact_182_insert__Collect) ).

fof(fact_183_insert__Collect,axiom,
    ! [A_2,P_1] : insert1415133716_state(A_2,collec307967673_state(P_1)) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fimplies,cOMBB_2144135922_state(fNot,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2))),P_1)),
    file('theBenchmark.p',fact_183_insert__Collect) ).

fof(fact_184_insert__Collect,axiom,
    ! [A_2,P_1] : insert1325755072e_bool(A_2,collec1974731493e_bool(P_1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2))),P_1)),
    file('theBenchmark.p',fact_184_insert__Collect) ).

fof(fact_185_insert__Collect,axiom,
    ! [A_2,P_1] : insert1556680138e_bool(A_2,collec1823980261e_bool(P_1)) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fimplies,cOMBB_1522210668e_bool(fNot,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2))),P_1)),
    file('theBenchmark.p',fact_185_insert__Collect) ).

fof(fact_186_insert__compr,axiom,
    ! [A_2,B] : insert_pname(A_2,B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B))),
    file('theBenchmark.p',fact_186_insert__compr) ).

fof(fact_187_insert__compr,axiom,
    ! [A_2,B] : insert1415133716_state(A_2,B) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),B))),
    file('theBenchmark.p',fact_187_insert__compr) ).

fof(fact_188_insert__compr,axiom,
    ! [A_2,B] : insert1325755072e_bool(A_2,B) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),B))),
    file('theBenchmark.p',fact_188_insert__compr) ).

fof(fact_189_insert__compr,axiom,
    ! [A_2,B] : insert1556680138e_bool(A_2,B) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),B))),
    file('theBenchmark.p',fact_189_insert__compr) ).

fof(fact_190_insertI1,axiom,
    ! [A_2,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(A_2,B))),
    file('theBenchmark.p',fact_190_insertI1) ).

fof(fact_191_insertI1,axiom,
    ! [A_2,B] : hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(A_2,B))),
    file('theBenchmark.p',fact_191_insertI1) ).

fof(fact_192_equalityE,axiom,
    ! [A,B] :
      ( A = B
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
         => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ) ),
    file('theBenchmark.p',fact_192_equalityE) ).

fof(fact_193_equalityE,axiom,
    ! [A,B] :
      ( A = B
     => ~ ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
         => ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A)) ) ),
    file('theBenchmark.p',fact_193_equalityE) ).

fof(fact_194_subset__trans,axiom,
    ! [C_2,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_2))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_2)) ) ),
    file('theBenchmark.p',fact_194_subset__trans) ).

fof(fact_195_subset__trans,axiom,
    ! [C_2,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),C_2))
       => hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),C_2)) ) ),
    file('theBenchmark.p',fact_195_subset__trans) ).

fof(fact_196_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ),
    file('theBenchmark.p',fact_196_set__mp) ).

fof(fact_197_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
       => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B)) ) ),
    file('theBenchmark.p',fact_197_set__mp) ).

fof(fact_198_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ),
    file('theBenchmark.p',fact_198_set__rev__mp) ).

fof(fact_199_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
       => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B)) ) ),
    file('theBenchmark.p',fact_199_set__rev__mp) ).

fof(fact_200_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ),
    file('theBenchmark.p',fact_200_in__mono) ).

fof(fact_201_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
       => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B)) ) ),
    file('theBenchmark.p',fact_201_in__mono) ).

fof(fact_202_equalityD2,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ),
    file('theBenchmark.p',fact_202_equalityD2) ).

fof(fact_203_equalityD2,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A)) ),
    file('theBenchmark.p',fact_203_equalityD2) ).

fof(fact_204_equalityD1,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    file('theBenchmark.p',fact_204_equalityD1) ).

fof(fact_205_equalityD1,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) ),
    file('theBenchmark.p',fact_205_equalityD1) ).

fof(fact_206_set__eq__subset,axiom,
    ! [A,B] :
      ( ( is_fun_pname_bool(B)
        & is_fun_pname_bool(A) )
     => ( A = B
      <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_206_set__eq__subset) ).

fof(fact_207_set__eq__subset,axiom,
    ! [A,B] :
      ( A = B
    <=> ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A))
        & hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) ) ),
    file('theBenchmark.p',fact_207_set__eq__subset) ).

fof(fact_208_subset__refl,axiom,
    ! [A] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),A)),
    file('theBenchmark.p',fact_208_subset__refl) ).

fof(fact_209_subset__refl,axiom,
    ! [A] : hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),A)),
    file('theBenchmark.p',fact_209_subset__refl) ).

fof(fact_210_rev__image__eqI,axiom,
    ! [B_1,F,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => ( B_1 = hAPP_p1422361149_state(F,X_2)
       => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_2003357581_state(F,A))) ) ),
    file('theBenchmark.p',fact_210_rev__image__eqI) ).

fof(fact_211_imageI,axiom,
    ! [F,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,hAPP_p1422361149_state(F,X_2)),image_2003357581_state(F,A))) ),
    file('theBenchmark.p',fact_211_imageI) ).

fof(fact_212_image__iff,axiom,
    ! [Z,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,Z),image_2003357581_state(F,A)))
    <=> ? [X_1] :
          ( Z = hAPP_p1422361149_state(F,X_1)
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
          & is_pname(X_1) ) ),
    file('theBenchmark.p',fact_212_image__iff) ).

fof(fact_213_finite__Collect__disjI,axiom,
    ! [P_1,Q_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,P_1),Q_1))))
    <=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(P_1))) ) ),
    file('theBenchmark.p',fact_213_finite__Collect__disjI) ).

fof(fact_214_finite__Collect__disjI,axiom,
    ! [P_1,Q_1] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,P_1),Q_1))))
    <=> ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(Q_1)))
        & hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(P_1))) ) ),
    file('theBenchmark.p',fact_214_finite__Collect__disjI) ).

fof(fact_215_finite__Collect__disjI,axiom,
    ! [P_1,Q_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,P_1),Q_1))))
    <=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(P_1))) ) ),
    file('theBenchmark.p',fact_215_finite__Collect__disjI) ).

fof(fact_216_finite__Collect__disjI,axiom,
    ! [P_1,Q_1] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,P_1),Q_1))))
    <=> ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(Q_1)))
        & hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(P_1))) ) ),
    file('theBenchmark.p',fact_216_finite__Collect__disjI) ).

fof(fact_217_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_217_insert__compr__raw) ).

fof(fact_218_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert1415133716_state(X_1,Xa) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),X_1)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),Xa))),
    file('theBenchmark.p',fact_218_insert__compr__raw) ).

fof(fact_219_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_219_insert__compr__raw) ).

fof(fact_220_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert1556680138e_bool(X_1,Xa) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),X_1)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),Xa))),
    file('theBenchmark.p',fact_220_insert__compr__raw) ).

fof(fact_221_singleton__inject,axiom,
    ! [A_2,B_1] :
      ( ( is_pname(B_1)
        & is_pname(A_2) )
     => ( insert_pname(A_2,bot_bo844097828e_bool) = insert_pname(B_1,bot_bo844097828e_bool)
       => A_2 = B_1 ) ),
    file('theBenchmark.p',fact_221_singleton__inject) ).

fof(fact_222_singleton__inject,axiom,
    ! [A_2,B_1] :
      ( insert1415133716_state(A_2,bot_bo620288102e_bool) = insert1415133716_state(B_1,bot_bo620288102e_bool)
     => A_2 = B_1 ),
    file('theBenchmark.p',fact_222_singleton__inject) ).

fof(fact_223_singletonE,axiom,
    ! [B_1,A_2] :
      ( ( is_pname(A_2)
        & is_pname(B_1) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_2,bot_bo844097828e_bool)))
       => B_1 = A_2 ) ),
    file('theBenchmark.p',fact_223_singletonE) ).

fof(fact_224_singletonE,axiom,
    ! [B_1,A_2] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),insert1415133716_state(A_2,bot_bo620288102e_bool)))
     => B_1 = A_2 ),
    file('theBenchmark.p',fact_224_singletonE) ).

fof(fact_225_doubleton__eq__iff,axiom,
    ! [A_2,B_1,C_1,D_1] :
      ( ( is_pname(D_1)
        & is_pname(C_1)
        & is_pname(B_1)
        & is_pname(A_2) )
     => ( insert_pname(A_2,insert_pname(B_1,bot_bo844097828e_bool)) = insert_pname(C_1,insert_pname(D_1,bot_bo844097828e_bool))
      <=> ( ( B_1 = C_1
            & A_2 = D_1 )
          | ( B_1 = D_1
            & A_2 = C_1 ) ) ) ),
    file('theBenchmark.p',fact_225_doubleton__eq__iff) ).

fof(fact_226_doubleton__eq__iff,axiom,
    ! [A_2,B_1,C_1,D_1] :
      ( insert1415133716_state(A_2,insert1415133716_state(B_1,bot_bo620288102e_bool)) = insert1415133716_state(C_1,insert1415133716_state(D_1,bot_bo620288102e_bool))
    <=> ( ( B_1 = C_1
          & A_2 = D_1 )
        | ( B_1 = D_1
          & A_2 = C_1 ) ) ),
    file('theBenchmark.p',fact_226_doubleton__eq__iff) ).

fof(fact_227_singleton__iff,axiom,
    ! [B_1,A_2] :
      ( ( is_pname(A_2)
        & is_pname(B_1) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_2,bot_bo844097828e_bool)))
      <=> B_1 = A_2 ) ),
    file('theBenchmark.p',fact_227_singleton__iff) ).

fof(fact_228_singleton__iff,axiom,
    ! [B_1,A_2] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),insert1415133716_state(A_2,bot_bo620288102e_bool)))
    <=> B_1 = A_2 ),
    file('theBenchmark.p',fact_228_singleton__iff) ).

fof(fact_229_insert__not__empty,axiom,
    ! [A_2,A] : insert_pname(A_2,A) != bot_bo844097828e_bool,
    file('theBenchmark.p',fact_229_insert__not__empty) ).

fof(fact_230_insert__not__empty,axiom,
    ! [A_2,A] : insert1415133716_state(A_2,A) != bot_bo620288102e_bool,
    file('theBenchmark.p',fact_230_insert__not__empty) ).

fof(fact_231_empty__not__insert,axiom,
    ! [A_2,A] : bot_bo844097828e_bool != insert_pname(A_2,A),
    file('theBenchmark.p',fact_231_empty__not__insert) ).

fof(fact_232_empty__not__insert,axiom,
    ! [A_2,A] : bot_bo620288102e_bool != insert1415133716_state(A_2,A),
    file('theBenchmark.p',fact_232_empty__not__insert) ).

fof(fact_233_finite__insert,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_2,A)))
    <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    file('theBenchmark.p',fact_233_finite__insert) ).

fof(fact_234_finite__insert,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(A_2,A)))
    <=> hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) ),
    file('theBenchmark.p',fact_234_finite__insert) ).

fof(fact_235_finite__insert,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_2,A)))
    <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    file('theBenchmark.p',fact_235_finite__insert) ).

fof(fact_236_finite__insert,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(A_2,A)))
    <=> hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)) ),
    file('theBenchmark.p',fact_236_finite__insert) ).

fof(fact_237_subset__empty,axiom,
    ! [A] :
      ( is_fun_pname_bool(A)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),bot_bo844097828e_bool))
      <=> A = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_237_subset__empty) ).

fof(fact_238_subset__empty,axiom,
    ! [A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),bot_bo620288102e_bool))
    <=> A = bot_bo620288102e_bool ),
    file('theBenchmark.p',fact_238_subset__empty) ).

fof(fact_239_image__is__empty,axiom,
    ! [F,A] :
      ( is_fun_pname_bool(A)
     => ( image_2003357581_state(F,A) = bot_bo620288102e_bool
      <=> A = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_239_image__is__empty) ).

fof(fact_240_image__empty,axiom,
    ! [F] : image_2003357581_state(F,bot_bo844097828e_bool) = bot_bo620288102e_bool,
    file('theBenchmark.p',fact_240_image__empty) ).

fof(fact_241_empty__is__image,axiom,
    ! [F,A] :
      ( is_fun_pname_bool(A)
     => ( bot_bo620288102e_bool = image_2003357581_state(F,A)
      <=> A = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_241_empty__is__image) ).

fof(fact_242_finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ),
    file('theBenchmark.p',fact_242_finite__subset) ).

fof(fact_243_finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),B))
     => ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,B))
       => hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)) ) ),
    file('theBenchmark.p',fact_243_finite__subset) ).

fof(fact_244_finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ),
    file('theBenchmark.p',fact_244_finite__subset) ).

fof(fact_245_finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
     => ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))
       => hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) ) ),
    file('theBenchmark.p',fact_245_finite__subset) ).

fof(fact_246_rev__finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ),
    file('theBenchmark.p',fact_246_rev__finite__subset) ).

fof(fact_247_rev__finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,B))
     => ( hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),B))
       => hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)) ) ),
    file('theBenchmark.p',fact_247_rev__finite__subset) ).

fof(fact_248_rev__finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ),
    file('theBenchmark.p',fact_248_rev__finite__subset) ).

fof(fact_249_rev__finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
       => hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) ) ),
    file('theBenchmark.p',fact_249_rev__finite__subset) ).

fof(fact_250_insert__mono,axiom,
    ! [A_2,C_2,D] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_2),D))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(A_2,C_2)),insert_pname(A_2,D))) ),
    file('theBenchmark.p',fact_250_insert__mono) ).

fof(fact_251_insert__mono,axiom,
    ! [A_2,C_2,D] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,C_2),D))
     => hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(A_2,C_2)),insert1415133716_state(A_2,D))) ),
    file('theBenchmark.p',fact_251_insert__mono) ).

fof(fact_252_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
    <=> hBOOL(hAPP_pname_bool(A,X_2)) ),
    file('theBenchmark.p',fact_252_mem__def) ).

fof(fact_253_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
    <=> hBOOL(hAPP_H78829294e_bool(A,X_2)) ),
    file('theBenchmark.p',fact_253_mem__def) ).

fof(fact_254_Collect__def,axiom,
    ! [P_1] :
      ( is_fun_pname_bool(P_1)
     => collect_pname(P_1) = P_1 ),
    file('theBenchmark.p',fact_254_Collect__def) ).

fof(fact_255_Collect__def,axiom,
    ! [P_1] : collec307967673_state(P_1) = P_1,
    file('theBenchmark.p',fact_255_Collect__def) ).

fof(fact_256_Collect__def,axiom,
    ! [P_1] :
      ( is_fun1661590463l_bool(P_1)
     => collec1974731493e_bool(P_1) = P_1 ),
    file('theBenchmark.p',fact_256_Collect__def) ).

fof(fact_257_Collect__def,axiom,
    ! [P_1] : collec1823980261e_bool(P_1) = P_1,
    file('theBenchmark.p',fact_257_Collect__def) ).

fof(fact_258_subset__insertI2,axiom,
    ! [B_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(B_1,B))) ),
    file('theBenchmark.p',fact_258_subset__insertI2) ).

fof(fact_259_subset__insertI2,axiom,
    ! [B_1,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
     => hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),insert1415133716_state(B_1,B))) ),
    file('theBenchmark.p',fact_259_subset__insertI2) ).

fof(fact_260_subset__insert,axiom,
    ! [B,X_2,A] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,B)))
      <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ),
    file('theBenchmark.p',fact_260_subset__insert) ).

fof(fact_261_subset__insert,axiom,
    ! [B,X_2,A] :
      ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),insert1415133716_state(X_2,B)))
      <=> hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) ) ),
    file('theBenchmark.p',fact_261_subset__insert) ).

fof(fact_262_insert__subset,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_2,A)),B))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ),
    file('theBenchmark.p',fact_262_insert__subset) ).

fof(fact_263_insert__subset,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(X_2,A)),B))
    <=> ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
        & hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B)) ) ),
    file('theBenchmark.p',fact_263_insert__subset) ).

fof(fact_264_subset__insertI,axiom,
    ! [B,A_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),insert_pname(A_2,B))),
    file('theBenchmark.p',fact_264_subset__insertI) ).

fof(fact_265_subset__insertI,axiom,
    ! [B,A_2] : hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),insert1415133716_state(A_2,B))),
    file('theBenchmark.p',fact_265_subset__insertI) ).

fof(fact_266_insert__image,axiom,
    ! [F,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => insert1415133716_state(hAPP_p1422361149_state(F,X_2),image_2003357581_state(F,A)) = image_2003357581_state(F,A) ),
    file('theBenchmark.p',fact_266_insert__image) ).

fof(fact_267_image__insert,axiom,
    ! [F,A_2,B] : image_2003357581_state(F,insert_pname(A_2,B)) = insert1415133716_state(hAPP_p1422361149_state(F,A_2),image_2003357581_state(F,B)),
    file('theBenchmark.p',fact_267_image__insert) ).

fof(fact_268_image__mono,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,image_2003357581_state(F,A)),image_2003357581_state(F,B))) ),
    file('theBenchmark.p',fact_268_image__mono) ).

fof(fact_269_subset__image__iff,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_2003357581_state(F,A)))
    <=> ? [AA] :
          ( B = image_2003357581_state(F,AA)
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A))
          & is_fun_pname_bool(AA) ) ),
    file('theBenchmark.p',fact_269_subset__image__iff) ).

fof(fact_270_domI,axiom,
    ! [M,A_2,B_1] :
      ( hAPP_p799580910on_com(M,A_2) = some_com(B_1)
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),dom_pname_com(M))) ),
    file('theBenchmark.p',fact_270_domI) ).

fof(fact_271_Collect__conv__if,axiom,
    ! [P_1,A_2] :
      ( ( ~ hBOOL(hAPP_pname_bool(P_1,A_2))
       => collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),P_1)) = bot_bo844097828e_bool )
      & ( hBOOL(hAPP_pname_bool(P_1,A_2))
       => collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),P_1)) = insert_pname(A_2,bot_bo844097828e_bool) ) ),
    file('theBenchmark.p',fact_271_Collect__conv__if) ).

fof(fact_272_Collect__conv__if,axiom,
    ! [P_1,A_2] :
      ( ( ~ hBOOL(hAPP_H78829294e_bool(P_1,A_2))
       => collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)),P_1)) = bot_bo620288102e_bool )
      & ( hBOOL(hAPP_H78829294e_bool(P_1,A_2))
       => collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)),P_1)) = insert1415133716_state(A_2,bot_bo620288102e_bool) ) ),
    file('theBenchmark.p',fact_272_Collect__conv__if) ).

fof(fact_273_Collect__conv__if,axiom,
    ! [P_1,A_2] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,A_2))
       => collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)),P_1)) = bot_bo1649642514l_bool )
      & ( hBOOL(hAPP_f1664156314l_bool(P_1,A_2))
       => collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)),P_1)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool) ) ),
    file('theBenchmark.p',fact_273_Collect__conv__if) ).

fof(fact_274_Collect__conv__if,axiom,
    ! [P_1,A_2] :
      ( ( ~ hBOOL(hAPP_f971112728l_bool(P_1,A_2))
       => collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)),P_1)) = bot_bo535777328l_bool )
      & ( hBOOL(hAPP_f971112728l_bool(P_1,A_2))
       => collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)),P_1)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool) ) ),
    file('theBenchmark.p',fact_274_Collect__conv__if) ).

fof(fact_275_Collect__conv__if2,axiom,
    ! [P_1,A_2] :
      ( ( ~ hBOOL(hAPP_pname_bool(P_1,A_2))
       => collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_2)),P_1)) = bot_bo844097828e_bool )
      & ( hBOOL(hAPP_pname_bool(P_1,A_2))
       => collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_2)),P_1)) = insert_pname(A_2,bot_bo844097828e_bool) ) ),
    file('theBenchmark.p',fact_275_Collect__conv__if2) ).

fof(fact_276_Collect__conv__if2,axiom,
    ! [P_1,A_2] :
      ( ( ~ hBOOL(hAPP_H78829294e_bool(P_1,A_2))
       => collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,A_2)),P_1)) = bot_bo620288102e_bool )
      & ( hBOOL(hAPP_H78829294e_bool(P_1,A_2))
       => collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,A_2)),P_1)) = insert1415133716_state(A_2,bot_bo620288102e_bool) ) ),
    file('theBenchmark.p',fact_276_Collect__conv__if2) ).

fof(fact_277_Collect__conv__if2,axiom,
    ! [P_1,A_2] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,A_2))
       => collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_2)),P_1)) = bot_bo1649642514l_bool )
      & ( hBOOL(hAPP_f1664156314l_bool(P_1,A_2))
       => collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_2)),P_1)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool) ) ),
    file('theBenchmark.p',fact_277_Collect__conv__if2) ).

fof(fact_278_Collect__conv__if2,axiom,
    ! [P_1,A_2] :
      ( ( ~ hBOOL(hAPP_f971112728l_bool(P_1,A_2))
       => collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,A_2)),P_1)) = bot_bo535777328l_bool )
      & ( hBOOL(hAPP_f971112728l_bool(P_1,A_2))
       => collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,A_2)),P_1)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool) ) ),
    file('theBenchmark.p',fact_278_Collect__conv__if2) ).

fof(fact_279_singleton__conv,axiom,
    ! [A_2] : collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)) = insert_pname(A_2,bot_bo844097828e_bool),
    file('theBenchmark.p',fact_279_singleton__conv) ).

fof(fact_280_singleton__conv,axiom,
    ! [A_2] : collec307967673_state(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)) = insert1415133716_state(A_2,bot_bo620288102e_bool),
    file('theBenchmark.p',fact_280_singleton__conv) ).

fof(fact_281_singleton__conv,axiom,
    ! [A_2] : collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool),
    file('theBenchmark.p',fact_281_singleton__conv) ).

fof(fact_282_singleton__conv,axiom,
    ! [A_2] : collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool),
    file('theBenchmark.p',fact_282_singleton__conv) ).

fof(fact_283_singleton__conv2,axiom,
    ! [A_2] : collect_pname(hAPP_p61793385e_bool(fequal_pname,A_2)) = insert_pname(A_2,bot_bo844097828e_bool),
    file('theBenchmark.p',fact_283_singleton__conv2) ).

fof(fact_284_singleton__conv2,axiom,
    ! [A_2] : collec307967673_state(hAPP_H1049623551e_bool(fequal1111551311_state,A_2)) = insert1415133716_state(A_2,bot_bo620288102e_bool),
    file('theBenchmark.p',fact_284_singleton__conv2) ).

fof(fact_285_singleton__conv2,axiom,
    ! [A_2] : collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,A_2)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool),
    file('theBenchmark.p',fact_285_singleton__conv2) ).

fof(fact_286_singleton__conv2,axiom,
    ! [A_2] : collec1823980261e_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,A_2)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool),
    file('theBenchmark.p',fact_286_singleton__conv2) ).

fof(fact_287_MGF__lemma1,axiom,
    ! [C_1,G] :
      ( hBOOL(hoare_165779456gleton)
     => ( ! [X_1] :
            ( is_pname(X_1)
           => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),dom_pname_com(body)))
             => hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,X_1)),bot_bo620288102e_bool))) ) )
       => ( hBOOL(wt(C_1))
         => hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,C_1),bot_bo620288102e_bool))) ) ) ),
    file('theBenchmark.p',fact_287_MGF__lemma1) ).

fof(fact_288_WT__bodiesD,axiom,
    ! [Pn,B_2] :
      ( hBOOL(wT_bodies)
     => ( hAPP_p799580910on_com(body,Pn) = some_com(B_2)
       => hBOOL(wt(B_2)) ) ),
    file('theBenchmark.p',fact_288_WT__bodiesD) ).

fof(fact_289_imageE,axiom,
    ! [B_1,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_2003357581_state(F,A)))
     => ~ ! [X_1] :
            ( is_pname(X_1)
           => ( B_1 = hAPP_p1422361149_state(F,X_1)
             => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ) ) ),
    file('theBenchmark.p',fact_289_imageE) ).

fof(fact_290_finite__subset__induct,axiom,
    ! [P_1,A,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Fa),A))
       => ( hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool))
         => ( ! [A_1,F_1] :
                ( ( is_fun_pname_bool(F_1)
                  & is_pname(A_1) )
               => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
                 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
                   => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),F_1))
                     => ( hBOOL(hAPP_f1664156314l_bool(P_1,F_1))
                       => hBOOL(hAPP_f1664156314l_bool(P_1,insert_pname(A_1,F_1))) ) ) ) ) )
           => hBOOL(hAPP_f1664156314l_bool(P_1,Fa)) ) ) ) ),
    file('theBenchmark.p',fact_290_finite__subset__induct) ).

fof(fact_291_finite__subset__induct,axiom,
    ! [P_1,A,Fa] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,Fa),A))
       => ( hBOOL(hAPP_f971112728l_bool(P_1,bot_bo620288102e_bool))
         => ( ! [A_1,F_1] :
                ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,F_1))
               => ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_1),A))
                 => ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_1),F_1))
                   => ( hBOOL(hAPP_f971112728l_bool(P_1,F_1))
                     => hBOOL(hAPP_f971112728l_bool(P_1,insert1415133716_state(A_1,F_1))) ) ) ) )
           => hBOOL(hAPP_f971112728l_bool(P_1,Fa)) ) ) ) ),
    file('theBenchmark.p',fact_291_finite__subset__induct) ).

fof(fact_292_finite__subset__induct,axiom,
    ! [P_1,A,Fa] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,Fa),A))
       => ( hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool))
         => ( ! [A_1,F_1] :
                ( ( is_fun1661590463l_bool(F_1)
                  & is_fun_pname_bool(A_1) )
               => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
                 => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_1),A))
                   => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_1),F_1))
                     => ( hBOOL(hAPP_f1935102916l_bool(P_1,F_1))
                       => hBOOL(hAPP_f1935102916l_bool(P_1,insert1325755072e_bool(A_1,F_1))) ) ) ) ) )
           => hBOOL(hAPP_f1935102916l_bool(P_1,Fa)) ) ) ) ),
    file('theBenchmark.p',fact_292_finite__subset__induct) ).

fof(fact_293_finite__subset__induct,axiom,
    ! [P_1,A,Fa] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,Fa))
     => ( hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,Fa),A))
       => ( hBOOL(hAPP_f166538662l_bool(P_1,bot_bo535777328l_bool))
         => ( ! [A_1,F_1] :
                ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,F_1))
               => ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_1),A))
                 => ( ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_1),F_1))
                   => ( hBOOL(hAPP_f166538662l_bool(P_1,F_1))
                     => hBOOL(hAPP_f166538662l_bool(P_1,insert1556680138e_bool(A_1,F_1))) ) ) ) )
           => hBOOL(hAPP_f166538662l_bool(P_1,Fa)) ) ) ) ),
    file('theBenchmark.p',fact_293_finite__subset__induct) ).

fof(fact_294_WTs__elim__cases_I7_J,axiom,
    ! [P] :
      ( hBOOL(wt(hAPP_pname_com(body_1,P)))
     => ~ ! [Y_1] : hAPP_p799580910on_com(body,P) != some_com(Y_1) ),
    file('theBenchmark.p',fact_294_WTs__elim__cases_I7_J) ).

fof(fact_295_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( is_pname(X_1)
         => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
           => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    file('theBenchmark.p',fact_295_subsetI) ).

fof(fact_296_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),A))
         => hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),B)) )
     => hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) ),
    file('theBenchmark.p',fact_296_subsetI) ).

fof(fact_297_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))
     => ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_2003357581_state(F,A)))
       => ? [C] :
            ( B = image_2003357581_state(F,C)
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A))
            & is_fun_pname_bool(C) ) ) ),
    file('theBenchmark.p',fact_297_finite__subset__image) ).

fof(fact_298_finite__dom__body,axiom,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,dom_pname_com(body))),
    file('theBenchmark.p',fact_298_finite__dom__body) ).

fof(fact_299_com_Osimps_I6_J,axiom,
    ! [Pname_1,Pname] :
      ( ( is_pname(Pname)
        & is_pname(Pname_1) )
     => ( hAPP_pname_com(body_1,Pname_1) = hAPP_pname_com(body_1,Pname)
      <=> Pname_1 = Pname ) ),
    file('theBenchmark.p',fact_299_com_Osimps_I6_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_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_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_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U,axiom,
    ! [P,Q] :
      ( is_pname(P)
     => hAPP_pname_pname(cOMBK_pname_pname(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U) ).

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

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

fof(help_COMBB_1_1_COMBB_000tc__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_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_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
    ! [P,Q] :
      ( is_pname(P)
     => hAPP_f1297739591_pname(cOMBK_948730864e_bool(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O,axiom,
    ! [P,Q] :
      ( is_fun_pname_bool(P)
     => hAPP_p61793385e_bool(cOMBK_37193422_pname(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) ).

fof(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com,axiom,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_H78829294e_bool(hAPP_H1049623551e_bool(fequal1111551311_state,X),Y)) ),
    file('theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com) ).

fof(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_H78829294e_bool(hAPP_H1049623551e_bool(fequal1111551311_state,X),Y))
      | X != Y ),
    file('theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com) ).

fof(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00,axiom,
    ! [P,Q,R] : hAPP_pname_com(cOMBB_923936821_pname(P,Q),R) = hAPP_option_com_com(P,hAPP_p799580910on_com(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00) ).

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,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) ).

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_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_H78829294e_bool(cOMBK_659609255_state(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__) ).

fof(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____jfehddehev_,axiom,
    ! [P,Q] :
      ( is_pname(P)
     => hAPP_H1621176307_pname(cOMBK_168215364_state(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____jfehddehev_) ).

fof(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__,axiom,
    ! [P,Q] : hAPP_p1422361149_state(cOMBK_367030522_pname(P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__) ).

fof(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple,axiom,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,X),Y)) ),
    file('theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) ).

fof(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,X),Y))
      | X != Y ),
    file('theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) ).

fof(help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____jfehddehev__O,axiom,
    ! [P,Q,R] : hAPP_p1422361149_state(cOMBB_699532858_pname(P,Q),R) = hAPP_c1126217667_state(P,hAPP_pname_com(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____jfehddehev__O) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel,axiom,
    ! [P,Q,R] : hAPP_H78829294e_bool(cOMBB_2144135922_state(P,Q),R) = hAPP_bool_bool(P,hAPP_H78829294e_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) ).

fof(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__,axiom,
    ! [P,Q,R] : hAPP_H78829294e_bool(cOMBS_458705923l_bool(P,Q),R) = hAPP_bool_bool(hAPP_H1187982158l_bool(P,R),hAPP_H78829294e_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006,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_006) ).

fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
    ! [P,Q,R] : hAPP_f1935102916l_bool(cOMBS_811933079l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f32027384l_bool(P,R),hAPP_f1935102916l_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).

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_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____jfe,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_f971112728l_bool(cOMBK_129401207e_bool(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____jfe) ).

fof(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____jf,axiom,
    ! [P,Q] :
      ( is_pname(P)
     => hAPP_f560369737_pname(cOMBK_1589414042e_bool(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____jf) ).

fof(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___007,axiom,
    ! [P,Q] : hAPP_f888949707_state(cOMBK_1503445380e_bool(P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___007) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_,axiom,
    ! [P,Q] :
      ( is_fun_pname_bool(P)
     => hAPP_H356885323e_bool(cOMBK_2035509764_state(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I,axiom,
    ! [P,Q] : hAPP_p442853985e_bool(cOMBK_1706929794_pname(P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__,axiom,
    ! [P,Q,R] : hAPP_f971112728l_bool(cOMBB_1522210668e_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f971112728l_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008,axiom,
    ! [P,Q,R] : hAPP_H1187982158l_bool(cOMBB_962198420_state(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_H78829294e_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008) ).

fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I,axiom,
    ! [P,Q,R] : hAPP_f971112728l_bool(cOMBS_2066081387l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f637090980l_bool(P,R),hAPP_f971112728l_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009,axiom,
    ! [P,Q,R] : hAPP_f32027384l_bool(cOMBB_689948150l_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f1935102916l_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_010,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_010) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Hoare____Mirabel,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_f166538662l_bool(cOMBK_482404831l_bool(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Hoare____Mirabel) ).

fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__,axiom,
    ! [P,Q,R] : hAPP_H78829294e_bool(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(P),Q),R) = hAPP_H78829294e_bool(hAPP_H1049623551e_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011,axiom,
    ! [P,Q,R] : hAPP_f637090980l_bool(cOMBB_1585081418e_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f971112728l_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011) ).

fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__,axiom,
    ! [P,Q,R] : hAPP_f166538662l_bool(cOMBS_1358309691l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f2143399574l_bool(P,R),hAPP_f166538662l_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__) ).

fof(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___012,axiom,
    ! [P,Q] : hAPP_f1387463497_state(cOMBK_701929478e_bool(P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___012) ).

fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_013,axiom,
    ! [P,Q] : hAPP_H1049623551e_bool(cOMBK_1039769424_state(P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_013) ).

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

fof(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___014,axiom,
    ! [P,Q,R] : hAPP_H78829294e_bool(hAPP_f98417237e_bool(cOMBC_1734175330l_bool(P),Q),R) = hAPP_f971112728l_bool(hAPP_H30606679l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___014) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_015,axiom,
    ! [P,Q,R] : hAPP_f2143399574l_bool(cOMBB_404111180l_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f166538662l_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_015) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I,axiom,
    ! [P,Q,R] : hAPP_f971112728l_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(P),Q),R) = hAPP_f971112728l_bool(hAPP_f72706945l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I) ).

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

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_016,axiom,
    ! [P,Q,R] : hAPP_f971112728l_bool(hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(P),Q),R) = hAPP_f166538662l_bool(hAPP_f210337421l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_016) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__,axiom,
    ! [P,Q,R] : hAPP_f166538662l_bool(hAPP_f585161855l_bool(cOMBC_1691491604l_bool(P),Q),R) = hAPP_f166538662l_bool(hAPP_f585161855l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfe,axiom,
    ! [P,Q,R] : hAPP_f468958928l_bool(hAPP_f667366769l_bool(cOMBC_747715418l_bool(P),Q),R) = hAPP_f468958928l_bool(hAPP_f667366769l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfe) ).

fof(conj_0,hypothesis,
    hBOOL(hoare_165779456gleton),
    file('theBenchmark.p',conj_0) ).

fof(conj_1,hypothesis,
    hBOOL(wT_bodies),
    file('theBenchmark.p',conj_1) ).

fof(conj_2,hypothesis,
    hBOOL(hAPP_f971112728l_bool(finite364844667_state,fa)),
    file('theBenchmark.p',conj_2) ).

fof(conj_3,hypothesis,
    ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y)),fa)),
    file('theBenchmark.p',conj_3) ).

fof(conj_4,hypothesis,
    hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,fa),image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,cOMBB_923936821_pname(the_com,body)),dom_pname_com(body)))),
    file('theBenchmark.p',conj_4) ).

fof(conj_5,hypothesis,
    hAPP_p799580910on_com(body,pn) = some_com(y),
    file('theBenchmark.p',conj_5) ).

fof(conj_6,hypothesis,
    hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),fa)),
    file('theBenchmark.p',conj_6) ).

fof(conj_7,conjecture,
    hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,y),bot_bo620288102e_bool))),
    file('theBenchmark.p',conj_7) ).

fof(f_1_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_1_2,plain,
    ! [U_1,U_0] :
      ( is_fun_pname_bool(cOMBB_647938656_pname(U_1,U_0))
      | ~ is_fun_pname_bool(U_0) ),
    inference(variable_rename,[status(thm)],[f_1_1]) ).

fof(f_1_3,plain,
    ! [U_0,U_1] :
      ( is_fun_pname_bool(cOMBB_647938656_pname(U_1,U_0))
      | ~ is_fun_pname_bool(U_0) ),
    inference(definitional_conversion,[status(esa)],[f_1_2]) ).

cnf(f_1_4,plain,
    ( is_fun_pname_bool(cOMBB_647938656_pname(U_1,U_0))
    | ~ is_fun_pname_bool(U_0) ),
    inference(clausify,[status(thm)],[f_1_3]) ).

fof(f_2_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_2_2,plain,
    ! [U_3,U_2] :
      ( is_fun1661590463l_bool(cOMBB_307249310e_bool(U_3,U_2))
      | ~ is_fun1661590463l_bool(U_2) ),
    inference(variable_rename,[status(thm)],[f_2_1]) ).

fof(f_2_3,plain,
    ! [U_2,U_3] :
      ( is_fun1661590463l_bool(cOMBB_307249310e_bool(U_3,U_2))
      | ~ is_fun1661590463l_bool(U_2) ),
    inference(definitional_conversion,[status(esa)],[f_2_2]) ).

cnf(f_2_4,plain,
    ( is_fun1661590463l_bool(cOMBB_307249310e_bool(U_3,U_2))
    | ~ is_fun1661590463l_bool(U_2) ),
    inference(clausify,[status(thm)],[f_2_3]) ).

fof(f_3_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_3_2,plain,
    ! [U_4] :
      ( is_fun_pname_bool(cOMBK_bool_pname(U_4))
      | ~ is_bool(U_4) ),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

fof(f_3_3,plain,
    ! [U_4] :
      ( is_fun_pname_bool(cOMBK_bool_pname(U_4))
      | ~ is_bool(U_4) ),
    inference(definitional_conversion,[status(esa)],[f_3_2]) ).

cnf(f_3_4,plain,
    ( is_fun_pname_bool(cOMBK_bool_pname(U_4))
    | ~ is_bool(U_4) ),
    inference(clausify,[status(thm)],[f_3_3]) ).

fof(f_4_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_4_2,plain,
    ! [U_5] :
      ( is_fun1661590463l_bool(cOMBK_1857069011e_bool(U_5))
      | ~ is_bool(U_5) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

fof(f_4_3,plain,
    ! [U_5] :
      ( is_fun1661590463l_bool(cOMBK_1857069011e_bool(U_5))
      | ~ is_bool(U_5) ),
    inference(definitional_conversion,[status(esa)],[f_4_2]) ).

cnf(f_4_4,plain,
    ( is_fun1661590463l_bool(cOMBK_1857069011e_bool(U_5))
    | ~ is_bool(U_5) ),
    inference(clausify,[status(thm)],[f_4_3]) ).

fof(f_5_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_5_2,plain,
    ! [U_7,U_6] :
      ( is_fun_pname_bool(cOMBS_568398431l_bool(U_7,U_6))
      | ~ is_fun_pname_bool(U_6) ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

fof(f_5_3,plain,
    ! [U_6,U_7] :
      ( is_fun_pname_bool(cOMBS_568398431l_bool(U_7,U_6))
      | ~ is_fun_pname_bool(U_6) ),
    inference(definitional_conversion,[status(esa)],[f_5_2]) ).

cnf(f_5_4,plain,
    ( is_fun_pname_bool(cOMBS_568398431l_bool(U_7,U_6))
    | ~ is_fun_pname_bool(U_6) ),
    inference(clausify,[status(thm)],[f_5_3]) ).

fof(f_6_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_6_2,plain,
    ! [U_9,U_8] :
      ( is_fun1661590463l_bool(cOMBS_350070575l_bool(U_9,U_8))
      | ~ is_fun1661590463l_bool(U_8) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

fof(f_6_3,plain,
    ! [U_8,U_9] :
      ( is_fun1661590463l_bool(cOMBS_350070575l_bool(U_9,U_8))
      | ~ is_fun1661590463l_bool(U_8) ),
    inference(definitional_conversion,[status(esa)],[f_6_2]) ).

cnf(f_6_4,plain,
    ( is_fun1661590463l_bool(cOMBS_350070575l_bool(U_9,U_8))
    | ~ is_fun1661590463l_bool(U_8) ),
    inference(clausify,[status(thm)],[f_6_3]) ).

fof(f_7_1,plain,
    ! [B_1_1] : is_bool(wt(B_1_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Com_OWT]) ).

fof(f_7_2,plain,
    ! [U_10] : is_bool(wt(U_10)),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

fof(f_7_3,plain,
    ! [U_10] : is_bool(wt(U_10)),
    inference(definitional_conversion,[status(esa)],[f_7_2]) ).

cnf(f_7_4,plain,
    is_bool(wt(U_10)),
    inference(clausify,[status(thm)],[f_7_3]) ).

fof(f_8_1,plain,
    is_bool(wT_bodies),
    inference(fof_nnf,[status(thm)],[gsy_c_Com_OWT__bodies]) ).

fof(f_8_2,plain,
    is_bool(wT_bodies),
    inference(definitional_conversion,[status(esa)],[f_8_1]) ).

cnf(f_8_3,plain,
    is_bool(wT_bodies),
    inference(clausify,[status(thm)],[f_8_2]) ).

fof(f_9_1,plain,
    is_fun1661590463l_bool(finite_finite_pname),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofinite_000tc__Com__Opname]) ).

fof(f_9_2,plain,
    is_fun1661590463l_bool(finite_finite_pname),
    inference(definitional_conversion,[status(esa)],[f_9_1]) ).

cnf(f_9_3,plain,
    is_fun1661590463l_bool(finite_finite_pname),
    inference(clausify,[status(thm)],[f_9_2]) ).

fof(f_10_1,plain,
    is_pname(undefined_pname(pname)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Com__Opname]) ).

fof(f_10_2,plain,
    is_pname(undefined_pname(pname)),
    inference(definitional_conversion,[status(esa)],[f_10_1]) ).

cnf(f_10_3,plain,
    is_pname(undefined_pname(pname)),
    inference(clausify,[status(thm)],[f_10_2]) ).

fof(f_11_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_11_2,plain,
    is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
    inference(definitional_conversion,[status(esa)],[f_11_1]) ).

cnf(f_11_3,plain,
    is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
    inference(clausify,[status(thm)],[f_11_2]) ).

fof(f_12_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_12_2,plain,
    is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
    inference(definitional_conversion,[status(esa)],[f_12_1]) ).

cnf(f_12_3,plain,
    is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
    inference(clausify,[status(thm)],[f_12_2]) ).

fof(f_13_1,plain,
    is_bool(hoare_165779456gleton),
    inference(fof_nnf,[status(thm)],[gsy_c_Hoare__Mirabelle__jfehddehev_Ostate__not__singleton]) ).

fof(f_13_2,plain,
    is_bool(hoare_165779456gleton),
    inference(definitional_conversion,[status(esa)],[f_13_1]) ).

cnf(f_13_3,plain,
    is_bool(hoare_165779456gleton),
    inference(clausify,[status(thm)],[f_13_2]) ).

fof(f_14_1,plain,
    ! [B_1_1] : is_fun_pname_bool(dom_pname_com(B_1_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom]) ).

fof(f_14_2,plain,
    ! [U_11] : is_fun_pname_bool(dom_pname_com(U_11)),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

fof(f_14_3,plain,
    ! [U_11] : is_fun_pname_bool(dom_pname_com(U_11)),
    inference(definitional_conversion,[status(esa)],[f_14_2]) ).

cnf(f_14_4,plain,
    is_fun_pname_bool(dom_pname_com(U_11)),
    inference(clausify,[status(thm)],[f_14_3]) ).

fof(f_15_1,plain,
    ! [B_1_1] : is_fun1661590463l_bool(dom_fu2081503504ol_com(B_1_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Map_Odom_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Ocom]) ).

fof(f_15_2,plain,
    ! [U_12] : is_fun1661590463l_bool(dom_fu2081503504ol_com(U_12)),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

fof(f_15_3,plain,
    ! [U_12] : is_fun1661590463l_bool(dom_fu2081503504ol_com(U_12)),
    inference(definitional_conversion,[status(esa)],[f_15_2]) ).

cnf(f_15_4,plain,
    is_fun1661590463l_bool(dom_fu2081503504ol_com(U_12)),
    inference(clausify,[status(thm)],[f_15_3]) ).

fof(f_16_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_16_2,plain,
    is_fun_pname_bool(bot_bo844097828e_bool),
    inference(definitional_conversion,[status(esa)],[f_16_1]) ).

cnf(f_16_3,plain,
    is_fun_pname_bool(bot_bo844097828e_bool),
    inference(clausify,[status(thm)],[f_16_2]) ).

fof(f_17_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_17_2,plain,
    is_fun1661590463l_bool(bot_bo1649642514l_bool),
    inference(definitional_conversion,[status(esa)],[f_17_1]) ).

cnf(f_17_3,plain,
    is_fun1661590463l_bool(bot_bo1649642514l_bool),
    inference(clausify,[status(thm)],[f_17_2]) ).

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

fof(f_18_2,plain,
    ! [U_13] :
      ( is_fun_pname_bool(collect_pname(U_13))
      | ~ is_fun_pname_bool(U_13) ),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

fof(f_18_3,plain,
    ! [U_13] :
      ( is_fun_pname_bool(collect_pname(U_13))
      | ~ is_fun_pname_bool(U_13) ),
    inference(definitional_conversion,[status(esa)],[f_18_2]) ).

cnf(f_18_4,plain,
    ( is_fun_pname_bool(collect_pname(U_13))
    | ~ is_fun_pname_bool(U_13) ),
    inference(clausify,[status(thm)],[f_18_3]) ).

fof(f_19_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_19_2,plain,
    ! [U_14] :
      ( is_fun1661590463l_bool(collec1974731493e_bool(U_14))
      | ~ is_fun1661590463l_bool(U_14) ),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

fof(f_19_3,plain,
    ! [U_14] :
      ( is_fun1661590463l_bool(collec1974731493e_bool(U_14))
      | ~ is_fun1661590463l_bool(U_14) ),
    inference(definitional_conversion,[status(esa)],[f_19_2]) ).

cnf(f_19_4,plain,
    ( is_fun1661590463l_bool(collec1974731493e_bool(U_14))
    | ~ is_fun1661590463l_bool(U_14) ),
    inference(clausify,[status(thm)],[f_19_3]) ).

fof(f_20_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_20_2,plain,
    ! [U_16,U_15] :
      ( is_fun_pname_bool(image_pname_pname(U_16,U_15))
      | ~ is_fun_pname_bool(U_15) ),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

fof(f_20_3,plain,
    ! [U_15,U_16] :
      ( is_fun_pname_bool(image_pname_pname(U_16,U_15))
      | ~ is_fun_pname_bool(U_15) ),
    inference(definitional_conversion,[status(esa)],[f_20_2]) ).

cnf(f_20_4,plain,
    ( is_fun_pname_bool(image_pname_pname(U_16,U_15))
    | ~ is_fun_pname_bool(U_15) ),
    inference(clausify,[status(thm)],[f_20_3]) ).

fof(f_21_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_21_2,plain,
    ! [U_18,U_17] :
      ( is_fun1661590463l_bool(image_47868345e_bool(U_18,U_17))
      | ~ is_fun_pname_bool(U_17) ),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

fof(f_21_3,plain,
    ! [U_17,U_18] :
      ( is_fun1661590463l_bool(image_47868345e_bool(U_18,U_17))
      | ~ is_fun_pname_bool(U_17) ),
    inference(definitional_conversion,[status(esa)],[f_21_2]) ).

cnf(f_21_4,plain,
    ( is_fun1661590463l_bool(image_47868345e_bool(U_18,U_17))
    | ~ is_fun_pname_bool(U_17) ),
    inference(clausify,[status(thm)],[f_21_3]) ).

fof(f_22_1,plain,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_54689091_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta]) ).

fof(f_22_2,plain,
    ! [U_20,U_19] : is_fun_pname_bool(image_54689091_pname(U_20,U_19)),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

fof(f_22_3,plain,
    ! [U_19,U_20] : is_fun_pname_bool(image_54689091_pname(U_20,U_19)),
    inference(definitional_conversion,[status(esa)],[f_22_2]) ).

cnf(f_22_4,plain,
    is_fun_pname_bool(image_54689091_pname(U_20,U_19)),
    inference(clausify,[status(thm)],[f_22_3]) ).

fof(f_23_1,plain,
    ! [B_1_1,B_2_1] : is_fun1661590463l_bool(image_2131964411e_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta_001]) ).

fof(f_23_2,plain,
    ! [U_22,U_21] : is_fun1661590463l_bool(image_2131964411e_bool(U_22,U_21)),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

fof(f_23_3,plain,
    ! [U_21,U_22] : is_fun1661590463l_bool(image_2131964411e_bool(U_22,U_21)),
    inference(definitional_conversion,[status(esa)],[f_23_2]) ).

cnf(f_23_4,plain,
    is_fun1661590463l_bool(image_2131964411e_bool(U_22,U_21)),
    inference(clausify,[status(thm)],[f_23_3]) ).

fof(f_24_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_24_2,plain,
    ! [U_24,U_23] :
      ( is_fun_pname_bool(image_1283814551_pname(U_24,U_23))
      | ~ is_fun1661590463l_bool(U_23) ),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

fof(f_24_3,plain,
    ! [U_24,U_23] :
      ( is_fun_pname_bool(image_1283814551_pname(U_24,U_23))
      | ~ is_fun1661590463l_bool(U_23) ),
    inference(definitional_conversion,[status(esa)],[f_24_2]) ).

cnf(f_24_4,plain,
    ( is_fun_pname_bool(image_1283814551_pname(U_24,U_23))
    | ~ is_fun1661590463l_bool(U_23) ),
    inference(clausify,[status(thm)],[f_24_3]) ).

fof(f_25_1,plain,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_187965177_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__]) ).

fof(f_25_2,plain,
    ! [U_26,U_25] : is_fun_pname_bool(image_187965177_pname(U_26,U_25)),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

fof(f_25_3,plain,
    ! [U_25,U_26] : is_fun_pname_bool(image_187965177_pname(U_26,U_25)),
    inference(definitional_conversion,[status(esa)],[f_25_2]) ).

cnf(f_25_4,plain,
    is_fun_pname_bool(image_187965177_pname(U_26,U_25)),
    inference(clausify,[status(thm)],[f_25_3]) ).

fof(f_26_1,plain,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_1705983821_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL]) ).

fof(f_26_2,plain,
    ! [U_28,U_27] : is_fun_pname_bool(image_1705983821_pname(U_28,U_27)),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

fof(f_26_3,plain,
    ! [U_27,U_28] : is_fun_pname_bool(image_1705983821_pname(U_28,U_27)),
    inference(definitional_conversion,[status(esa)],[f_26_2]) ).

cnf(f_26_4,plain,
    is_fun_pname_bool(image_1705983821_pname(U_28,U_27)),
    inference(clausify,[status(thm)],[f_26_3]) ).

fof(f_27_1,plain,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_1619336331_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otri]) ).

fof(f_27_2,plain,
    ! [U_30,U_29] : is_fun_pname_bool(image_1619336331_pname(U_30,U_29)),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

fof(f_27_3,plain,
    ! [U_29,U_30] : is_fun_pname_bool(image_1619336331_pname(U_30,U_29)),
    inference(definitional_conversion,[status(esa)],[f_27_2]) ).

cnf(f_27_4,plain,
    is_fun_pname_bool(image_1619336331_pname(U_30,U_29)),
    inference(clausify,[status(thm)],[f_27_3]) ).

fof(f_28_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_28_2,plain,
    ! [U_32,U_31] :
      ( is_fun_pname_bool(insert_pname(U_32,U_31))
      | ~ is_fun_pname_bool(U_31)
      | ~ is_pname(U_32) ),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

fof(f_28_3,plain,
    ! [U_32,U_31] :
      ( is_fun_pname_bool(insert_pname(U_32,U_31))
      | ~ is_fun_pname_bool(U_31)
      | ~ is_pname(U_32) ),
    inference(definitional_conversion,[status(esa)],[f_28_2]) ).

cnf(f_28_4,plain,
    ( is_fun_pname_bool(insert_pname(U_32,U_31))
    | ~ is_fun_pname_bool(U_31)
    | ~ is_pname(U_32) ),
    inference(clausify,[status(thm)],[f_28_3]) ).

fof(f_29_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_29_2,plain,
    ! [U_34,U_33] :
      ( is_fun1661590463l_bool(insert1325755072e_bool(U_34,U_33))
      | ~ is_fun1661590463l_bool(U_33)
      | ~ is_fun_pname_bool(U_34) ),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

fof(f_29_3,plain,
    ! [U_33,U_34] :
      ( is_fun1661590463l_bool(insert1325755072e_bool(U_34,U_33))
      | ~ is_fun1661590463l_bool(U_33)
      | ~ is_fun_pname_bool(U_34) ),
    inference(definitional_conversion,[status(esa)],[f_29_2]) ).

cnf(f_29_4,plain,
    ( is_fun1661590463l_bool(insert1325755072e_bool(U_34,U_33))
    | ~ is_fun1661590463l_bool(U_33)
    | ~ is_fun_pname_bool(U_34) ),
    inference(clausify,[status(thm)],[f_29_3]) ).

fof(f_30_1,plain,
    is_bool(fFalse),
    inference(fof_nnf,[status(thm)],[gsy_c_fFalse]) ).

fof(f_30_2,plain,
    is_bool(fFalse),
    inference(definitional_conversion,[status(esa)],[f_30_1]) ).

cnf(f_30_3,plain,
    is_bool(fFalse),
    inference(clausify,[status(thm)],[f_30_2]) ).

fof(f_31_1,plain,
    is_bool(fTrue),
    inference(fof_nnf,[status(thm)],[gsy_c_fTrue]) ).

fof(f_31_2,plain,
    is_bool(fTrue),
    inference(definitional_conversion,[status(esa)],[f_31_1]) ).

cnf(f_31_3,plain,
    is_bool(fTrue),
    inference(clausify,[status(thm)],[f_31_2]) ).

fof(f_32_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_32_2,plain,
    ! [U_36,U_35] :
      ( is_pname(hAPP_pname_pname(U_36,U_35))
      | ~ is_pname(U_35) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

fof(f_32_3,plain,
    ! [U_35,U_36] :
      ( is_pname(hAPP_pname_pname(U_36,U_35))
      | ~ is_pname(U_35) ),
    inference(definitional_conversion,[status(esa)],[f_32_2]) ).

cnf(f_32_4,plain,
    ( is_pname(hAPP_pname_pname(U_36,U_35))
    | ~ is_pname(U_35) ),
    inference(clausify,[status(thm)],[f_32_3]) ).

fof(f_33_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_33_2,plain,
    ! [U_38,U_37] :
      ( is_bool(hAPP_pname_bool(U_38,U_37))
      | ~ is_pname(U_37)
      | ~ is_fun_pname_bool(U_38) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

fof(f_33_3,plain,
    ! [U_37,U_38] :
      ( is_bool(hAPP_pname_bool(U_38,U_37))
      | ~ is_pname(U_37)
      | ~ is_fun_pname_bool(U_38) ),
    inference(definitional_conversion,[status(esa)],[f_33_2]) ).

cnf(f_33_4,plain,
    ( is_bool(hAPP_pname_bool(U_38,U_37))
    | ~ is_pname(U_37)
    | ~ is_fun_pname_bool(U_38) ),
    inference(clausify,[status(thm)],[f_33_3]) ).

fof(f_34_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_34_2,plain,
    ! [U_40,U_39] :
      ( is_fun_pname_bool(hAPP_p61793385e_bool(U_40,U_39))
      | ~ is_pname(U_39) ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

fof(f_34_3,plain,
    ! [U_40,U_39] :
      ( is_fun_pname_bool(hAPP_p61793385e_bool(U_40,U_39))
      | ~ is_pname(U_39) ),
    inference(definitional_conversion,[status(esa)],[f_34_2]) ).

cnf(f_34_4,plain,
    ( is_fun_pname_bool(hAPP_p61793385e_bool(U_40,U_39))
    | ~ is_pname(U_39) ),
    inference(clausify,[status(thm)],[f_34_3]) ).

fof(f_35_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_35_2,plain,
    ! [U_42,U_41] :
      ( is_fun1661590463l_bool(hAPP_p338031245l_bool(U_42,U_41))
      | ~ is_pname(U_41) ),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

fof(f_35_3,plain,
    ! [U_41,U_42] :
      ( is_fun1661590463l_bool(hAPP_p338031245l_bool(U_42,U_41))
      | ~ is_pname(U_41) ),
    inference(definitional_conversion,[status(esa)],[f_35_2]) ).

cnf(f_35_4,plain,
    ( is_fun1661590463l_bool(hAPP_p338031245l_bool(U_42,U_41))
    | ~ is_pname(U_41) ),
    inference(clausify,[status(thm)],[f_35_3]) ).

fof(f_36_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_36_2,plain,
    ! [U_44,U_43] :
      ( is_bool(hAPP_bool_bool(U_44,U_43))
      | ~ is_bool(U_43) ),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

fof(f_36_3,plain,
    ! [U_43,U_44] :
      ( is_bool(hAPP_bool_bool(U_44,U_43))
      | ~ is_bool(U_43) ),
    inference(definitional_conversion,[status(esa)],[f_36_2]) ).

cnf(f_36_4,plain,
    ( is_bool(hAPP_bool_bool(U_44,U_43))
    | ~ is_bool(U_43) ),
    inference(clausify,[status(thm)],[f_36_3]) ).

fof(f_37_1,plain,
    ! [B_1_1,B_2_1] : is_pname(hAPP_H1621176307_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0]) ).

fof(f_37_2,plain,
    ! [U_46,U_45] : is_pname(hAPP_H1621176307_pname(U_46,U_45)),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

fof(f_37_3,plain,
    ! [U_45,U_46] : is_pname(hAPP_H1621176307_pname(U_46,U_45)),
    inference(definitional_conversion,[status(esa)],[f_37_2]) ).

cnf(f_37_4,plain,
    is_pname(hAPP_H1621176307_pname(U_46,U_45)),
    inference(clausify,[status(thm)],[f_37_3]) ).

fof(f_38_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_H78829294e_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_002]) ).

fof(f_38_2,plain,
    ! [U_48,U_47] : is_bool(hAPP_H78829294e_bool(U_48,U_47)),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

fof(f_38_3,plain,
    ! [U_47,U_48] : is_bool(hAPP_H78829294e_bool(U_48,U_47)),
    inference(definitional_conversion,[status(esa)],[f_38_2]) ).

cnf(f_38_4,plain,
    is_bool(hAPP_H78829294e_bool(U_48,U_47)),
    inference(clausify,[status(thm)],[f_38_3]) ).

fof(f_39_1,plain,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_H356885323e_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_003]) ).

fof(f_39_2,plain,
    ! [U_50,U_49] : is_fun_pname_bool(hAPP_H356885323e_bool(U_50,U_49)),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

fof(f_39_3,plain,
    ! [U_49,U_50] : is_fun_pname_bool(hAPP_H356885323e_bool(U_50,U_49)),
    inference(definitional_conversion,[status(esa)],[f_39_2]) ).

cnf(f_39_4,plain,
    is_fun_pname_bool(hAPP_H356885323e_bool(U_50,U_49)),
    inference(clausify,[status(thm)],[f_39_3]) ).

fof(f_40_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_40_2,plain,
    ! [U_52,U_51] :
      ( is_pname(hAPP_f1297739591_pname(U_52,U_51))
      | ~ is_fun_pname_bool(U_51) ),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

fof(f_40_3,plain,
    ! [U_51,U_52] :
      ( is_pname(hAPP_f1297739591_pname(U_52,U_51))
      | ~ is_fun_pname_bool(U_51) ),
    inference(definitional_conversion,[status(esa)],[f_40_2]) ).

cnf(f_40_4,plain,
    ( is_pname(hAPP_f1297739591_pname(U_52,U_51))
    | ~ is_fun_pname_bool(U_51) ),
    inference(clausify,[status(thm)],[f_40_3]) ).

fof(f_41_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_41_2,plain,
    ! [U_54,U_53] :
      ( is_bool(hAPP_f1664156314l_bool(U_54,U_53))
      | ~ is_fun_pname_bool(U_53)
      | ~ is_fun1661590463l_bool(U_54) ),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

fof(f_41_3,plain,
    ! [U_53,U_54] :
      ( is_bool(hAPP_f1664156314l_bool(U_54,U_53))
      | ~ is_fun_pname_bool(U_53)
      | ~ is_fun1661590463l_bool(U_54) ),
    inference(definitional_conversion,[status(esa)],[f_41_2]) ).

cnf(f_41_4,plain,
    ( is_bool(hAPP_f1664156314l_bool(U_54,U_53))
    | ~ is_fun_pname_bool(U_53)
    | ~ is_fun1661590463l_bool(U_54) ),
    inference(clausify,[status(thm)],[f_41_3]) ).

fof(f_42_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_42_2,plain,
    ! [U_56,U_55] :
      ( is_fun_pname_bool(hAPP_f759274231e_bool(U_56,U_55))
      | ~ is_fun_pname_bool(U_55) ),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

fof(f_42_3,plain,
    ! [U_55,U_56] :
      ( is_fun_pname_bool(hAPP_f759274231e_bool(U_56,U_55))
      | ~ is_fun_pname_bool(U_55) ),
    inference(definitional_conversion,[status(esa)],[f_42_2]) ).

cnf(f_42_4,plain,
    ( is_fun_pname_bool(hAPP_f759274231e_bool(U_56,U_55))
    | ~ is_fun_pname_bool(U_55) ),
    inference(clausify,[status(thm)],[f_42_3]) ).

fof(f_43_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_43_2,plain,
    ! [U_58,U_57] :
      ( is_fun1661590463l_bool(hAPP_f434788991l_bool(U_58,U_57))
      | ~ is_fun_pname_bool(U_57) ),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

fof(f_43_3,plain,
    ! [U_57,U_58] :
      ( is_fun1661590463l_bool(hAPP_f434788991l_bool(U_58,U_57))
      | ~ is_fun_pname_bool(U_57) ),
    inference(definitional_conversion,[status(esa)],[f_43_2]) ).

cnf(f_43_4,plain,
    ( is_fun1661590463l_bool(hAPP_f434788991l_bool(U_58,U_57))
    | ~ is_fun_pname_bool(U_57) ),
    inference(clausify,[status(thm)],[f_43_3]) ).

fof(f_44_1,plain,
    ! [B_1_1,B_2_1] : is_pname(hAPP_f560369737_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O]) ).

fof(f_44_2,plain,
    ! [U_60,U_59] : is_pname(hAPP_f560369737_pname(U_60,U_59)),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

fof(f_44_3,plain,
    ! [U_59,U_60] : is_pname(hAPP_f560369737_pname(U_60,U_59)),
    inference(definitional_conversion,[status(esa)],[f_44_2]) ).

cnf(f_44_4,plain,
    is_pname(hAPP_f560369737_pname(U_60,U_59)),
    inference(clausify,[status(thm)],[f_44_3]) ).

fof(f_45_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f971112728l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O_004]) ).

fof(f_45_2,plain,
    ! [U_62,U_61] : is_bool(hAPP_f971112728l_bool(U_62,U_61)),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

fof(f_45_3,plain,
    ! [U_61,U_62] : is_bool(hAPP_f971112728l_bool(U_62,U_61)),
    inference(definitional_conversion,[status(esa)],[f_45_2]) ).

cnf(f_45_4,plain,
    is_bool(hAPP_f971112728l_bool(U_62,U_61)),
    inference(clausify,[status(thm)],[f_45_3]) ).

fof(f_46_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_46_2,plain,
    ! [U_64,U_63] :
      ( is_bool(hAPP_f1935102916l_bool(U_64,U_63))
      | ~ is_fun1661590463l_bool(U_63) ),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

fof(f_46_3,plain,
    ! [U_63,U_64] :
      ( is_bool(hAPP_f1935102916l_bool(U_64,U_63))
      | ~ is_fun1661590463l_bool(U_63) ),
    inference(definitional_conversion,[status(esa)],[f_46_2]) ).

cnf(f_46_4,plain,
    ( is_bool(hAPP_f1935102916l_bool(U_64,U_63))
    | ~ is_fun1661590463l_bool(U_63) ),
    inference(clausify,[status(thm)],[f_46_3]) ).

fof(f_47_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_005]) ).

fof(f_47_2,plain,
    ! [U_66,U_65] :
      ( is_fun1661590463l_bool(hAPP_f559147733l_bool(U_66,U_65))
      | ~ is_fun1661590463l_bool(U_65) ),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

fof(f_47_3,plain,
    ! [U_65,U_66] :
      ( is_fun1661590463l_bool(hAPP_f559147733l_bool(U_66,U_65))
      | ~ is_fun1661590463l_bool(U_65) ),
    inference(definitional_conversion,[status(esa)],[f_47_2]) ).

cnf(f_47_4,plain,
    ( is_fun1661590463l_bool(hAPP_f559147733l_bool(U_66,U_65))
    | ~ is_fun1661590463l_bool(U_65) ),
    inference(clausify,[status(thm)],[f_47_3]) ).

fof(f_48_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f166538662l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It]) ).

fof(f_48_2,plain,
    ! [U_68,U_67] : is_bool(hAPP_f166538662l_bool(U_68,U_67)),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

fof(f_48_3,plain,
    ! [U_67,U_68] : is_bool(hAPP_f166538662l_bool(U_68,U_67)),
    inference(definitional_conversion,[status(esa)],[f_48_2]) ).

cnf(f_48_4,plain,
    is_bool(hAPP_f166538662l_bool(U_68,U_67)),
    inference(clausify,[status(thm)],[f_48_3]) ).

fof(f_49_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_49_2,plain,
    ! [U_70,U_69] : is_bool(hAPP_f389811538l_bool(U_70,U_69)),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

fof(f_49_3,plain,
    ! [U_69,U_70] : is_bool(hAPP_f389811538l_bool(U_70,U_69)),
    inference(definitional_conversion,[status(esa)],[f_49_2]) ).

cnf(f_49_4,plain,
    is_bool(hAPP_f389811538l_bool(U_70,U_69)),
    inference(clausify,[status(thm)],[f_49_3]) ).

fof(f_50_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f468958928l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__O]) ).

fof(f_50_2,plain,
    ! [U_72,U_71] : is_bool(hAPP_f468958928l_bool(U_72,U_71)),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

fof(f_50_3,plain,
    ! [U_71,U_72] : is_bool(hAPP_f468958928l_bool(U_72,U_71)),
    inference(definitional_conversion,[status(esa)],[f_50_2]) ).

cnf(f_50_4,plain,
    is_bool(hAPP_f468958928l_bool(U_72,U_71)),
    inference(clausify,[status(thm)],[f_50_3]) ).

fof(f_51_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f595608956l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo]) ).

fof(f_51_2,plain,
    ! [U_74,U_73] : is_bool(hAPP_f595608956l_bool(U_74,U_73)),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

fof(f_51_3,plain,
    ! [U_73,U_74] : is_bool(hAPP_f595608956l_bool(U_74,U_73)),
    inference(definitional_conversion,[status(esa)],[f_51_2]) ).

cnf(f_51_4,plain,
    is_bool(hAPP_f595608956l_bool(U_74,U_73)),
    inference(clausify,[status(thm)],[f_51_3]) ).

fof(f_52_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1022807134l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfeh]) ).

fof(f_52_2,plain,
    ! [U_76,U_75] : is_bool(hAPP_f1022807134l_bool(U_76,U_75)),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

fof(f_52_3,plain,
    ! [U_75,U_76] : is_bool(hAPP_f1022807134l_bool(U_76,U_75)),
    inference(definitional_conversion,[status(esa)],[f_52_2]) ).

cnf(f_52_4,plain,
    is_bool(hAPP_f1022807134l_bool(U_76,U_75)),
    inference(clausify,[status(thm)],[f_52_3]) ).

fof(f_53_1,plain,
    is_pname(pn),
    inference(fof_nnf,[status(thm)],[gsy_v_pn]) ).

fof(f_53_2,plain,
    is_pname(pn),
    inference(definitional_conversion,[status(esa)],[f_53_1]) ).

cnf(f_53_3,plain,
    is_pname(pn),
    inference(clausify,[status(thm)],[f_53_2]) ).

fof(f_54_1,plain,
    ! [G] : hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),bot_bo620288102e_bool)),
    inference(fof_nnf,[status(thm)],[fact_0_empty]) ).

fof(f_54_2,plain,
    ! [U_77] : hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_77),bot_bo620288102e_bool)),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

fof(f_54_3,plain,
    ! [U_77] : hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_77),bot_bo620288102e_bool)),
    inference(definitional_conversion,[status(esa)],[f_54_2]) ).

cnf(f_54_4,plain,
    hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_77),bot_bo620288102e_bool)),
    inference(clausify,[status(thm)],[f_54_3]) ).

fof(f_55_1,plain,
    ! [Ts,G] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,Ts),G)) ),
    inference(fof_nnf,[status(thm)],[fact_1_asm]) ).

fof(f_55_2,plain,
    ! [U_79,U_78] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_78),U_79))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_79),U_78)) ),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

fof(f_55_3,plain,
    ! [U_78,U_79] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_78),U_79))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_79),U_78)) ),
    inference(definitional_conversion,[status(esa)],[f_55_2]) ).

cnf(f_55_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_78),U_79))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_79),U_78)) ),
    inference(clausify,[status(thm)],[f_55_3]) ).

fof(f_56_1,plain,
    ! [Ts,G,Ts_1] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,Ts),Ts_1))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts_1)) ),
    inference(fof_nnf,[status(thm)],[fact_2_weaken]) ).

fof(f_56_2,plain,
    ! [U_82,U_81,U_80] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_81),U_82))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_82),U_80))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_81),U_80)) ),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

fof(f_56_3,plain,
    ! [U_80,U_81,U_82] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_81),U_82))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_82),U_80))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_81),U_80)) ),
    inference(definitional_conversion,[status(esa)],[f_56_2]) ).

cnf(f_56_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_81),U_82))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_82),U_80))
    | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_81),U_80)) ),
    inference(clausify,[status(thm)],[f_56_3]) ).

fof(f_57_1,plain,
    ! [G,G_1,Ts] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,G_1),G))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G_1),Ts)) ),
    inference(fof_nnf,[status(thm)],[fact_3_thin]) ).

fof(f_57_2,plain,
    ! [U_85,U_84,U_83] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_85),U_83))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_84),U_85))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_84),U_83)) ),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

fof(f_57_3,plain,
    ! [U_83,U_84,U_85] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_85),U_83))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_84),U_85))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_84),U_83)) ),
    inference(definitional_conversion,[status(esa)],[f_57_2]) ).

cnf(f_57_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_85),U_83))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_84),U_85))
    | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_84),U_83)) ),
    inference(clausify,[status(thm)],[f_57_3]) ).

fof(f_58_1,plain,
    ! [G,G_1,Ts] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),G_1))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G_1),Ts)) ),
    inference(fof_nnf,[status(thm)],[fact_4_cut]) ).

fof(f_58_2,plain,
    ! [U_88,U_87,U_86] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_88),U_86))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_88),U_87))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_87),U_86)) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

fof(f_58_3,plain,
    ! [U_87,U_88,U_86] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_88),U_86))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_88),U_87))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_87),U_86)) ),
    inference(definitional_conversion,[status(esa)],[f_58_2]) ).

cnf(f_58_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_88),U_86))
    | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_88),U_87))
    | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_87),U_86)) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

fof(f_59_1,plain,
    ! [Ts,G,T] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(T,Ts)))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(T,bot_bo620288102e_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_5_hoare__derivs_Oinsert]) ).

fof(f_59_2,plain,
    ! [U_91,U_90,U_89] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_90),insert1415133716_state(U_89,U_91)))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_90),U_91))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_90),insert1415133716_state(U_89,bot_bo620288102e_bool))) ),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

fof(f_59_3,plain,
    ! [U_89,U_90,U_91] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_90),insert1415133716_state(U_89,U_91)))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_90),U_91))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_90),insert1415133716_state(U_89,bot_bo620288102e_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_59_2]) ).

cnf(f_59_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_90),insert1415133716_state(U_89,U_91)))
    | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_90),U_91))
    | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_90),insert1415133716_state(U_89,bot_bo620288102e_bool))) ),
    inference(clausify,[status(thm)],[f_59_3]) ).

fof(f_60_1,plain,
    ! [G,T,Ts] :
      ( ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),Ts))
        & hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(T,bot_bo620288102e_bool))) )
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(T,Ts))) ),
    inference(fof_nnf,[status(thm)],[fact_6_derivs__insertD]) ).

fof(f_60_2,plain,
    ! [U_94,U_93,U_92] :
      ( ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_94),U_92))
        & hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_94),insert1415133716_state(U_93,bot_bo620288102e_bool))) )
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_94),insert1415133716_state(U_93,U_92))) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

fof(f_60_3,plain,
    ( ! [U_93,U_92,U_94] :
        ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_94),U_92))
        | ~ sP0(U_93,U_92,U_94) )
    & ! [U_93,U_92,U_94] :
        ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_94),insert1415133716_state(U_93,bot_bo620288102e_bool)))
        | ~ sP0(U_93,U_92,U_94) )
    & ! [U_93,U_92,U_94] :
        ( sP0(U_93,U_92,U_94)
        | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_94),insert1415133716_state(U_93,U_92))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_60_2]) ).

cnf(f_60_4,plain,
    ( sP0(U_93,U_92,U_94)
    | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_94),insert1415133716_state(U_93,U_92))) ),
    inference(clausify,[status(thm)],[f_60_3]) ).

cnf(f_60_5,plain,
    ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_94),insert1415133716_state(U_93,bot_bo620288102e_bool)))
    | ~ sP0(U_93,U_92,U_94) ),
    inference(clausify,[status(thm)],[f_60_3]) ).

cnf(f_60_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_94),U_92))
    | ~ sP0(U_93,U_92,U_94) ),
    inference(clausify,[status(thm)],[f_60_3]) ).

fof(f_61_1,plain,
    ! [Pn_1,G] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1)),bot_bo620288102e_bool)))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,Pn_1)),G)),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,Pn_1))),bot_bo620288102e_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_7_MGT__BodyN]) ).

fof(f_61_2,plain,
    ! [U_96,U_95] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_95),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,U_96)),bot_bo620288102e_bool)))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,U_96)),U_95)),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,U_96))),bot_bo620288102e_bool))) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

fof(f_61_3,plain,
    ! [U_95,U_96] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_95),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,U_96)),bot_bo620288102e_bool)))
      | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,U_96)),U_95)),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,U_96))),bot_bo620288102e_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_61_2]) ).

cnf(f_61_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_95),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,U_96)),bot_bo620288102e_bool)))
    | ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,U_96)),U_95)),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_option_com_com(the_com,hAPP_p799580910on_com(body,U_96))),bot_bo620288102e_bool))) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

fof(f_62_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_8_finite__Collect__subsets]) ).

fof(f_62_2,plain,
    ! [U_97] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),U_97))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_97)) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

fof(f_62_3,plain,
    ! [U_97] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),U_97))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_97)) ),
    inference(definitional_conversion,[status(esa)],[f_62_2]) ).

cnf(f_62_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),U_97))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_97)) ),
    inference(clausify,[status(thm)],[f_62_3]) ).

fof(f_63_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(ord_le1285840794e_bool),A))))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) ),
    inference(fof_nnf,[status(thm)],[fact_9_finite__Collect__subsets]) ).

fof(f_63_2,plain,
    ! [U_98] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(ord_le1285840794e_bool),U_98))))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_98)) ),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

fof(f_63_3,plain,
    ! [U_98] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(ord_le1285840794e_bool),U_98))))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_98)) ),
    inference(definitional_conversion,[status(esa)],[f_63_2]) ).

cnf(f_63_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(ord_le1285840794e_bool),U_98))))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_98)) ),
    inference(clausify,[status(thm)],[f_63_3]) ).

fof(f_64_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),A))))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_10_finite__Collect__subsets]) ).

fof(f_64_2,plain,
    ! [U_99] :
      ( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),U_99))))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_99)) ),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

fof(f_64_3,plain,
    ! [U_99] :
      ( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),U_99))))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_99)) ),
    inference(definitional_conversion,[status(esa)],[f_64_2]) ).

cnf(f_64_4,plain,
    ( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),U_99))))
    | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_99)) ),
    inference(clausify,[status(thm)],[f_64_3]) ).

fof(f_65_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f1022807134l_bool(finite34021339l_bool,collec256567069l_bool(hAPP_f667366769l_bool(cOMBC_747715418l_bool(ord_le889598034l_bool),A))))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_11_finite__Collect__subsets]) ).

fof(f_65_2,plain,
    ! [U_100] :
      ( hBOOL(hAPP_f1022807134l_bool(finite34021339l_bool,collec256567069l_bool(hAPP_f667366769l_bool(cOMBC_747715418l_bool(ord_le889598034l_bool),U_100))))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_100)) ),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

fof(f_65_3,plain,
    ! [U_100] :
      ( hBOOL(hAPP_f1022807134l_bool(finite34021339l_bool,collec256567069l_bool(hAPP_f667366769l_bool(cOMBC_747715418l_bool(ord_le889598034l_bool),U_100))))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_100)) ),
    inference(definitional_conversion,[status(esa)],[f_65_2]) ).

cnf(f_65_4,plain,
    ( hBOOL(hAPP_f1022807134l_bool(finite34021339l_bool,collec256567069l_bool(hAPP_f667366769l_bool(cOMBC_747715418l_bool(ord_le889598034l_bool),U_100))))
    | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_100)) ),
    inference(clausify,[status(thm)],[f_65_3]) ).

fof(f_66_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(hAPP_f585161855l_bool(cOMBC_1691491604l_bool(ord_le287025148l_bool),A))))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_12_finite__Collect__subsets]) ).

fof(f_66_2,plain,
    ! [U_101] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(hAPP_f585161855l_bool(cOMBC_1691491604l_bool(ord_le287025148l_bool),U_101))))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_101)) ),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

fof(f_66_3,plain,
    ! [U_101] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(hAPP_f585161855l_bool(cOMBC_1691491604l_bool(ord_le287025148l_bool),U_101))))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_101)) ),
    inference(definitional_conversion,[status(esa)],[f_66_2]) ).

cnf(f_66_4,plain,
    ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(hAPP_f585161855l_bool(cOMBC_1691491604l_bool(ord_le287025148l_bool),U_101))))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_101)) ),
    inference(clausify,[status(thm)],[f_66_3]) ).

fof(f_67_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_13_finite__Collect__subsets]) ).

fof(f_67_2,plain,
    ! [U_102] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),U_102))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_102)) ),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

fof(f_67_3,plain,
    ! [U_102] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),U_102))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_102)) ),
    inference(definitional_conversion,[status(esa)],[f_67_2]) ).

cnf(f_67_4,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),U_102))))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_102)) ),
    inference(clausify,[status(thm)],[f_67_3]) ).

fof(f_68_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_2003357581_state(H,Fa)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_14_finite__imageI]) ).

fof(f_68_2,plain,
    ! [U_104,U_103] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_2003357581_state(U_104,U_103)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_103)) ),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

fof(f_68_3,plain,
    ! [U_103,U_104] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_2003357581_state(U_104,U_103)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_103)) ),
    inference(definitional_conversion,[status(esa)],[f_68_2]) ).

cnf(f_68_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_2003357581_state(U_104,U_103)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_103)) ),
    inference(clausify,[status(thm)],[f_68_3]) ).

fof(f_69_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(H,Fa)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_15_finite__imageI]) ).

fof(f_69_2,plain,
    ! [U_106,U_105] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(U_106,U_105)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_105)) ),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

fof(f_69_3,plain,
    ! [U_105,U_106] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(U_106,U_105)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_105)) ),
    inference(definitional_conversion,[status(esa)],[f_69_2]) ).

cnf(f_69_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(U_106,U_105)))
    | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_105)) ),
    inference(clausify,[status(thm)],[f_69_3]) ).

fof(f_70_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1619336331_pname(H,Fa)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_16_finite__imageI]) ).

fof(f_70_2,plain,
    ! [U_108,U_107] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1619336331_pname(U_108,U_107)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_107)) ),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

fof(f_70_3,plain,
    ! [U_107,U_108] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1619336331_pname(U_108,U_107)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_107)) ),
    inference(definitional_conversion,[status(esa)],[f_70_2]) ).

cnf(f_70_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1619336331_pname(U_108,U_107)))
    | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_107)) ),
    inference(clausify,[status(thm)],[f_70_3]) ).

fof(f_71_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_187965177_pname(H,Fa)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_17_finite__imageI]) ).

fof(f_71_2,plain,
    ! [U_110,U_109] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_187965177_pname(U_110,U_109)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_109)) ),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

fof(f_71_3,plain,
    ! [U_109,U_110] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_187965177_pname(U_110,U_109)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_109)) ),
    inference(definitional_conversion,[status(esa)],[f_71_2]) ).

cnf(f_71_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_187965177_pname(U_110,U_109)))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_109)) ),
    inference(clausify,[status(thm)],[f_71_3]) ).

fof(f_72_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(H,Fa)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_18_finite__imageI]) ).

fof(f_72_2,plain,
    ! [U_112,U_111] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_112,U_111)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_111)) ),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

fof(f_72_3,plain,
    ! [U_111,U_112] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_112,U_111)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_111)) ),
    inference(definitional_conversion,[status(esa)],[f_72_2]) ).

cnf(f_72_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_112,U_111)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_111)) ),
    inference(clausify,[status(thm)],[f_72_3]) ).

fof(f_73_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_677922117_state(H,Fa)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_19_finite__imageI]) ).

fof(f_73_2,plain,
    ! [U_114,U_113] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_677922117_state(U_114,U_113)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_113)) ),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

fof(f_73_3,plain,
    ! [U_113,U_114] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_677922117_state(U_114,U_113)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_113)) ),
    inference(definitional_conversion,[status(esa)],[f_73_2]) ).

cnf(f_73_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_677922117_state(U_114,U_113)))
    | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_113)) ),
    inference(clausify,[status(thm)],[f_73_3]) ).

fof(f_74_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_892968839_state(H,Fa)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_20_finite__imageI]) ).

fof(f_74_2,plain,
    ! [U_116,U_115] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_892968839_state(U_116,U_115)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_115)) ),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

fof(f_74_3,plain,
    ! [U_115,U_116] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_892968839_state(U_116,U_115)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_115)) ),
    inference(definitional_conversion,[status(esa)],[f_74_2]) ).

cnf(f_74_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_892968839_state(U_116,U_115)))
    | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_115)) ),
    inference(clausify,[status(thm)],[f_74_3]) ).

fof(f_75_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_18964633_state(H,Fa)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_21_finite__imageI]) ).

fof(f_75_2,plain,
    ! [U_118,U_117] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_18964633_state(U_118,U_117)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_117)) ),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

fof(f_75_3,plain,
    ! [U_117,U_118] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_18964633_state(U_118,U_117)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_117)) ),
    inference(definitional_conversion,[status(esa)],[f_75_2]) ).

cnf(f_75_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_18964633_state(U_118,U_117)))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_117)) ),
    inference(clausify,[status(thm)],[f_75_3]) ).

fof(f_76_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_516545147_state(H,Fa)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_22_finite__imageI]) ).

fof(f_76_2,plain,
    ! [U_120,U_119] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_516545147_state(U_120,U_119)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_119)) ),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

fof(f_76_3,plain,
    ! [U_119,U_120] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_516545147_state(U_120,U_119)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_119)) ),
    inference(definitional_conversion,[status(esa)],[f_76_2]) ).

cnf(f_76_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,image_516545147_state(U_120,U_119)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_119)) ),
    inference(clausify,[status(thm)],[f_76_3]) ).

fof(f_77_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(H,Fa)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_23_finite__imageI]) ).

fof(f_77_2,plain,
    ! [U_122,U_121] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(U_122,U_121)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_121)) ),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ! [U_121,U_122] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(U_122,U_121)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_121)) ),
    inference(definitional_conversion,[status(esa)],[f_77_2]) ).

cnf(f_77_4,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(U_122,U_121)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_121)) ),
    inference(clausify,[status(thm)],[f_77_3]) ).

fof(f_78_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,image_288317893l_bool(H,Fa)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_24_finite__imageI]) ).

fof(f_78_2,plain,
    ! [U_124,U_123] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,image_288317893l_bool(U_124,U_123)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_123)) ),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

fof(f_78_3,plain,
    ! [U_123,U_124] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,image_288317893l_bool(U_124,U_123)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_123)) ),
    inference(definitional_conversion,[status(esa)],[f_78_2]) ).

cnf(f_78_4,plain,
    ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,image_288317893l_bool(U_124,U_123)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_123)) ),
    inference(clausify,[status(thm)],[f_78_3]) ).

fof(f_79_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,image_70449425e_bool(H,Fa)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_25_finite__imageI]) ).

fof(f_79_2,plain,
    ! [U_126,U_125] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,image_70449425e_bool(U_126,U_125)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_125)) ),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

fof(f_79_3,plain,
    ! [U_125,U_126] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,image_70449425e_bool(U_126,U_125)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_125)) ),
    inference(definitional_conversion,[status(esa)],[f_79_2]) ).

cnf(f_79_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,image_70449425e_bool(U_126,U_125)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_125)) ),
    inference(clausify,[status(thm)],[f_79_3]) ).

fof(f_80_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(H,Fa)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_26_finite__imageI]) ).

fof(f_80_2,plain,
    ! [U_128,U_127] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_128,U_127)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_127)) ),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

fof(f_80_3,plain,
    ! [U_127,U_128] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_128,U_127)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_127)) ),
    inference(definitional_conversion,[status(esa)],[f_80_2]) ).

cnf(f_80_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_128,U_127)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_127)) ),
    inference(clausify,[status(thm)],[f_80_3]) ).

fof(f_81_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1210605179l_bool(H,Fa)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_27_finite__imageI]) ).

fof(f_81_2,plain,
    ! [U_130,U_129] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1210605179l_bool(U_130,U_129)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_129)) ),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

fof(f_81_3,plain,
    ! [U_129,U_130] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1210605179l_bool(U_130,U_129)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_129)) ),
    inference(definitional_conversion,[status(esa)],[f_81_2]) ).

cnf(f_81_4,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1210605179l_bool(U_130,U_129)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_129)) ),
    inference(clausify,[status(thm)],[f_81_3]) ).

fof(f_82_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,image_1761575943l_bool(H,Fa)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_28_finite__imageI]) ).

fof(f_82_2,plain,
    ! [U_132,U_131] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,image_1761575943l_bool(U_132,U_131)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_131)) ),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

fof(f_82_3,plain,
    ! [U_131,U_132] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,image_1761575943l_bool(U_132,U_131)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_131)) ),
    inference(definitional_conversion,[status(esa)],[f_82_2]) ).

cnf(f_82_4,plain,
    ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,image_1761575943l_bool(U_132,U_131)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_131)) ),
    inference(clausify,[status(thm)],[f_82_3]) ).

fof(f_83_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,image_1828608335e_bool(H,Fa)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_29_finite__imageI]) ).

fof(f_83_2,plain,
    ! [U_134,U_133] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,image_1828608335e_bool(U_134,U_133)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_133)) ),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

fof(f_83_3,plain,
    ! [U_133,U_134] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,image_1828608335e_bool(U_134,U_133)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_133)) ),
    inference(definitional_conversion,[status(esa)],[f_83_2]) ).

cnf(f_83_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,image_1828608335e_bool(U_134,U_133)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_133)) ),
    inference(clausify,[status(thm)],[f_83_3]) ).

fof(f_84_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_2131964411e_bool(H,Fa)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_30_finite__imageI]) ).

fof(f_84_2,plain,
    ! [U_136,U_135] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_2131964411e_bool(U_136,U_135)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_135)) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

fof(f_84_3,plain,
    ! [U_135,U_136] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_2131964411e_bool(U_136,U_135)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_135)) ),
    inference(definitional_conversion,[status(esa)],[f_84_2]) ).

cnf(f_84_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_2131964411e_bool(U_136,U_135)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_135)) ),
    inference(clausify,[status(thm)],[f_84_3]) ).

fof(f_85_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_54689091_pname(H,Fa)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_31_finite__imageI]) ).

fof(f_85_2,plain,
    ! [U_138,U_137] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_54689091_pname(U_138,U_137)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_137)) ),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

fof(f_85_3,plain,
    ! [U_137,U_138] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_54689091_pname(U_138,U_137)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_137)) ),
    inference(definitional_conversion,[status(esa)],[f_85_2]) ).

cnf(f_85_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_54689091_pname(U_138,U_137)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_137)) ),
    inference(clausify,[status(thm)],[f_85_3]) ).

fof(f_86_1,plain,
    ! [H,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(H,Fa)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_32_finite__imageI]) ).

fof(f_86_2,plain,
    ! [U_140,U_139] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(U_140,U_139)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_139)) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

fof(f_86_3,plain,
    ! [U_139,U_140] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(U_140,U_139)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_139)) ),
    inference(definitional_conversion,[status(esa)],[f_86_2]) ).

cnf(f_86_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(U_140,U_139)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_139)) ),
    inference(clausify,[status(thm)],[f_86_3]) ).

fof(f_87_1,plain,
    ! [A] : hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,bot_bo620288102e_bool),A)),
    inference(fof_nnf,[status(thm)],[fact_33_empty__subsetI]) ).

fof(f_87_2,plain,
    ! [U_141] : hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,bot_bo620288102e_bool),U_141)),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

fof(f_87_3,plain,
    ! [U_141] : hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,bot_bo620288102e_bool),U_141)),
    inference(definitional_conversion,[status(esa)],[f_87_2]) ).

cnf(f_87_4,plain,
    hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,bot_bo620288102e_bool),U_141)),
    inference(clausify,[status(thm)],[f_87_3]) ).

fof(f_88_1,plain,
    ! [A] : hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,bot_bo1649642514l_bool),A)),
    inference(fof_nnf,[status(thm)],[fact_34_empty__subsetI]) ).

fof(f_88_2,plain,
    ! [U_142] : hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,bot_bo1649642514l_bool),U_142)),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

fof(f_88_3,plain,
    ! [U_142] : hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,bot_bo1649642514l_bool),U_142)),
    inference(definitional_conversion,[status(esa)],[f_88_2]) ).

cnf(f_88_4,plain,
    hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,bot_bo1649642514l_bool),U_142)),
    inference(clausify,[status(thm)],[f_88_3]) ).

fof(f_89_1,plain,
    ! [A] : hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,bot_bo535777328l_bool),A)),
    inference(fof_nnf,[status(thm)],[fact_35_empty__subsetI]) ).

fof(f_89_2,plain,
    ! [U_143] : hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,bot_bo535777328l_bool),U_143)),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

fof(f_89_3,plain,
    ! [U_143] : hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,bot_bo535777328l_bool),U_143)),
    inference(definitional_conversion,[status(esa)],[f_89_2]) ).

cnf(f_89_4,plain,
    hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,bot_bo535777328l_bool),U_143)),
    inference(clausify,[status(thm)],[f_89_3]) ).

fof(f_90_1,plain,
    ! [A] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),A)),
    inference(fof_nnf,[status(thm)],[fact_36_empty__subsetI]) ).

fof(f_90_2,plain,
    ! [U_144] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),U_144)),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

fof(f_90_3,plain,
    ! [U_144] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),U_144)),
    inference(definitional_conversion,[status(esa)],[f_90_2]) ).

cnf(f_90_4,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),U_144)),
    inference(clausify,[status(thm)],[f_90_3]) ).

fof(f_91_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(A_2,A)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) ),
    inference(fof_nnf,[status(thm)],[fact_37_finite_OinsertI]) ).

fof(f_91_2,plain,
    ! [U_146,U_145] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(U_146,U_145)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_145)) ),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

fof(f_91_3,plain,
    ! [U_145,U_146] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(U_146,U_145)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_145)) ),
    inference(definitional_conversion,[status(esa)],[f_91_2]) ).

cnf(f_91_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(U_146,U_145)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_145)) ),
    inference(clausify,[status(thm)],[f_91_3]) ).

fof(f_92_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_2,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_38_finite_OinsertI]) ).

fof(f_92_2,plain,
    ! [U_148,U_147] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_148,U_147)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_147)) ),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

fof(f_92_3,plain,
    ! [U_147,U_148] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_148,U_147)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_147)) ),
    inference(definitional_conversion,[status(esa)],[f_92_2]) ).

cnf(f_92_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_148,U_147)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_147)) ),
    inference(clausify,[status(thm)],[f_92_3]) ).

fof(f_93_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(A_2,A)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_39_finite_OinsertI]) ).

fof(f_93_2,plain,
    ! [U_150,U_149] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(U_150,U_149)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_149)) ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

fof(f_93_3,plain,
    ! [U_149,U_150] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(U_150,U_149)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_149)) ),
    inference(definitional_conversion,[status(esa)],[f_93_2]) ).

cnf(f_93_4,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(U_150,U_149)))
    | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_149)) ),
    inference(clausify,[status(thm)],[f_93_3]) ).

fof(f_94_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,insert203537868l_bool(A_2,A)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_40_finite_OinsertI]) ).

fof(f_94_2,plain,
    ! [U_152,U_151] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,insert203537868l_bool(U_152,U_151)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_151)) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

fof(f_94_3,plain,
    ! [U_151,U_152] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,insert203537868l_bool(U_152,U_151)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_151)) ),
    inference(definitional_conversion,[status(esa)],[f_94_2]) ).

cnf(f_94_4,plain,
    ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,insert203537868l_bool(U_152,U_151)))
    | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_151)) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

fof(f_95_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(A_2,A)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_41_finite_OinsertI]) ).

fof(f_95_2,plain,
    ! [U_154,U_153] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(U_154,U_153)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_153)) ),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

fof(f_95_3,plain,
    ! [U_153,U_154] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(U_154,U_153)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_153)) ),
    inference(definitional_conversion,[status(esa)],[f_95_2]) ).

cnf(f_95_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(U_154,U_153)))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_153)) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

fof(f_96_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_2,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_42_finite_OinsertI]) ).

fof(f_96_2,plain,
    ! [U_156,U_155] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_156,U_155)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_155)) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ! [U_155,U_156] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_156,U_155)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_155)) ),
    inference(definitional_conversion,[status(esa)],[f_96_2]) ).

cnf(f_96_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_156,U_155)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_155)) ),
    inference(clausify,[status(thm)],[f_96_3]) ).

fof(f_97_1,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    inference(fof_nnf,[status(thm)],[fact_43_finite_OemptyI]) ).

fof(f_97_2,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    inference(definitional_conversion,[status(esa)],[f_97_1]) ).

cnf(f_97_3,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    inference(clausify,[status(thm)],[f_97_2]) ).

fof(f_98_1,plain,
    hBOOL(hAPP_f971112728l_bool(finite364844667_state,bot_bo620288102e_bool)),
    inference(fof_nnf,[status(thm)],[fact_44_finite_OemptyI]) ).

fof(f_98_2,plain,
    hBOOL(hAPP_f971112728l_bool(finite364844667_state,bot_bo620288102e_bool)),
    inference(definitional_conversion,[status(esa)],[f_98_1]) ).

cnf(f_98_3,plain,
    hBOOL(hAPP_f971112728l_bool(finite364844667_state,bot_bo620288102e_bool)),
    inference(clausify,[status(thm)],[f_98_2]) ).

fof(f_99_1,plain,
    hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,bot_bo1537088220l_bool)),
    inference(fof_nnf,[status(thm)],[fact_45_finite_OemptyI]) ).

fof(f_99_2,plain,
    hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,bot_bo1537088220l_bool)),
    inference(definitional_conversion,[status(esa)],[f_99_1]) ).

cnf(f_99_3,plain,
    hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,bot_bo1537088220l_bool)),
    inference(clausify,[status(thm)],[f_99_2]) ).

fof(f_100_1,plain,
    hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,bot_bo1761158942l_bool)),
    inference(fof_nnf,[status(thm)],[fact_46_finite_OemptyI]) ).

fof(f_100_2,plain,
    hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,bot_bo1761158942l_bool)),
    inference(definitional_conversion,[status(esa)],[f_100_1]) ).

cnf(f_100_3,plain,
    hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,bot_bo1761158942l_bool)),
    inference(clausify,[status(thm)],[f_100_2]) ).

fof(f_101_1,plain,
    hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,bot_bo535777328l_bool)),
    inference(fof_nnf,[status(thm)],[fact_47_finite_OemptyI]) ).

fof(f_101_2,plain,
    hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,bot_bo535777328l_bool)),
    inference(definitional_conversion,[status(esa)],[f_101_1]) ).

cnf(f_101_3,plain,
    hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,bot_bo535777328l_bool)),
    inference(clausify,[status(thm)],[f_101_2]) ).

fof(f_102_1,plain,
    hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)),
    inference(fof_nnf,[status(thm)],[fact_48_finite_OemptyI]) ).

fof(f_102_2,plain,
    hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)),
    inference(definitional_conversion,[status(esa)],[f_102_1]) ).

cnf(f_102_3,plain,
    hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)),
    inference(clausify,[status(thm)],[f_102_2]) ).

fof(f_103_1,plain,
    ! [Q_1,P_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,P_1),Q_1))))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
        & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(P_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_49_finite__Collect__conjI]) ).

fof(f_103_2,plain,
    ! [U_158,U_157] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,U_157),U_158))))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_158)))
        & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_157))) ) ),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

fof(f_103_3,plain,
    ( ! [U_157,U_158] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_158)))
        | ~ sP1(U_157,U_158) )
    & ! [U_157,U_158] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_157)))
        | ~ sP1(U_157,U_158) )
    & ! [U_157,U_158] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,U_157),U_158))))
        | sP1(U_157,U_158) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_103_2]) ).

cnf(f_103_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,U_157),U_158))))
    | sP1(U_157,U_158) ),
    inference(clausify,[status(thm)],[f_103_3]) ).

cnf(f_103_5,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_157)))
    | ~ sP1(U_157,U_158) ),
    inference(clausify,[status(thm)],[f_103_3]) ).

cnf(f_103_6,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_158)))
    | ~ sP1(U_157,U_158) ),
    inference(clausify,[status(thm)],[f_103_3]) ).

fof(f_104_1,plain,
    ! [Q_1,P_1] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,P_1),Q_1))))
      | ( ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(Q_1)))
        & ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(P_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_50_finite__Collect__conjI]) ).

fof(f_104_2,plain,
    ! [U_160,U_159] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,U_159),U_160))))
      | ( ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_160)))
        & ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_159))) ) ),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

fof(f_104_3,plain,
    ( ! [U_159,U_160] :
        ( ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_160)))
        | ~ sP2(U_159,U_160) )
    & ! [U_159,U_160] :
        ( ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_159)))
        | ~ sP2(U_159,U_160) )
    & ! [U_159,U_160] :
        ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,U_159),U_160))))
        | sP2(U_159,U_160) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_104_2]) ).

cnf(f_104_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,U_159),U_160))))
    | sP2(U_159,U_160) ),
    inference(clausify,[status(thm)],[f_104_3]) ).

cnf(f_104_5,plain,
    ( ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_159)))
    | ~ sP2(U_159,U_160) ),
    inference(clausify,[status(thm)],[f_104_3]) ).

cnf(f_104_6,plain,
    ( ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_160)))
    | ~ sP2(U_159,U_160) ),
    inference(clausify,[status(thm)],[f_104_3]) ).

fof(f_105_1,plain,
    ! [Q_1,P_1] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(cOMBS_811933079l_bool(cOMBB_689948150l_bool(fconj,P_1),Q_1))))
      | ( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(Q_1)))
        & ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(P_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_51_finite__Collect__conjI]) ).

fof(f_105_2,plain,
    ! [U_162,U_161] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(cOMBS_811933079l_bool(cOMBB_689948150l_bool(fconj,U_161),U_162))))
      | ( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(U_162)))
        & ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(U_161))) ) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

fof(f_105_3,plain,
    ( ! [U_161,U_162] :
        ( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(U_162)))
        | ~ sP3(U_161,U_162) )
    & ! [U_161,U_162] :
        ( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(U_161)))
        | ~ sP3(U_161,U_162) )
    & ! [U_161,U_162] :
        ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(cOMBS_811933079l_bool(cOMBB_689948150l_bool(fconj,U_161),U_162))))
        | sP3(U_161,U_162) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_105_2]) ).

cnf(f_105_4,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(cOMBS_811933079l_bool(cOMBB_689948150l_bool(fconj,U_161),U_162))))
    | sP3(U_161,U_162) ),
    inference(clausify,[status(thm)],[f_105_3]) ).

cnf(f_105_5,plain,
    ( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(U_161)))
    | ~ sP3(U_161,U_162) ),
    inference(clausify,[status(thm)],[f_105_3]) ).

cnf(f_105_6,plain,
    ( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(U_162)))
    | ~ sP3(U_161,U_162) ),
    inference(clausify,[status(thm)],[f_105_3]) ).

fof(f_106_1,plain,
    ! [Q_1,P_1] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(cOMBS_1358309691l_bool(cOMBB_404111180l_bool(fconj,P_1),Q_1))))
      | ( ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(Q_1)))
        & ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(P_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_52_finite__Collect__conjI]) ).

fof(f_106_2,plain,
    ! [U_164,U_163] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(cOMBS_1358309691l_bool(cOMBB_404111180l_bool(fconj,U_163),U_164))))
      | ( ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(U_164)))
        & ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(U_163))) ) ),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

fof(f_106_3,plain,
    ( ! [U_163,U_164] :
        ( ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(U_164)))
        | ~ sP4(U_163,U_164) )
    & ! [U_163,U_164] :
        ( ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(U_163)))
        | ~ sP4(U_163,U_164) )
    & ! [U_163,U_164] :
        ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(cOMBS_1358309691l_bool(cOMBB_404111180l_bool(fconj,U_163),U_164))))
        | sP4(U_163,U_164) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_106_2]) ).

cnf(f_106_4,plain,
    ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(cOMBS_1358309691l_bool(cOMBB_404111180l_bool(fconj,U_163),U_164))))
    | sP4(U_163,U_164) ),
    inference(clausify,[status(thm)],[f_106_3]) ).

cnf(f_106_5,plain,
    ( ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(U_163)))
    | ~ sP4(U_163,U_164) ),
    inference(clausify,[status(thm)],[f_106_3]) ).

cnf(f_106_6,plain,
    ( ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,collec488126193l_bool(U_164)))
    | ~ sP4(U_163,U_164) ),
    inference(clausify,[status(thm)],[f_106_3]) ).

fof(f_107_1,plain,
    ! [Q_1,P_1] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,P_1),Q_1))))
      | ( ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(Q_1)))
        & ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(P_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_53_finite__Collect__conjI]) ).

fof(f_107_2,plain,
    ! [U_166,U_165] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,U_165),U_166))))
      | ( ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_166)))
        & ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_165))) ) ),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

fof(f_107_3,plain,
    ( ! [U_165,U_166] :
        ( ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_166)))
        | ~ sP5(U_165,U_166) )
    & ! [U_165,U_166] :
        ( ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_165)))
        | ~ sP5(U_165,U_166) )
    & ! [U_165,U_166] :
        ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,U_165),U_166))))
        | sP5(U_165,U_166) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_107_2]) ).

cnf(f_107_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,U_165),U_166))))
    | sP5(U_165,U_166) ),
    inference(clausify,[status(thm)],[f_107_3]) ).

cnf(f_107_5,plain,
    ( ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_165)))
    | ~ sP5(U_165,U_166) ),
    inference(clausify,[status(thm)],[f_107_3]) ).

cnf(f_107_6,plain,
    ( ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_166)))
    | ~ sP5(U_165,U_166) ),
    inference(clausify,[status(thm)],[f_107_3]) ).

fof(f_108_1,plain,
    ! [Q_1,P_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,P_1),Q_1))))
      | ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
        & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(P_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_54_finite__Collect__conjI]) ).

fof(f_108_2,plain,
    ! [U_168,U_167] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,U_167),U_168))))
      | ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_168)))
        & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_167))) ) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

fof(f_108_3,plain,
    ( ! [U_167,U_168] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_168)))
        | ~ sP6(U_167,U_168) )
    & ! [U_167,U_168] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_167)))
        | ~ sP6(U_167,U_168) )
    & ! [U_167,U_168] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,U_167),U_168))))
        | sP6(U_167,U_168) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_108_2]) ).

cnf(f_108_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,U_167),U_168))))
    | sP6(U_167,U_168) ),
    inference(clausify,[status(thm)],[f_108_3]) ).

cnf(f_108_5,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_167)))
    | ~ sP6(U_167,U_168) ),
    inference(clausify,[status(thm)],[f_108_3]) ).

cnf(f_108_6,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_168)))
    | ~ sP6(U_167,U_168) ),
    inference(clausify,[status(thm)],[f_108_3]) ).

fof(f_109_1,plain,
    ! [C_1,A] :
      ( ( ( image_2003357581_state(cOMBK_367030522_pname(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool)
          | A = bot_bo844097828e_bool )
        & ( image_2003357581_state(cOMBK_367030522_pname(C_1),A) = bot_bo620288102e_bool
          | A != bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_55_image__constant__conv]) ).

fof(f_109_2,plain,
    ! [U_170,U_169] :
      ( ( ( image_2003357581_state(cOMBK_367030522_pname(U_170),U_169) = insert1415133716_state(U_170,bot_bo620288102e_bool)
          | U_169 = bot_bo844097828e_bool )
        & ( image_2003357581_state(cOMBK_367030522_pname(U_170),U_169) = bot_bo620288102e_bool
          | U_169 != bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(U_169) ),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

fof(f_109_3,plain,
    ( ! [U_170,U_169] :
        ( image_2003357581_state(cOMBK_367030522_pname(U_170),U_169) = insert1415133716_state(U_170,bot_bo620288102e_bool)
        | U_169 = bot_bo844097828e_bool
        | ~ sP7(U_170,U_169) )
    & ! [U_170,U_169] :
        ( image_2003357581_state(cOMBK_367030522_pname(U_170),U_169) = bot_bo620288102e_bool
        | U_169 != bot_bo844097828e_bool
        | ~ sP7(U_170,U_169) )
    & ! [U_170,U_169] :
        ( sP7(U_170,U_169)
        | ~ is_fun_pname_bool(U_169) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_109_2]) ).

cnf(f_109_4,plain,
    ( sP7(U_170,U_169)
    | ~ is_fun_pname_bool(U_169) ),
    inference(clausify,[status(thm)],[f_109_3]) ).

cnf(f_109_5,plain,
    ( image_2003357581_state(cOMBK_367030522_pname(U_170),U_169) = bot_bo620288102e_bool
    | U_169 != bot_bo844097828e_bool
    | ~ sP7(U_170,U_169) ),
    inference(clausify,[status(thm)],[f_109_3]) ).

cnf(f_109_6,plain,
    ( image_2003357581_state(cOMBK_367030522_pname(U_170),U_169) = insert1415133716_state(U_170,bot_bo620288102e_bool)
    | U_169 = bot_bo844097828e_bool
    | ~ sP7(U_170,U_169) ),
    inference(clausify,[status(thm)],[f_109_3]) ).

fof(f_110_1,plain,
    ! [C_1,A] :
      ( ( image_54689091_pname(cOMBK_168215364_state(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool)
        | A = bot_bo620288102e_bool )
      & ( image_54689091_pname(cOMBK_168215364_state(C_1),A) = bot_bo844097828e_bool
        | A != bot_bo620288102e_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_56_image__constant__conv]) ).

fof(f_110_2,plain,
    ! [U_172,U_171] :
      ( ( image_54689091_pname(cOMBK_168215364_state(U_172),U_171) = insert_pname(U_172,bot_bo844097828e_bool)
        | U_171 = bot_bo620288102e_bool )
      & ( image_54689091_pname(cOMBK_168215364_state(U_172),U_171) = bot_bo844097828e_bool
        | U_171 != bot_bo620288102e_bool ) ),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

fof(f_110_3,plain,
    ( ! [U_176,U_174] :
        ( image_54689091_pname(cOMBK_168215364_state(U_176),U_174) = insert_pname(U_176,bot_bo844097828e_bool)
        | U_174 = bot_bo620288102e_bool )
    & ! [U_175,U_173] :
        ( image_54689091_pname(cOMBK_168215364_state(U_175),U_173) = bot_bo844097828e_bool
        | U_173 != bot_bo620288102e_bool ) ),
    inference(miniscope,[status(thm)],[f_110_2]) ).

fof(f_110_4,plain,
    ( ! [U_174,U_176] :
        ( image_54689091_pname(cOMBK_168215364_state(U_176),U_174) = insert_pname(U_176,bot_bo844097828e_bool)
        | U_174 = bot_bo620288102e_bool )
    & ! [U_175,U_173] :
        ( image_54689091_pname(cOMBK_168215364_state(U_175),U_173) = bot_bo844097828e_bool
        | U_173 != bot_bo620288102e_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_110_3]) ).

cnf(f_110_5,plain,
    ( image_54689091_pname(cOMBK_168215364_state(U_175),U_173) = bot_bo844097828e_bool
    | U_173 != bot_bo620288102e_bool ),
    inference(clausify,[status(thm)],[f_110_4]) ).

cnf(f_110_6,plain,
    ( image_54689091_pname(cOMBK_168215364_state(U_176),U_174) = insert_pname(U_176,bot_bo844097828e_bool)
    | U_174 = bot_bo620288102e_bool ),
    inference(clausify,[status(thm)],[f_110_4]) ).

fof(f_111_1,plain,
    ! [C_1,A] :
      ( ( image_2131964411e_bool(cOMBK_2035509764_state(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool)
        | A = bot_bo620288102e_bool )
      & ( image_2131964411e_bool(cOMBK_2035509764_state(C_1),A) = bot_bo1649642514l_bool
        | A != bot_bo620288102e_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_57_image__constant__conv]) ).

fof(f_111_2,plain,
    ! [U_178,U_177] :
      ( ( image_2131964411e_bool(cOMBK_2035509764_state(U_178),U_177) = insert1325755072e_bool(U_178,bot_bo1649642514l_bool)
        | U_177 = bot_bo620288102e_bool )
      & ( image_2131964411e_bool(cOMBK_2035509764_state(U_178),U_177) = bot_bo1649642514l_bool
        | U_177 != bot_bo620288102e_bool ) ),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

fof(f_111_3,plain,
    ( ! [U_182,U_180] :
        ( image_2131964411e_bool(cOMBK_2035509764_state(U_182),U_180) = insert1325755072e_bool(U_182,bot_bo1649642514l_bool)
        | U_180 = bot_bo620288102e_bool )
    & ! [U_181,U_179] :
        ( image_2131964411e_bool(cOMBK_2035509764_state(U_181),U_179) = bot_bo1649642514l_bool
        | U_179 != bot_bo620288102e_bool ) ),
    inference(miniscope,[status(thm)],[f_111_2]) ).

fof(f_111_4,plain,
    ( ! [U_180,U_182] :
        ( image_2131964411e_bool(cOMBK_2035509764_state(U_182),U_180) = insert1325755072e_bool(U_182,bot_bo1649642514l_bool)
        | U_180 = bot_bo620288102e_bool )
    & ! [U_179,U_181] :
        ( image_2131964411e_bool(cOMBK_2035509764_state(U_181),U_179) = bot_bo1649642514l_bool
        | U_179 != bot_bo620288102e_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_111_3]) ).

cnf(f_111_5,plain,
    ( image_2131964411e_bool(cOMBK_2035509764_state(U_181),U_179) = bot_bo1649642514l_bool
    | U_179 != bot_bo620288102e_bool ),
    inference(clausify,[status(thm)],[f_111_4]) ).

cnf(f_111_6,plain,
    ( image_2131964411e_bool(cOMBK_2035509764_state(U_182),U_180) = insert1325755072e_bool(U_182,bot_bo1649642514l_bool)
    | U_180 = bot_bo620288102e_bool ),
    inference(clausify,[status(thm)],[f_111_4]) ).

fof(f_112_1,plain,
    ! [C_1,A] :
      ( ( image_1828608335e_bool(cOMBK_1039769424_state(C_1),A) = insert1556680138e_bool(C_1,bot_bo535777328l_bool)
        | A = bot_bo620288102e_bool )
      & ( image_1828608335e_bool(cOMBK_1039769424_state(C_1),A) = bot_bo535777328l_bool
        | A != bot_bo620288102e_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_58_image__constant__conv]) ).

fof(f_112_2,plain,
    ! [U_184,U_183] :
      ( ( image_1828608335e_bool(cOMBK_1039769424_state(U_184),U_183) = insert1556680138e_bool(U_184,bot_bo535777328l_bool)
        | U_183 = bot_bo620288102e_bool )
      & ( image_1828608335e_bool(cOMBK_1039769424_state(U_184),U_183) = bot_bo535777328l_bool
        | U_183 != bot_bo620288102e_bool ) ),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

fof(f_112_3,plain,
    ( ! [U_188,U_186] :
        ( image_1828608335e_bool(cOMBK_1039769424_state(U_188),U_186) = insert1556680138e_bool(U_188,bot_bo535777328l_bool)
        | U_186 = bot_bo620288102e_bool )
    & ! [U_187,U_185] :
        ( image_1828608335e_bool(cOMBK_1039769424_state(U_187),U_185) = bot_bo535777328l_bool
        | U_185 != bot_bo620288102e_bool ) ),
    inference(miniscope,[status(thm)],[f_112_2]) ).

fof(f_112_4,plain,
    ( ! [U_186,U_188] :
        ( image_1828608335e_bool(cOMBK_1039769424_state(U_188),U_186) = insert1556680138e_bool(U_188,bot_bo535777328l_bool)
        | U_186 = bot_bo620288102e_bool )
    & ! [U_187,U_185] :
        ( image_1828608335e_bool(cOMBK_1039769424_state(U_187),U_185) = bot_bo535777328l_bool
        | U_185 != bot_bo620288102e_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_112_3]) ).

cnf(f_112_5,plain,
    ( image_1828608335e_bool(cOMBK_1039769424_state(U_187),U_185) = bot_bo535777328l_bool
    | U_185 != bot_bo620288102e_bool ),
    inference(clausify,[status(thm)],[f_112_4]) ).

cnf(f_112_6,plain,
    ( image_1828608335e_bool(cOMBK_1039769424_state(U_188),U_186) = insert1556680138e_bool(U_188,bot_bo535777328l_bool)
    | U_186 = bot_bo620288102e_bool ),
    inference(clausify,[status(thm)],[f_112_4]) ).

fof(f_113_1,plain,
    ! [C_1,A] :
      ( ( ( image_47868345e_bool(cOMBK_37193422_pname(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool)
          | A = bot_bo844097828e_bool )
        & ( image_47868345e_bool(cOMBK_37193422_pname(C_1),A) = bot_bo1649642514l_bool
          | A != bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_59_image__constant__conv]) ).

fof(f_113_2,plain,
    ! [U_190,U_189] :
      ( ( ( image_47868345e_bool(cOMBK_37193422_pname(U_190),U_189) = insert1325755072e_bool(U_190,bot_bo1649642514l_bool)
          | U_189 = bot_bo844097828e_bool )
        & ( image_47868345e_bool(cOMBK_37193422_pname(U_190),U_189) = bot_bo1649642514l_bool
          | U_189 != bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(U_189) ),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

fof(f_113_3,plain,
    ( ! [U_190,U_189] :
        ( image_47868345e_bool(cOMBK_37193422_pname(U_190),U_189) = insert1325755072e_bool(U_190,bot_bo1649642514l_bool)
        | U_189 = bot_bo844097828e_bool
        | ~ sP8(U_190,U_189) )
    & ! [U_190,U_189] :
        ( image_47868345e_bool(cOMBK_37193422_pname(U_190),U_189) = bot_bo1649642514l_bool
        | U_189 != bot_bo844097828e_bool
        | ~ sP8(U_190,U_189) )
    & ! [U_190,U_189] :
        ( sP8(U_190,U_189)
        | ~ is_fun_pname_bool(U_189) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_113_2]) ).

cnf(f_113_4,plain,
    ( sP8(U_190,U_189)
    | ~ is_fun_pname_bool(U_189) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

cnf(f_113_5,plain,
    ( image_47868345e_bool(cOMBK_37193422_pname(U_190),U_189) = bot_bo1649642514l_bool
    | U_189 != bot_bo844097828e_bool
    | ~ sP8(U_190,U_189) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

cnf(f_113_6,plain,
    ( image_47868345e_bool(cOMBK_37193422_pname(U_190),U_189) = insert1325755072e_bool(U_190,bot_bo1649642514l_bool)
    | U_189 = bot_bo844097828e_bool
    | ~ sP8(U_190,U_189) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

fof(f_114_1,plain,
    ! [C_1,A] :
      ( ( ( image_70449425e_bool(cOMBK_1706929794_pname(C_1),A) = insert1556680138e_bool(C_1,bot_bo535777328l_bool)
          | A = bot_bo844097828e_bool )
        & ( image_70449425e_bool(cOMBK_1706929794_pname(C_1),A) = bot_bo535777328l_bool
          | A != bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_60_image__constant__conv]) ).

fof(f_114_2,plain,
    ! [U_192,U_191] :
      ( ( ( image_70449425e_bool(cOMBK_1706929794_pname(U_192),U_191) = insert1556680138e_bool(U_192,bot_bo535777328l_bool)
          | U_191 = bot_bo844097828e_bool )
        & ( image_70449425e_bool(cOMBK_1706929794_pname(U_192),U_191) = bot_bo535777328l_bool
          | U_191 != bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(U_191) ),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

fof(f_114_3,plain,
    ( ! [U_192,U_191] :
        ( image_70449425e_bool(cOMBK_1706929794_pname(U_192),U_191) = insert1556680138e_bool(U_192,bot_bo535777328l_bool)
        | U_191 = bot_bo844097828e_bool
        | ~ sP9(U_192,U_191) )
    & ! [U_192,U_191] :
        ( image_70449425e_bool(cOMBK_1706929794_pname(U_192),U_191) = bot_bo535777328l_bool
        | U_191 != bot_bo844097828e_bool
        | ~ sP9(U_192,U_191) )
    & ! [U_192,U_191] :
        ( sP9(U_192,U_191)
        | ~ is_fun_pname_bool(U_191) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_114_2]) ).

cnf(f_114_4,plain,
    ( sP9(U_192,U_191)
    | ~ is_fun_pname_bool(U_191) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

cnf(f_114_5,plain,
    ( image_70449425e_bool(cOMBK_1706929794_pname(U_192),U_191) = bot_bo535777328l_bool
    | U_191 != bot_bo844097828e_bool
    | ~ sP9(U_192,U_191) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

cnf(f_114_6,plain,
    ( image_70449425e_bool(cOMBK_1706929794_pname(U_192),U_191) = insert1556680138e_bool(U_192,bot_bo535777328l_bool)
    | U_191 = bot_bo844097828e_bool
    | ~ sP9(U_192,U_191) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

fof(f_115_1,plain,
    ! [C_1,A] :
      ( ( ( image_pname_pname(cOMBK_pname_pname(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool)
          | A = bot_bo844097828e_bool )
        & ( image_pname_pname(cOMBK_pname_pname(C_1),A) = bot_bo844097828e_bool
          | A != bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_61_image__constant__conv]) ).

fof(f_115_2,plain,
    ! [U_194,U_193] :
      ( ( ( image_pname_pname(cOMBK_pname_pname(U_194),U_193) = insert_pname(U_194,bot_bo844097828e_bool)
          | U_193 = bot_bo844097828e_bool )
        & ( image_pname_pname(cOMBK_pname_pname(U_194),U_193) = bot_bo844097828e_bool
          | U_193 != bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(U_193) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

fof(f_115_3,plain,
    ( ! [U_194,U_193] :
        ( image_pname_pname(cOMBK_pname_pname(U_194),U_193) = insert_pname(U_194,bot_bo844097828e_bool)
        | U_193 = bot_bo844097828e_bool
        | ~ sP10(U_194,U_193) )
    & ! [U_194,U_193] :
        ( image_pname_pname(cOMBK_pname_pname(U_194),U_193) = bot_bo844097828e_bool
        | U_193 != bot_bo844097828e_bool
        | ~ sP10(U_194,U_193) )
    & ! [U_194,U_193] :
        ( sP10(U_194,U_193)
        | ~ is_fun_pname_bool(U_193) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_115_2]) ).

cnf(f_115_4,plain,
    ( sP10(U_194,U_193)
    | ~ is_fun_pname_bool(U_193) ),
    inference(clausify,[status(thm)],[f_115_3]) ).

cnf(f_115_5,plain,
    ( image_pname_pname(cOMBK_pname_pname(U_194),U_193) = bot_bo844097828e_bool
    | U_193 != bot_bo844097828e_bool
    | ~ sP10(U_194,U_193) ),
    inference(clausify,[status(thm)],[f_115_3]) ).

cnf(f_115_6,plain,
    ( image_pname_pname(cOMBK_pname_pname(U_194),U_193) = insert_pname(U_194,bot_bo844097828e_bool)
    | U_193 = bot_bo844097828e_bool
    | ~ sP10(U_194,U_193) ),
    inference(clausify,[status(thm)],[f_115_3]) ).

fof(f_116_1,plain,
    ! [C_1,A] :
      ( ( ( image_516545147_state(cOMBK_1503445380e_bool(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool)
          | A = bot_bo1649642514l_bool )
        & ( image_516545147_state(cOMBK_1503445380e_bool(C_1),A) = bot_bo620288102e_bool
          | A != bot_bo1649642514l_bool ) )
      | ~ is_fun1661590463l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_62_image__constant__conv]) ).

fof(f_116_2,plain,
    ! [U_196,U_195] :
      ( ( ( image_516545147_state(cOMBK_1503445380e_bool(U_196),U_195) = insert1415133716_state(U_196,bot_bo620288102e_bool)
          | U_195 = bot_bo1649642514l_bool )
        & ( image_516545147_state(cOMBK_1503445380e_bool(U_196),U_195) = bot_bo620288102e_bool
          | U_195 != bot_bo1649642514l_bool ) )
      | ~ is_fun1661590463l_bool(U_195) ),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

fof(f_116_3,plain,
    ( ! [U_195,U_196] :
        ( image_516545147_state(cOMBK_1503445380e_bool(U_196),U_195) = insert1415133716_state(U_196,bot_bo620288102e_bool)
        | U_195 = bot_bo1649642514l_bool
        | ~ sP11(U_195,U_196) )
    & ! [U_195,U_196] :
        ( image_516545147_state(cOMBK_1503445380e_bool(U_196),U_195) = bot_bo620288102e_bool
        | U_195 != bot_bo1649642514l_bool
        | ~ sP11(U_195,U_196) )
    & ! [U_195,U_196] :
        ( sP11(U_195,U_196)
        | ~ is_fun1661590463l_bool(U_195) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_116_2]) ).

cnf(f_116_4,plain,
    ( sP11(U_195,U_196)
    | ~ is_fun1661590463l_bool(U_195) ),
    inference(clausify,[status(thm)],[f_116_3]) ).

cnf(f_116_5,plain,
    ( image_516545147_state(cOMBK_1503445380e_bool(U_196),U_195) = bot_bo620288102e_bool
    | U_195 != bot_bo1649642514l_bool
    | ~ sP11(U_195,U_196) ),
    inference(clausify,[status(thm)],[f_116_3]) ).

cnf(f_116_6,plain,
    ( image_516545147_state(cOMBK_1503445380e_bool(U_196),U_195) = insert1415133716_state(U_196,bot_bo620288102e_bool)
    | U_195 = bot_bo1649642514l_bool
    | ~ sP11(U_195,U_196) ),
    inference(clausify,[status(thm)],[f_116_3]) ).

fof(f_117_1,plain,
    ! [C_1,A] :
      ( ( image_18964633_state(cOMBK_701929478e_bool(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool)
        | A = bot_bo535777328l_bool )
      & ( image_18964633_state(cOMBK_701929478e_bool(C_1),A) = bot_bo620288102e_bool
        | A != bot_bo535777328l_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_63_image__constant__conv]) ).

fof(f_117_2,plain,
    ! [U_198,U_197] :
      ( ( image_18964633_state(cOMBK_701929478e_bool(U_198),U_197) = insert1415133716_state(U_198,bot_bo620288102e_bool)
        | U_197 = bot_bo535777328l_bool )
      & ( image_18964633_state(cOMBK_701929478e_bool(U_198),U_197) = bot_bo620288102e_bool
        | U_197 != bot_bo535777328l_bool ) ),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

fof(f_117_3,plain,
    ( ! [U_202,U_200] :
        ( image_18964633_state(cOMBK_701929478e_bool(U_202),U_200) = insert1415133716_state(U_202,bot_bo620288102e_bool)
        | U_200 = bot_bo535777328l_bool )
    & ! [U_201,U_199] :
        ( image_18964633_state(cOMBK_701929478e_bool(U_201),U_199) = bot_bo620288102e_bool
        | U_199 != bot_bo535777328l_bool ) ),
    inference(miniscope,[status(thm)],[f_117_2]) ).

fof(f_117_4,plain,
    ( ! [U_200,U_202] :
        ( image_18964633_state(cOMBK_701929478e_bool(U_202),U_200) = insert1415133716_state(U_202,bot_bo620288102e_bool)
        | U_200 = bot_bo535777328l_bool )
    & ! [U_199,U_201] :
        ( image_18964633_state(cOMBK_701929478e_bool(U_201),U_199) = bot_bo620288102e_bool
        | U_199 != bot_bo535777328l_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_117_3]) ).

cnf(f_117_5,plain,
    ( image_18964633_state(cOMBK_701929478e_bool(U_201),U_199) = bot_bo620288102e_bool
    | U_199 != bot_bo535777328l_bool ),
    inference(clausify,[status(thm)],[f_117_4]) ).

cnf(f_117_6,plain,
    ( image_18964633_state(cOMBK_701929478e_bool(U_202),U_200) = insert1415133716_state(U_202,bot_bo620288102e_bool)
    | U_200 = bot_bo535777328l_bool ),
    inference(clausify,[status(thm)],[f_117_4]) ).

fof(f_118_1,plain,
    ! [C_1,A] :
      ( ( ( image_1283814551_pname(cOMBK_948730864e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool)
          | A = bot_bo1649642514l_bool )
        & ( image_1283814551_pname(cOMBK_948730864e_bool(C_1),A) = bot_bo844097828e_bool
          | A != bot_bo1649642514l_bool ) )
      | ~ is_fun1661590463l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_64_image__constant__conv]) ).

fof(f_118_2,plain,
    ! [U_204,U_203] :
      ( ( ( image_1283814551_pname(cOMBK_948730864e_bool(U_204),U_203) = insert_pname(U_204,bot_bo844097828e_bool)
          | U_203 = bot_bo1649642514l_bool )
        & ( image_1283814551_pname(cOMBK_948730864e_bool(U_204),U_203) = bot_bo844097828e_bool
          | U_203 != bot_bo1649642514l_bool ) )
      | ~ is_fun1661590463l_bool(U_203) ),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

fof(f_118_3,plain,
    ( ! [U_203,U_204] :
        ( image_1283814551_pname(cOMBK_948730864e_bool(U_204),U_203) = insert_pname(U_204,bot_bo844097828e_bool)
        | U_203 = bot_bo1649642514l_bool
        | ~ sP12(U_203,U_204) )
    & ! [U_203,U_204] :
        ( image_1283814551_pname(cOMBK_948730864e_bool(U_204),U_203) = bot_bo844097828e_bool
        | U_203 != bot_bo1649642514l_bool
        | ~ sP12(U_203,U_204) )
    & ! [U_203,U_204] :
        ( sP12(U_203,U_204)
        | ~ is_fun1661590463l_bool(U_203) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_118_2]) ).

cnf(f_118_4,plain,
    ( sP12(U_203,U_204)
    | ~ is_fun1661590463l_bool(U_203) ),
    inference(clausify,[status(thm)],[f_118_3]) ).

cnf(f_118_5,plain,
    ( image_1283814551_pname(cOMBK_948730864e_bool(U_204),U_203) = bot_bo844097828e_bool
    | U_203 != bot_bo1649642514l_bool
    | ~ sP12(U_203,U_204) ),
    inference(clausify,[status(thm)],[f_118_3]) ).

cnf(f_118_6,plain,
    ( image_1283814551_pname(cOMBK_948730864e_bool(U_204),U_203) = insert_pname(U_204,bot_bo844097828e_bool)
    | U_203 = bot_bo1649642514l_bool
    | ~ sP12(U_203,U_204) ),
    inference(clausify,[status(thm)],[f_118_3]) ).

fof(f_119_1,plain,
    ! [C_1,A] :
      ( ( image_187965177_pname(cOMBK_1589414042e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool)
        | A = bot_bo535777328l_bool )
      & ( image_187965177_pname(cOMBK_1589414042e_bool(C_1),A) = bot_bo844097828e_bool
        | A != bot_bo535777328l_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_65_image__constant__conv]) ).

fof(f_119_2,plain,
    ! [U_206,U_205] :
      ( ( image_187965177_pname(cOMBK_1589414042e_bool(U_206),U_205) = insert_pname(U_206,bot_bo844097828e_bool)
        | U_205 = bot_bo535777328l_bool )
      & ( image_187965177_pname(cOMBK_1589414042e_bool(U_206),U_205) = bot_bo844097828e_bool
        | U_205 != bot_bo535777328l_bool ) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

fof(f_119_3,plain,
    ( ! [U_210,U_208] :
        ( image_187965177_pname(cOMBK_1589414042e_bool(U_210),U_208) = insert_pname(U_210,bot_bo844097828e_bool)
        | U_208 = bot_bo535777328l_bool )
    & ! [U_209,U_207] :
        ( image_187965177_pname(cOMBK_1589414042e_bool(U_209),U_207) = bot_bo844097828e_bool
        | U_207 != bot_bo535777328l_bool ) ),
    inference(miniscope,[status(thm)],[f_119_2]) ).

fof(f_119_4,plain,
    ( ! [U_208,U_210] :
        ( image_187965177_pname(cOMBK_1589414042e_bool(U_210),U_208) = insert_pname(U_210,bot_bo844097828e_bool)
        | U_208 = bot_bo535777328l_bool )
    & ! [U_207,U_209] :
        ( image_187965177_pname(cOMBK_1589414042e_bool(U_209),U_207) = bot_bo844097828e_bool
        | U_207 != bot_bo535777328l_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_119_3]) ).

cnf(f_119_5,plain,
    ( image_187965177_pname(cOMBK_1589414042e_bool(U_209),U_207) = bot_bo844097828e_bool
    | U_207 != bot_bo535777328l_bool ),
    inference(clausify,[status(thm)],[f_119_4]) ).

cnf(f_119_6,plain,
    ( image_187965177_pname(cOMBK_1589414042e_bool(U_210),U_208) = insert_pname(U_210,bot_bo844097828e_bool)
    | U_208 = bot_bo535777328l_bool ),
    inference(clausify,[status(thm)],[f_119_4]) ).

fof(f_120_1,plain,
    ! [C_1,X_2,A] :
      ( image_2003357581_state(cOMBK_367030522_pname(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_66_image__constant]) ).

fof(f_120_2,plain,
    ! [U_213,U_212,U_211] :
      ( image_2003357581_state(cOMBK_367030522_pname(U_213),U_211) = insert1415133716_state(U_213,bot_bo620288102e_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_212),U_211)) ),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

fof(f_120_3,plain,
    ! [U_212,U_211,U_213] :
      ( image_2003357581_state(cOMBK_367030522_pname(U_213),U_211) = insert1415133716_state(U_213,bot_bo620288102e_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_212),U_211)) ),
    inference(definitional_conversion,[status(esa)],[f_120_2]) ).

cnf(f_120_4,plain,
    ( image_2003357581_state(cOMBK_367030522_pname(U_213),U_211) = insert1415133716_state(U_213,bot_bo620288102e_bool)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_212),U_211)) ),
    inference(clausify,[status(thm)],[f_120_3]) ).

fof(f_121_1,plain,
    ! [C_1,X_2,A] :
      ( image_54689091_pname(cOMBK_168215364_state(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool)
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_67_image__constant]) ).

fof(f_121_2,plain,
    ! [U_216,U_215,U_214] :
      ( image_54689091_pname(cOMBK_168215364_state(U_216),U_214) = insert_pname(U_216,bot_bo844097828e_bool)
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_215),U_214)) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

fof(f_121_3,plain,
    ! [U_215,U_216,U_214] :
      ( image_54689091_pname(cOMBK_168215364_state(U_216),U_214) = insert_pname(U_216,bot_bo844097828e_bool)
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_215),U_214)) ),
    inference(definitional_conversion,[status(esa)],[f_121_2]) ).

cnf(f_121_4,plain,
    ( image_54689091_pname(cOMBK_168215364_state(U_216),U_214) = insert_pname(U_216,bot_bo844097828e_bool)
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_215),U_214)) ),
    inference(clausify,[status(thm)],[f_121_3]) ).

fof(f_122_1,plain,
    ! [C_1,X_2,A] :
      ( image_2131964411e_bool(cOMBK_2035509764_state(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool)
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_68_image__constant]) ).

fof(f_122_2,plain,
    ! [U_219,U_218,U_217] :
      ( image_2131964411e_bool(cOMBK_2035509764_state(U_219),U_217) = insert1325755072e_bool(U_219,bot_bo1649642514l_bool)
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_218),U_217)) ),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

fof(f_122_3,plain,
    ! [U_217,U_218,U_219] :
      ( image_2131964411e_bool(cOMBK_2035509764_state(U_219),U_217) = insert1325755072e_bool(U_219,bot_bo1649642514l_bool)
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_218),U_217)) ),
    inference(definitional_conversion,[status(esa)],[f_122_2]) ).

cnf(f_122_4,plain,
    ( image_2131964411e_bool(cOMBK_2035509764_state(U_219),U_217) = insert1325755072e_bool(U_219,bot_bo1649642514l_bool)
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_218),U_217)) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

fof(f_123_1,plain,
    ! [C_1,X_2,A] :
      ( image_1828608335e_bool(cOMBK_1039769424_state(C_1),A) = insert1556680138e_bool(C_1,bot_bo535777328l_bool)
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_69_image__constant]) ).

fof(f_123_2,plain,
    ! [U_222,U_221,U_220] :
      ( image_1828608335e_bool(cOMBK_1039769424_state(U_222),U_220) = insert1556680138e_bool(U_222,bot_bo535777328l_bool)
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_221),U_220)) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

fof(f_123_3,plain,
    ! [U_220,U_221,U_222] :
      ( image_1828608335e_bool(cOMBK_1039769424_state(U_222),U_220) = insert1556680138e_bool(U_222,bot_bo535777328l_bool)
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_221),U_220)) ),
    inference(definitional_conversion,[status(esa)],[f_123_2]) ).

cnf(f_123_4,plain,
    ( image_1828608335e_bool(cOMBK_1039769424_state(U_222),U_220) = insert1556680138e_bool(U_222,bot_bo535777328l_bool)
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_221),U_220)) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

fof(f_124_1,plain,
    ! [C_1,X_2,A] :
      ( image_47868345e_bool(cOMBK_37193422_pname(C_1),A) = insert1325755072e_bool(C_1,bot_bo1649642514l_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_70_image__constant]) ).

fof(f_124_2,plain,
    ! [U_225,U_224,U_223] :
      ( image_47868345e_bool(cOMBK_37193422_pname(U_225),U_223) = insert1325755072e_bool(U_225,bot_bo1649642514l_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_224),U_223)) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ! [U_223,U_224,U_225] :
      ( image_47868345e_bool(cOMBK_37193422_pname(U_225),U_223) = insert1325755072e_bool(U_225,bot_bo1649642514l_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_224),U_223)) ),
    inference(definitional_conversion,[status(esa)],[f_124_2]) ).

cnf(f_124_4,plain,
    ( image_47868345e_bool(cOMBK_37193422_pname(U_225),U_223) = insert1325755072e_bool(U_225,bot_bo1649642514l_bool)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_224),U_223)) ),
    inference(clausify,[status(thm)],[f_124_3]) ).

fof(f_125_1,plain,
    ! [C_1,X_2,A] :
      ( image_70449425e_bool(cOMBK_1706929794_pname(C_1),A) = insert1556680138e_bool(C_1,bot_bo535777328l_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_71_image__constant]) ).

fof(f_125_2,plain,
    ! [U_228,U_227,U_226] :
      ( image_70449425e_bool(cOMBK_1706929794_pname(U_228),U_226) = insert1556680138e_bool(U_228,bot_bo535777328l_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_227),U_226)) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ! [U_226,U_227,U_228] :
      ( image_70449425e_bool(cOMBK_1706929794_pname(U_228),U_226) = insert1556680138e_bool(U_228,bot_bo535777328l_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_227),U_226)) ),
    inference(definitional_conversion,[status(esa)],[f_125_2]) ).

cnf(f_125_4,plain,
    ( image_70449425e_bool(cOMBK_1706929794_pname(U_228),U_226) = insert1556680138e_bool(U_228,bot_bo535777328l_bool)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_227),U_226)) ),
    inference(clausify,[status(thm)],[f_125_3]) ).

fof(f_126_1,plain,
    ! [C_1,X_2,A] :
      ( image_pname_pname(cOMBK_pname_pname(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_72_image__constant]) ).

fof(f_126_2,plain,
    ! [U_231,U_230,U_229] :
      ( image_pname_pname(cOMBK_pname_pname(U_231),U_229) = insert_pname(U_231,bot_bo844097828e_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_230),U_229)) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ! [U_229,U_230,U_231] :
      ( image_pname_pname(cOMBK_pname_pname(U_231),U_229) = insert_pname(U_231,bot_bo844097828e_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_230),U_229)) ),
    inference(definitional_conversion,[status(esa)],[f_126_2]) ).

cnf(f_126_4,plain,
    ( image_pname_pname(cOMBK_pname_pname(U_231),U_229) = insert_pname(U_231,bot_bo844097828e_bool)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_230),U_229)) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

fof(f_127_1,plain,
    ! [C_1,X_2,A] :
      ( image_516545147_state(cOMBK_1503445380e_bool(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool)
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_73_image__constant]) ).

fof(f_127_2,plain,
    ! [U_234,U_233,U_232] :
      ( image_516545147_state(cOMBK_1503445380e_bool(U_234),U_232) = insert1415133716_state(U_234,bot_bo620288102e_bool)
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_233),U_232)) ),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

fof(f_127_3,plain,
    ! [U_232,U_233,U_234] :
      ( image_516545147_state(cOMBK_1503445380e_bool(U_234),U_232) = insert1415133716_state(U_234,bot_bo620288102e_bool)
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_233),U_232)) ),
    inference(definitional_conversion,[status(esa)],[f_127_2]) ).

cnf(f_127_4,plain,
    ( image_516545147_state(cOMBK_1503445380e_bool(U_234),U_232) = insert1415133716_state(U_234,bot_bo620288102e_bool)
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_233),U_232)) ),
    inference(clausify,[status(thm)],[f_127_3]) ).

fof(f_128_1,plain,
    ! [C_1,X_2,A] :
      ( image_18964633_state(cOMBK_701929478e_bool(C_1),A) = insert1415133716_state(C_1,bot_bo620288102e_bool)
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_74_image__constant]) ).

fof(f_128_2,plain,
    ! [U_237,U_236,U_235] :
      ( image_18964633_state(cOMBK_701929478e_bool(U_237),U_235) = insert1415133716_state(U_237,bot_bo620288102e_bool)
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_236),U_235)) ),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

fof(f_128_3,plain,
    ! [U_235,U_236,U_237] :
      ( image_18964633_state(cOMBK_701929478e_bool(U_237),U_235) = insert1415133716_state(U_237,bot_bo620288102e_bool)
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_236),U_235)) ),
    inference(definitional_conversion,[status(esa)],[f_128_2]) ).

cnf(f_128_4,plain,
    ( image_18964633_state(cOMBK_701929478e_bool(U_237),U_235) = insert1415133716_state(U_237,bot_bo620288102e_bool)
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_236),U_235)) ),
    inference(clausify,[status(thm)],[f_128_3]) ).

fof(f_129_1,plain,
    ! [C_1,X_2,A] :
      ( image_1283814551_pname(cOMBK_948730864e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool)
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_75_image__constant]) ).

fof(f_129_2,plain,
    ! [U_240,U_239,U_238] :
      ( image_1283814551_pname(cOMBK_948730864e_bool(U_240),U_238) = insert_pname(U_240,bot_bo844097828e_bool)
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_239),U_238)) ),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

fof(f_129_3,plain,
    ! [U_238,U_239,U_240] :
      ( image_1283814551_pname(cOMBK_948730864e_bool(U_240),U_238) = insert_pname(U_240,bot_bo844097828e_bool)
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_239),U_238)) ),
    inference(definitional_conversion,[status(esa)],[f_129_2]) ).

cnf(f_129_4,plain,
    ( image_1283814551_pname(cOMBK_948730864e_bool(U_240),U_238) = insert_pname(U_240,bot_bo844097828e_bool)
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_239),U_238)) ),
    inference(clausify,[status(thm)],[f_129_3]) ).

fof(f_130_1,plain,
    ! [C_1,X_2,A] :
      ( image_187965177_pname(cOMBK_1589414042e_bool(C_1),A) = insert_pname(C_1,bot_bo844097828e_bool)
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_76_image__constant]) ).

fof(f_130_2,plain,
    ! [U_243,U_242,U_241] :
      ( image_187965177_pname(cOMBK_1589414042e_bool(U_243),U_241) = insert_pname(U_243,bot_bo844097828e_bool)
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_242),U_241)) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

fof(f_130_3,plain,
    ! [U_241,U_242,U_243] :
      ( image_187965177_pname(cOMBK_1589414042e_bool(U_243),U_241) = insert_pname(U_243,bot_bo844097828e_bool)
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_242),U_241)) ),
    inference(definitional_conversion,[status(esa)],[f_130_2]) ).

cnf(f_130_4,plain,
    ( image_187965177_pname(cOMBK_1589414042e_bool(U_243),U_241) = insert_pname(U_243,bot_bo844097828e_bool)
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_242),U_241)) ),
    inference(clausify,[status(thm)],[f_130_3]) ).

fof(f_131_1,plain,
    ! [F,X_2,Y_2] :
      ( insert_pname(X_2,dom_pname_com(F)) = dom_pname_com(F)
      | hAPP_p799580910on_com(F,X_2) != some_com(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_77_insert__dom]) ).

fof(f_131_2,plain,
    ! [U_246,U_245,U_244] :
      ( insert_pname(U_245,dom_pname_com(U_246)) = dom_pname_com(U_246)
      | hAPP_p799580910on_com(U_246,U_245) != some_com(U_244) ),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

fof(f_131_3,plain,
    ! [U_246,U_245] :
      ( ! [U_244] : hAPP_p799580910on_com(U_246,U_245) != some_com(U_244)
      | insert_pname(U_245,dom_pname_com(U_246)) = dom_pname_com(U_246) ),
    inference(miniscope,[status(thm)],[f_131_2]) ).

fof(f_131_4,plain,
    ! [U_244,U_245,U_246] :
      ( hAPP_p799580910on_com(U_246,U_245) != some_com(U_244)
      | insert_pname(U_245,dom_pname_com(U_246)) = dom_pname_com(U_246) ),
    inference(definitional_conversion,[status(esa)],[f_131_3]) ).

cnf(f_131_5,plain,
    ( hAPP_p799580910on_com(U_246,U_245) != some_com(U_244)
    | insert_pname(U_245,dom_pname_com(U_246)) = dom_pname_com(U_246) ),
    inference(clausify,[status(thm)],[f_131_4]) ).

fof(f_132_1,plain,
    ! [F,X_2,Y_2] :
      ( insert1325755072e_bool(X_2,dom_fu2081503504ol_com(F)) = dom_fu2081503504ol_com(F)
      | hAPP_f2138803836on_com(F,X_2) != some_com(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_78_insert__dom]) ).

fof(f_132_2,plain,
    ! [U_249,U_248,U_247] :
      ( insert1325755072e_bool(U_248,dom_fu2081503504ol_com(U_249)) = dom_fu2081503504ol_com(U_249)
      | hAPP_f2138803836on_com(U_249,U_248) != some_com(U_247) ),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

fof(f_132_3,plain,
    ! [U_249,U_248] :
      ( ! [U_247] : hAPP_f2138803836on_com(U_249,U_248) != some_com(U_247)
      | insert1325755072e_bool(U_248,dom_fu2081503504ol_com(U_249)) = dom_fu2081503504ol_com(U_249) ),
    inference(miniscope,[status(thm)],[f_132_2]) ).

fof(f_132_4,plain,
    ! [U_247,U_248,U_249] :
      ( hAPP_f2138803836on_com(U_249,U_248) != some_com(U_247)
      | insert1325755072e_bool(U_248,dom_fu2081503504ol_com(U_249)) = dom_fu2081503504ol_com(U_249) ),
    inference(definitional_conversion,[status(esa)],[f_132_3]) ).

cnf(f_132_5,plain,
    ( hAPP_f2138803836on_com(U_249,U_248) != some_com(U_247)
    | insert1325755072e_bool(U_248,dom_fu2081503504ol_com(U_249)) = dom_fu2081503504ol_com(U_249) ),
    inference(clausify,[status(thm)],[f_132_4]) ).

fof(f_133_1,plain,
    ! [F,X_2,Y_2] :
      ( insert1556680138e_bool(X_2,dom_fu1342267980ol_com(F)) = dom_fu1342267980ol_com(F)
      | hAPP_f2134636538on_com(F,X_2) != some_com(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_79_insert__dom]) ).

fof(f_133_2,plain,
    ! [U_252,U_251,U_250] :
      ( insert1556680138e_bool(U_251,dom_fu1342267980ol_com(U_252)) = dom_fu1342267980ol_com(U_252)
      | hAPP_f2134636538on_com(U_252,U_251) != some_com(U_250) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

fof(f_133_3,plain,
    ! [U_252,U_251] :
      ( ! [U_250] : hAPP_f2134636538on_com(U_252,U_251) != some_com(U_250)
      | insert1556680138e_bool(U_251,dom_fu1342267980ol_com(U_252)) = dom_fu1342267980ol_com(U_252) ),
    inference(miniscope,[status(thm)],[f_133_2]) ).

fof(f_133_4,plain,
    ! [U_250,U_251,U_252] :
      ( hAPP_f2134636538on_com(U_252,U_251) != some_com(U_250)
      | insert1556680138e_bool(U_251,dom_fu1342267980ol_com(U_252)) = dom_fu1342267980ol_com(U_252) ),
    inference(definitional_conversion,[status(esa)],[f_133_3]) ).

cnf(f_133_5,plain,
    ( hAPP_f2134636538on_com(U_252,U_251) != some_com(U_250)
    | insert1556680138e_bool(U_251,dom_fu1342267980ol_com(U_252)) = dom_fu1342267980ol_com(U_252) ),
    inference(clausify,[status(thm)],[f_133_4]) ).

fof(f_134_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_2003357581_state(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_80_finite__surj]) ).

fof(f_134_2,plain,
    ! [U_255,U_254,U_253] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_255))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_255),image_2003357581_state(U_254,U_253)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_253)) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

fof(f_134_3,plain,
    ! [U_253,U_254,U_255] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_255))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_255),image_2003357581_state(U_254,U_253)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_253)) ),
    inference(definitional_conversion,[status(esa)],[f_134_2]) ).

cnf(f_134_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_255))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_255),image_2003357581_state(U_254,U_253)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_253)) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

fof(f_135_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1705983821_pname(F,A)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_81_finite__surj]) ).

fof(f_135_2,plain,
    ! [U_258,U_257,U_256] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_258))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_258),image_1705983821_pname(U_257,U_256)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_256)) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

fof(f_135_3,plain,
    ! [U_257,U_256,U_258] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_258))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_258),image_1705983821_pname(U_257,U_256)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_256)) ),
    inference(definitional_conversion,[status(esa)],[f_135_2]) ).

cnf(f_135_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_258))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_258),image_1705983821_pname(U_257,U_256)))
    | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_256)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

fof(f_136_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1619336331_pname(F,A)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_82_finite__surj]) ).

fof(f_136_2,plain,
    ! [U_261,U_260,U_259] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_261))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_261),image_1619336331_pname(U_260,U_259)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_259)) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

fof(f_136_3,plain,
    ! [U_259,U_260,U_261] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_261))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_261),image_1619336331_pname(U_260,U_259)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_259)) ),
    inference(definitional_conversion,[status(esa)],[f_136_2]) ).

cnf(f_136_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_261))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_261),image_1619336331_pname(U_260,U_259)))
    | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_259)) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

fof(f_137_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_187965177_pname(F,A)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_83_finite__surj]) ).

fof(f_137_2,plain,
    ! [U_264,U_263,U_262] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_264))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_264),image_187965177_pname(U_263,U_262)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_262)) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

fof(f_137_3,plain,
    ! [U_262,U_263,U_264] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_264))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_264),image_187965177_pname(U_263,U_262)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_262)) ),
    inference(definitional_conversion,[status(esa)],[f_137_2]) ).

cnf(f_137_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_264))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_264),image_187965177_pname(U_263,U_262)))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_262)) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

fof(f_138_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1283814551_pname(F,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_84_finite__surj]) ).

fof(f_138_2,plain,
    ! [U_267,U_266,U_265] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_267))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_267),image_1283814551_pname(U_266,U_265)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_265)) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

fof(f_138_3,plain,
    ! [U_265,U_266,U_267] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_267))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_267),image_1283814551_pname(U_266,U_265)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_265)) ),
    inference(definitional_conversion,[status(esa)],[f_138_2]) ).

cnf(f_138_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_267))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_267),image_1283814551_pname(U_266,U_265)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_265)) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

fof(f_139_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_677922117_state(F,A)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_85_finite__surj]) ).

fof(f_139_2,plain,
    ! [U_270,U_269,U_268] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_270))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_270),image_677922117_state(U_269,U_268)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_268)) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

fof(f_139_3,plain,
    ! [U_268,U_269,U_270] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_270))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_270),image_677922117_state(U_269,U_268)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_268)) ),
    inference(definitional_conversion,[status(esa)],[f_139_2]) ).

cnf(f_139_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_270))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_270),image_677922117_state(U_269,U_268)))
    | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_268)) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

fof(f_140_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_892968839_state(F,A)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_86_finite__surj]) ).

fof(f_140_2,plain,
    ! [U_273,U_272,U_271] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_273))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_273),image_892968839_state(U_272,U_271)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_271)) ),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

fof(f_140_3,plain,
    ! [U_271,U_272,U_273] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_273))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_273),image_892968839_state(U_272,U_271)))
      | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_271)) ),
    inference(definitional_conversion,[status(esa)],[f_140_2]) ).

cnf(f_140_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_273))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_273),image_892968839_state(U_272,U_271)))
    | ~ hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_271)) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

fof(f_141_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_18964633_state(F,A)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_87_finite__surj]) ).

fof(f_141_2,plain,
    ! [U_276,U_275,U_274] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_276))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_276),image_18964633_state(U_275,U_274)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_274)) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

fof(f_141_3,plain,
    ! [U_274,U_275,U_276] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_276))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_276),image_18964633_state(U_275,U_274)))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_274)) ),
    inference(definitional_conversion,[status(esa)],[f_141_2]) ).

cnf(f_141_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_276))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_276),image_18964633_state(U_275,U_274)))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_274)) ),
    inference(clausify,[status(thm)],[f_141_3]) ).

fof(f_142_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_516545147_state(F,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_88_finite__surj]) ).

fof(f_142_2,plain,
    ! [U_279,U_278,U_277] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_279))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_279),image_516545147_state(U_278,U_277)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_277)) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

fof(f_142_3,plain,
    ! [U_277,U_278,U_279] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_279))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_279),image_516545147_state(U_278,U_277)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_277)) ),
    inference(definitional_conversion,[status(esa)],[f_142_2]) ).

cnf(f_142_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_279))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_279),image_516545147_state(U_278,U_277)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_277)) ),
    inference(clausify,[status(thm)],[f_142_3]) ).

fof(f_143_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,B))
      | ~ hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,B),image_1642285373l_bool(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_89_finite__surj]) ).

fof(f_143_2,plain,
    ! [U_282,U_281,U_280] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_282))
      | ~ hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,U_282),image_1642285373l_bool(U_281,U_280)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_280)) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

fof(f_143_3,plain,
    ! [U_280,U_281,U_282] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_282))
      | ~ hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,U_282),image_1642285373l_bool(U_281,U_280)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_280)) ),
    inference(definitional_conversion,[status(esa)],[f_143_2]) ).

cnf(f_143_4,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_282))
    | ~ hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,U_282),image_1642285373l_bool(U_281,U_280)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_280)) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

fof(f_144_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,B))
      | ~ hBOOL(hAPP_f468958928l_bool(hAPP_f667366769l_bool(ord_le889598034l_bool,B),image_288317893l_bool(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_90_finite__surj]) ).

fof(f_144_2,plain,
    ! [U_285,U_284,U_283] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_285))
      | ~ hBOOL(hAPP_f468958928l_bool(hAPP_f667366769l_bool(ord_le889598034l_bool,U_285),image_288317893l_bool(U_284,U_283)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_283)) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ! [U_283,U_284,U_285] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_285))
      | ~ hBOOL(hAPP_f468958928l_bool(hAPP_f667366769l_bool(ord_le889598034l_bool,U_285),image_288317893l_bool(U_284,U_283)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_283)) ),
    inference(definitional_conversion,[status(esa)],[f_144_2]) ).

cnf(f_144_4,plain,
    ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_285))
    | ~ hBOOL(hAPP_f468958928l_bool(hAPP_f667366769l_bool(ord_le889598034l_bool,U_285),image_288317893l_bool(U_284,U_283)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_283)) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_pname_pname(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_91_finite__surj]) ).

fof(f_145_2,plain,
    ! [U_288,U_287,U_286] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_288))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_288),image_pname_pname(U_287,U_286)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_286)) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

fof(f_145_3,plain,
    ! [U_287,U_288,U_286] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_288))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_288),image_pname_pname(U_287,U_286)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_286)) ),
    inference(definitional_conversion,[status(esa)],[f_145_2]) ).

cnf(f_145_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_288))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_288),image_pname_pname(U_287,U_286)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_286)) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

fof(f_146_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,B))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,B),image_70449425e_bool(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_92_finite__surj]) ).

fof(f_146_2,plain,
    ! [U_291,U_290,U_289] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_291))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_291),image_70449425e_bool(U_290,U_289)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_289)) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

fof(f_146_3,plain,
    ! [U_289,U_290,U_291] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_291))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_291),image_70449425e_bool(U_290,U_289)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_289)) ),
    inference(definitional_conversion,[status(esa)],[f_146_2]) ).

cnf(f_146_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_291))
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_291),image_70449425e_bool(U_290,U_289)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_289)) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

fof(f_147_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_47868345e_bool(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_93_finite__surj]) ).

fof(f_147_2,plain,
    ! [U_294,U_293,U_292] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_294))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_294),image_47868345e_bool(U_293,U_292)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_292)) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

fof(f_147_3,plain,
    ! [U_292,U_293,U_294] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_294))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_294),image_47868345e_bool(U_293,U_292)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_292)) ),
    inference(definitional_conversion,[status(esa)],[f_147_2]) ).

cnf(f_147_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_294))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_294),image_47868345e_bool(U_293,U_292)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_292)) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

fof(f_148_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,B))
      | ~ hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,B),image_1210605179l_bool(F,A)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) ),
    inference(fof_nnf,[status(thm)],[fact_94_finite__surj]) ).

fof(f_148_2,plain,
    ! [U_297,U_296,U_295] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_297))
      | ~ hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,U_297),image_1210605179l_bool(U_296,U_295)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_295)) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

fof(f_148_3,plain,
    ! [U_295,U_296,U_297] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_297))
      | ~ hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,U_297),image_1210605179l_bool(U_296,U_295)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_295)) ),
    inference(definitional_conversion,[status(esa)],[f_148_2]) ).

cnf(f_148_4,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_297))
    | ~ hBOOL(hAPP_f389811538l_bool(hAPP_f1759205631l_bool(ord_le1375671464l_bool,U_297),image_1210605179l_bool(U_296,U_295)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_295)) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

fof(f_149_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,B))
      | ~ hBOOL(hAPP_f468958928l_bool(hAPP_f667366769l_bool(ord_le889598034l_bool,B),image_1761575943l_bool(F,A)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) ),
    inference(fof_nnf,[status(thm)],[fact_95_finite__surj]) ).

fof(f_149_2,plain,
    ! [U_300,U_299,U_298] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_300))
      | ~ hBOOL(hAPP_f468958928l_bool(hAPP_f667366769l_bool(ord_le889598034l_bool,U_300),image_1761575943l_bool(U_299,U_298)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_298)) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

fof(f_149_3,plain,
    ! [U_298,U_299,U_300] :
      ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_300))
      | ~ hBOOL(hAPP_f468958928l_bool(hAPP_f667366769l_bool(ord_le889598034l_bool,U_300),image_1761575943l_bool(U_299,U_298)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_298)) ),
    inference(definitional_conversion,[status(esa)],[f_149_2]) ).

cnf(f_149_4,plain,
    ( hBOOL(hAPP_f468958928l_bool(finite796539827l_bool,U_300))
    | ~ hBOOL(hAPP_f468958928l_bool(hAPP_f667366769l_bool(ord_le889598034l_bool,U_300),image_1761575943l_bool(U_299,U_298)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_298)) ),
    inference(clausify,[status(thm)],[f_149_3]) ).

fof(f_150_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_54689091_pname(F,A)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) ),
    inference(fof_nnf,[status(thm)],[fact_96_finite__surj]) ).

fof(f_150_2,plain,
    ! [U_303,U_302,U_301] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_303))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_303),image_54689091_pname(U_302,U_301)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_301)) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

fof(f_150_3,plain,
    ! [U_301,U_302,U_303] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_303))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_303),image_54689091_pname(U_302,U_301)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_301)) ),
    inference(definitional_conversion,[status(esa)],[f_150_2]) ).

cnf(f_150_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_303))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_303),image_54689091_pname(U_302,U_301)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_301)) ),
    inference(clausify,[status(thm)],[f_150_3]) ).

fof(f_151_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,B))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,B),image_1828608335e_bool(F,A)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) ),
    inference(fof_nnf,[status(thm)],[fact_97_finite__surj]) ).

fof(f_151_2,plain,
    ! [U_306,U_305,U_304] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_306))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_306),image_1828608335e_bool(U_305,U_304)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_304)) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

fof(f_151_3,plain,
    ! [U_304,U_305,U_306] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_306))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_306),image_1828608335e_bool(U_305,U_304)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_304)) ),
    inference(definitional_conversion,[status(esa)],[f_151_2]) ).

cnf(f_151_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_306))
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_306),image_1828608335e_bool(U_305,U_304)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_304)) ),
    inference(clausify,[status(thm)],[f_151_3]) ).

fof(f_152_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_2131964411e_bool(F,A)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) ),
    inference(fof_nnf,[status(thm)],[fact_98_finite__surj]) ).

fof(f_152_2,plain,
    ! [U_309,U_308,U_307] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_309))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_309),image_2131964411e_bool(U_308,U_307)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_307)) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ! [U_307,U_308,U_309] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_309))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_309),image_2131964411e_bool(U_308,U_307)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_307)) ),
    inference(definitional_conversion,[status(esa)],[f_152_2]) ).

cnf(f_152_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_309))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_309),image_2131964411e_bool(U_308,U_307)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_307)) ),
    inference(clausify,[status(thm)],[f_152_3]) ).

fof(f_153_1,plain,
    ! [A,X_2] :
      ( A = insert1415133716_state(X_2,bot_bo620288102e_bool)
      | A = bot_bo620288102e_bool
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),insert1415133716_state(X_2,bot_bo620288102e_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_99_subset__singletonD]) ).

fof(f_153_2,plain,
    ! [U_311,U_310] :
      ( U_311 = insert1415133716_state(U_310,bot_bo620288102e_bool)
      | U_311 = bot_bo620288102e_bool
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_311),insert1415133716_state(U_310,bot_bo620288102e_bool))) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

fof(f_153_3,plain,
    ! [U_310,U_311] :
      ( U_311 = insert1415133716_state(U_310,bot_bo620288102e_bool)
      | U_311 = bot_bo620288102e_bool
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_311),insert1415133716_state(U_310,bot_bo620288102e_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_153_2]) ).

cnf(f_153_4,plain,
    ( U_311 = insert1415133716_state(U_310,bot_bo620288102e_bool)
    | U_311 = bot_bo620288102e_bool
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_311),insert1415133716_state(U_310,bot_bo620288102e_bool))) ),
    inference(clausify,[status(thm)],[f_153_3]) ).

fof(f_154_1,plain,
    ! [A,X_2] :
      ( A = insert1325755072e_bool(X_2,bot_bo1649642514l_bool)
      | A = bot_bo1649642514l_bool
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),insert1325755072e_bool(X_2,bot_bo1649642514l_bool)))
      | ~ is_fun1661590463l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_100_subset__singletonD]) ).

fof(f_154_2,plain,
    ! [U_313,U_312] :
      ( U_313 = insert1325755072e_bool(U_312,bot_bo1649642514l_bool)
      | U_313 = bot_bo1649642514l_bool
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_313),insert1325755072e_bool(U_312,bot_bo1649642514l_bool)))
      | ~ is_fun1661590463l_bool(U_313) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

fof(f_154_3,plain,
    ! [U_313] :
      ( ! [U_312] :
          ( U_313 = insert1325755072e_bool(U_312,bot_bo1649642514l_bool)
          | U_313 = bot_bo1649642514l_bool
          | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_313),insert1325755072e_bool(U_312,bot_bo1649642514l_bool))) )
      | ~ is_fun1661590463l_bool(U_313) ),
    inference(miniscope,[status(thm)],[f_154_2]) ).

fof(f_154_4,plain,
    ! [U_312,U_313] :
      ( U_313 = insert1325755072e_bool(U_312,bot_bo1649642514l_bool)
      | U_313 = bot_bo1649642514l_bool
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_313),insert1325755072e_bool(U_312,bot_bo1649642514l_bool)))
      | ~ is_fun1661590463l_bool(U_313) ),
    inference(definitional_conversion,[status(esa)],[f_154_3]) ).

cnf(f_154_5,plain,
    ( U_313 = insert1325755072e_bool(U_312,bot_bo1649642514l_bool)
    | U_313 = bot_bo1649642514l_bool
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_313),insert1325755072e_bool(U_312,bot_bo1649642514l_bool)))
    | ~ is_fun1661590463l_bool(U_313) ),
    inference(clausify,[status(thm)],[f_154_4]) ).

fof(f_155_1,plain,
    ! [A,X_2] :
      ( A = insert1556680138e_bool(X_2,bot_bo535777328l_bool)
      | A = bot_bo535777328l_bool
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),insert1556680138e_bool(X_2,bot_bo535777328l_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_101_subset__singletonD]) ).

fof(f_155_2,plain,
    ! [U_315,U_314] :
      ( U_315 = insert1556680138e_bool(U_314,bot_bo535777328l_bool)
      | U_315 = bot_bo535777328l_bool
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_315),insert1556680138e_bool(U_314,bot_bo535777328l_bool))) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

fof(f_155_3,plain,
    ! [U_314,U_315] :
      ( U_315 = insert1556680138e_bool(U_314,bot_bo535777328l_bool)
      | U_315 = bot_bo535777328l_bool
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_315),insert1556680138e_bool(U_314,bot_bo535777328l_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_155_2]) ).

cnf(f_155_4,plain,
    ( U_315 = insert1556680138e_bool(U_314,bot_bo535777328l_bool)
    | U_315 = bot_bo535777328l_bool
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_315),insert1556680138e_bool(U_314,bot_bo535777328l_bool))) ),
    inference(clausify,[status(thm)],[f_155_3]) ).

fof(f_156_1,plain,
    ! [A,X_2] :
      ( A = insert_pname(X_2,bot_bo844097828e_bool)
      | A = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,bot_bo844097828e_bool)))
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_102_subset__singletonD]) ).

fof(f_156_2,plain,
    ! [U_317,U_316] :
      ( U_317 = insert_pname(U_316,bot_bo844097828e_bool)
      | U_317 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_317),insert_pname(U_316,bot_bo844097828e_bool)))
      | ~ is_fun_pname_bool(U_317) ),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

fof(f_156_3,plain,
    ! [U_317] :
      ( ! [U_316] :
          ( U_317 = insert_pname(U_316,bot_bo844097828e_bool)
          | U_317 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_317),insert_pname(U_316,bot_bo844097828e_bool))) )
      | ~ is_fun_pname_bool(U_317) ),
    inference(miniscope,[status(thm)],[f_156_2]) ).

fof(f_156_4,plain,
    ! [U_316,U_317] :
      ( U_317 = insert_pname(U_316,bot_bo844097828e_bool)
      | U_317 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_317),insert_pname(U_316,bot_bo844097828e_bool)))
      | ~ is_fun_pname_bool(U_317) ),
    inference(definitional_conversion,[status(esa)],[f_156_3]) ).

cnf(f_156_5,plain,
    ( U_317 = insert_pname(U_316,bot_bo844097828e_bool)
    | U_317 = bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_317),insert_pname(U_316,bot_bo844097828e_bool)))
    | ~ is_fun_pname_bool(U_317) ),
    inference(clausify,[status(thm)],[f_156_4]) ).

fof(f_157_1,plain,
    ! [C_1] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,C_1),bot_bo620288102e_bool)))
      | ~ hBOOL(wt(C_1))
      | ~ hBOOL(wT_bodies)
      | ~ hBOOL(hoare_165779456gleton) ),
    inference(fof_nnf,[status(thm)],[fact_103_MGF]) ).

fof(f_157_2,plain,
    ! [U_318] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,U_318),bot_bo620288102e_bool)))
      | ~ hBOOL(wt(U_318))
      | ~ hBOOL(wT_bodies)
      | ~ hBOOL(hoare_165779456gleton) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

fof(f_157_3,plain,
    ( ! [U_318] :
        ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,U_318),bot_bo620288102e_bool)))
        | ~ hBOOL(wt(U_318)) )
    | ~ hBOOL(wT_bodies)
    | ~ hBOOL(hoare_165779456gleton) ),
    inference(miniscope,[status(thm)],[f_157_2]) ).

fof(f_157_4,plain,
    ! [U_318] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,U_318),bot_bo620288102e_bool)))
      | ~ hBOOL(wt(U_318))
      | ~ hBOOL(wT_bodies)
      | ~ hBOOL(hoare_165779456gleton) ),
    inference(definitional_conversion,[status(esa)],[f_157_3]) ).

cnf(f_157_5,plain,
    ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(bot_bo620288102e_bool),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,U_318),bot_bo620288102e_bool)))
    | ~ hBOOL(wt(U_318))
    | ~ hBOOL(wT_bodies)
    | ~ hBOOL(hoare_165779456gleton) ),
    inference(clausify,[status(thm)],[f_157_4]) ).

fof(f_158_1,plain,
    ! [A_2] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),bot_bo620288102e_bool)),
    inference(fof_nnf,[status(thm)],[fact_104_emptyE]) ).

fof(f_158_2,plain,
    ! [U_319] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_319),bot_bo620288102e_bool)),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

fof(f_158_3,plain,
    ! [U_319] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_319),bot_bo620288102e_bool)),
    inference(definitional_conversion,[status(esa)],[f_158_2]) ).

cnf(f_158_4,plain,
    ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_319),bot_bo620288102e_bool)),
    inference(clausify,[status(thm)],[f_158_3]) ).

fof(f_159_1,plain,
    ! [A_2] : ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),bot_bo1649642514l_bool)),
    inference(fof_nnf,[status(thm)],[fact_105_emptyE]) ).

fof(f_159_2,plain,
    ! [U_320] : ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_320),bot_bo1649642514l_bool)),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

fof(f_159_3,plain,
    ! [U_320] : ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_320),bot_bo1649642514l_bool)),
    inference(definitional_conversion,[status(esa)],[f_159_2]) ).

cnf(f_159_4,plain,
    ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_320),bot_bo1649642514l_bool)),
    inference(clausify,[status(thm)],[f_159_3]) ).

fof(f_160_1,plain,
    ! [A_2] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),bot_bo535777328l_bool)),
    inference(fof_nnf,[status(thm)],[fact_106_emptyE]) ).

fof(f_160_2,plain,
    ! [U_321] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_321),bot_bo535777328l_bool)),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

fof(f_160_3,plain,
    ! [U_321] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_321),bot_bo535777328l_bool)),
    inference(definitional_conversion,[status(esa)],[f_160_2]) ).

cnf(f_160_4,plain,
    ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_321),bot_bo535777328l_bool)),
    inference(clausify,[status(thm)],[f_160_3]) ).

fof(f_161_1,plain,
    ! [A_2] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),bot_bo844097828e_bool)),
    inference(fof_nnf,[status(thm)],[fact_107_emptyE]) ).

fof(f_161_2,plain,
    ! [U_322] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_322),bot_bo844097828e_bool)),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

fof(f_161_3,plain,
    ! [U_322] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_322),bot_bo844097828e_bool)),
    inference(definitional_conversion,[status(esa)],[f_161_2]) ).

cnf(f_161_4,plain,
    ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_322),bot_bo844097828e_bool)),
    inference(clausify,[status(thm)],[f_161_3]) ).

fof(f_162_1,plain,
    ! [B_1,A_2,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,B)))
      | ( A_2 != B_1
        & ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_108_insertCI]) ).

fof(f_162_2,plain,
    ! [U_325,U_324,U_323] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_324),insert1415133716_state(U_325,U_323)))
      | ( U_324 != U_325
        & ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_324),U_323)) ) ),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

fof(f_162_3,plain,
    ( ! [U_325,U_323,U_324] :
        ( U_324 != U_325
        | ~ sP13(U_325,U_323,U_324) )
    & ! [U_325,U_323,U_324] :
        ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_324),U_323))
        | ~ sP13(U_325,U_323,U_324) )
    & ! [U_325,U_323,U_324] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_324),insert1415133716_state(U_325,U_323)))
        | sP13(U_325,U_323,U_324) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_162_2]) ).

cnf(f_162_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_324),insert1415133716_state(U_325,U_323)))
    | sP13(U_325,U_323,U_324) ),
    inference(clausify,[status(thm)],[f_162_3]) ).

cnf(f_162_5,plain,
    ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_324),U_323))
    | ~ sP13(U_325,U_323,U_324) ),
    inference(clausify,[status(thm)],[f_162_3]) ).

cnf(f_162_6,plain,
    ( U_324 != U_325
    | ~ sP13(U_325,U_323,U_324) ),
    inference(clausify,[status(thm)],[f_162_3]) ).

fof(f_163_1,plain,
    ! [B_1,A_2,B] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),insert1325755072e_bool(B_1,B)))
      | ( A_2 != B_1
        & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_109_insertCI]) ).

fof(f_163_2,plain,
    ! [U_328,U_327,U_326] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_327),insert1325755072e_bool(U_328,U_326)))
      | ( U_327 != U_328
        & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_327),U_326)) ) ),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

fof(f_163_3,plain,
    ( ! [U_328,U_327,U_326] :
        ( U_327 != U_328
        | ~ sP14(U_328,U_327,U_326) )
    & ! [U_328,U_327,U_326] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_327),U_326))
        | ~ sP14(U_328,U_327,U_326) )
    & ! [U_328,U_327,U_326] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_327),insert1325755072e_bool(U_328,U_326)))
        | sP14(U_328,U_327,U_326) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_163_2]) ).

cnf(f_163_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_327),insert1325755072e_bool(U_328,U_326)))
    | sP14(U_328,U_327,U_326) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

cnf(f_163_5,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_327),U_326))
    | ~ sP14(U_328,U_327,U_326) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

cnf(f_163_6,plain,
    ( U_327 != U_328
    | ~ sP14(U_328,U_327,U_326) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

fof(f_164_1,plain,
    ! [B_1,A_2,B] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),insert1556680138e_bool(B_1,B)))
      | ( A_2 != B_1
        & ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_110_insertCI]) ).

fof(f_164_2,plain,
    ! [U_331,U_330,U_329] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_330),insert1556680138e_bool(U_331,U_329)))
      | ( U_330 != U_331
        & ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_330),U_329)) ) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

fof(f_164_3,plain,
    ( ! [U_329,U_331,U_330] :
        ( U_330 != U_331
        | ~ sP15(U_329,U_331,U_330) )
    & ! [U_329,U_331,U_330] :
        ( ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_330),U_329))
        | ~ sP15(U_329,U_331,U_330) )
    & ! [U_329,U_331,U_330] :
        ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_330),insert1556680138e_bool(U_331,U_329)))
        | sP15(U_329,U_331,U_330) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_164_2]) ).

cnf(f_164_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_330),insert1556680138e_bool(U_331,U_329)))
    | sP15(U_329,U_331,U_330) ),
    inference(clausify,[status(thm)],[f_164_3]) ).

cnf(f_164_5,plain,
    ( ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_330),U_329))
    | ~ sP15(U_329,U_331,U_330) ),
    inference(clausify,[status(thm)],[f_164_3]) ).

cnf(f_164_6,plain,
    ( U_330 != U_331
    | ~ sP15(U_329,U_331,U_330) ),
    inference(clausify,[status(thm)],[f_164_3]) ).

fof(f_165_1,plain,
    ! [B_1,A_2,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,B)))
      | ( A_2 != B_1
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_111_insertCI]) ).

fof(f_165_2,plain,
    ! [U_334,U_333,U_332] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_333),insert_pname(U_334,U_332)))
      | ( U_333 != U_334
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_333),U_332)) ) ),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

fof(f_165_3,plain,
    ( ! [U_332,U_333,U_334] :
        ( U_333 != U_334
        | ~ sP16(U_332,U_333,U_334) )
    & ! [U_332,U_333,U_334] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_333),U_332))
        | ~ sP16(U_332,U_333,U_334) )
    & ! [U_332,U_333,U_334] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_333),insert_pname(U_334,U_332)))
        | sP16(U_332,U_333,U_334) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_165_2]) ).

cnf(f_165_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_333),insert_pname(U_334,U_332)))
    | sP16(U_332,U_333,U_334) ),
    inference(clausify,[status(thm)],[f_165_3]) ).

cnf(f_165_5,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_333),U_332))
    | ~ sP16(U_332,U_333,U_334) ),
    inference(clausify,[status(thm)],[f_165_3]) ).

cnf(f_165_6,plain,
    ( U_333 != U_334
    | ~ sP16(U_332,U_333,U_334) ),
    inference(clausify,[status(thm)],[f_165_3]) ).

fof(f_166_1,plain,
    ! [A_2,B_1,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A))
      | A_2 = B_1
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,A))) ),
    inference(fof_nnf,[status(thm)],[fact_112_insertE]) ).

fof(f_166_2,plain,
    ! [U_337,U_336,U_335] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_337),U_335))
      | U_337 = U_336
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_337),insert1415133716_state(U_336,U_335))) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

fof(f_166_3,plain,
    ! [U_335,U_336,U_337] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_337),U_335))
      | U_337 = U_336
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_337),insert1415133716_state(U_336,U_335))) ),
    inference(definitional_conversion,[status(esa)],[f_166_2]) ).

cnf(f_166_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_337),U_335))
    | U_337 = U_336
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_337),insert1415133716_state(U_336,U_335))) ),
    inference(clausify,[status(thm)],[f_166_3]) ).

fof(f_167_1,plain,
    ! [A_2,B_1,A] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A))
      | A_2 = B_1
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),insert1325755072e_bool(B_1,A)))
      | ~ is_fun_pname_bool(B_1)
      | ~ is_fun_pname_bool(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_113_insertE]) ).

fof(f_167_2,plain,
    ! [U_340,U_339,U_338] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_340),U_338))
      | U_340 = U_339
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_340),insert1325755072e_bool(U_339,U_338)))
      | ~ is_fun_pname_bool(U_339)
      | ~ is_fun_pname_bool(U_340) ),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

fof(f_167_3,plain,
    ! [U_340,U_339] :
      ( ! [U_338] :
          ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_340),U_338))
          | U_340 = U_339
          | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_340),insert1325755072e_bool(U_339,U_338))) )
      | ~ is_fun_pname_bool(U_339)
      | ~ is_fun_pname_bool(U_340) ),
    inference(miniscope,[status(thm)],[f_167_2]) ).

fof(f_167_4,plain,
    ! [U_338,U_339,U_340] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_340),U_338))
      | U_340 = U_339
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_340),insert1325755072e_bool(U_339,U_338)))
      | ~ is_fun_pname_bool(U_339)
      | ~ is_fun_pname_bool(U_340) ),
    inference(definitional_conversion,[status(esa)],[f_167_3]) ).

cnf(f_167_5,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_340),U_338))
    | U_340 = U_339
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_340),insert1325755072e_bool(U_339,U_338)))
    | ~ is_fun_pname_bool(U_339)
    | ~ is_fun_pname_bool(U_340) ),
    inference(clausify,[status(thm)],[f_167_4]) ).

fof(f_168_1,plain,
    ! [A_2,B_1,A] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),A))
      | A_2 = B_1
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),insert1556680138e_bool(B_1,A))) ),
    inference(fof_nnf,[status(thm)],[fact_114_insertE]) ).

fof(f_168_2,plain,
    ! [U_343,U_342,U_341] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_343),U_341))
      | U_343 = U_342
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_343),insert1556680138e_bool(U_342,U_341))) ),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

fof(f_168_3,plain,
    ! [U_343,U_341,U_342] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_343),U_341))
      | U_343 = U_342
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_343),insert1556680138e_bool(U_342,U_341))) ),
    inference(definitional_conversion,[status(esa)],[f_168_2]) ).

cnf(f_168_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_343),U_341))
    | U_343 = U_342
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_343),insert1556680138e_bool(U_342,U_341))) ),
    inference(clausify,[status(thm)],[f_168_3]) ).

fof(f_169_1,plain,
    ! [A_2,B_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
      | A_2 = B_1
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,A)))
      | ~ is_pname(B_1)
      | ~ is_pname(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_115_insertE]) ).

fof(f_169_2,plain,
    ! [U_346,U_345,U_344] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_346),U_344))
      | U_346 = U_345
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_346),insert_pname(U_345,U_344)))
      | ~ is_pname(U_345)
      | ~ is_pname(U_346) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

fof(f_169_3,plain,
    ! [U_346,U_345] :
      ( ! [U_344] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_346),U_344))
          | U_346 = U_345
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_346),insert_pname(U_345,U_344))) )
      | ~ is_pname(U_345)
      | ~ is_pname(U_346) ),
    inference(miniscope,[status(thm)],[f_169_2]) ).

fof(f_169_4,plain,
    ! [U_344,U_345,U_346] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_346),U_344))
      | U_346 = U_345
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_346),insert_pname(U_345,U_344)))
      | ~ is_pname(U_345)
      | ~ is_pname(U_346) ),
    inference(definitional_conversion,[status(esa)],[f_169_3]) ).

cnf(f_169_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_346),U_344))
    | U_346 = U_345
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_346),insert_pname(U_345,U_344)))
    | ~ is_pname(U_345)
    | ~ is_pname(U_346) ),
    inference(clausify,[status(thm)],[f_169_4]) ).

fof(f_170_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_116_equalityI]) ).

fof(f_170_2,plain,
    ! [U_348,U_347] :
      ( U_348 = U_347
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_347),U_348))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_348),U_347)) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

fof(f_170_3,plain,
    ! [U_347,U_348] :
      ( U_348 = U_347
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_347),U_348))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_348),U_347)) ),
    inference(definitional_conversion,[status(esa)],[f_170_2]) ).

cnf(f_170_4,plain,
    ( U_348 = U_347
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_347),U_348))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_348),U_347)) ),
    inference(clausify,[status(thm)],[f_170_3]) ).

fof(f_171_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),A))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
      | ~ is_fun1661590463l_bool(B)
      | ~ is_fun1661590463l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_117_equalityI]) ).

fof(f_171_2,plain,
    ! [U_350,U_349] :
      ( U_350 = U_349
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_349),U_350))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_350),U_349))
      | ~ is_fun1661590463l_bool(U_349)
      | ~ is_fun1661590463l_bool(U_350) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

fof(f_171_3,plain,
    ! [U_349,U_350] :
      ( U_350 = U_349
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_349),U_350))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_350),U_349))
      | ~ is_fun1661590463l_bool(U_349)
      | ~ is_fun1661590463l_bool(U_350) ),
    inference(definitional_conversion,[status(esa)],[f_171_2]) ).

cnf(f_171_4,plain,
    ( U_350 = U_349
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_349),U_350))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_350),U_349))
    | ~ is_fun1661590463l_bool(U_349)
    | ~ is_fun1661590463l_bool(U_350) ),
    inference(clausify,[status(thm)],[f_171_3]) ).

fof(f_172_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,B),A))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_118_equalityI]) ).

fof(f_172_2,plain,
    ! [U_352,U_351] :
      ( U_352 = U_351
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_351),U_352))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_352),U_351)) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

fof(f_172_3,plain,
    ! [U_351,U_352] :
      ( U_352 = U_351
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_351),U_352))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_352),U_351)) ),
    inference(definitional_conversion,[status(esa)],[f_172_2]) ).

cnf(f_172_4,plain,
    ( U_352 = U_351
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_351),U_352))
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_352),U_351)) ),
    inference(clausify,[status(thm)],[f_172_3]) ).

fof(f_173_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | ~ is_fun_pname_bool(B)
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_119_equalityI]) ).

fof(f_173_2,plain,
    ! [U_354,U_353] :
      ( U_354 = U_353
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_353),U_354))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_354),U_353))
      | ~ is_fun_pname_bool(U_353)
      | ~ is_fun_pname_bool(U_354) ),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

fof(f_173_3,plain,
    ! [U_353,U_354] :
      ( U_354 = U_353
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_353),U_354))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_354),U_353))
      | ~ is_fun_pname_bool(U_353)
      | ~ is_fun_pname_bool(U_354) ),
    inference(definitional_conversion,[status(esa)],[f_173_2]) ).

cnf(f_173_4,plain,
    ( U_354 = U_353
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_353),U_354))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_354),U_353))
    | ~ is_fun_pname_bool(U_353)
    | ~ is_fun_pname_bool(U_354) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

fof(f_174_1,plain,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,C_1),B))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,C_1),A))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_120_subsetD]) ).

fof(f_174_2,plain,
    ! [U_357,U_356,U_355] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_357),U_355))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_357),U_356))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_356),U_355)) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

fof(f_174_3,plain,
    ! [U_355,U_356,U_357] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_357),U_355))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_357),U_356))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_356),U_355)) ),
    inference(definitional_conversion,[status(esa)],[f_174_2]) ).

cnf(f_174_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_357),U_355))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_357),U_356))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_356),U_355)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

fof(f_175_1,plain,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,C_1),B))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,C_1),A))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_121_subsetD]) ).

fof(f_175_2,plain,
    ! [U_360,U_359,U_358] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_360),U_358))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_360),U_359))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_359),U_358)) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

fof(f_175_3,plain,
    ! [U_358,U_359,U_360] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_360),U_358))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_360),U_359))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_359),U_358)) ),
    inference(definitional_conversion,[status(esa)],[f_175_2]) ).

cnf(f_175_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_360),U_358))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_360),U_359))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_359),U_358)) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

fof(f_176_1,plain,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,C_1),B))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,C_1),A))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_122_subsetD]) ).

fof(f_176_2,plain,
    ! [U_363,U_362,U_361] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_363),U_361))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_363),U_362))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_362),U_361)) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

fof(f_176_3,plain,
    ! [U_361,U_362,U_363] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_363),U_361))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_363),U_362))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_362),U_361)) ),
    inference(definitional_conversion,[status(esa)],[f_176_2]) ).

cnf(f_176_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_363),U_361))
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_363),U_362))
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_362),U_361)) ),
    inference(clausify,[status(thm)],[f_176_3]) ).

fof(f_177_1,plain,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_123_subsetD]) ).

fof(f_177_2,plain,
    ! [U_366,U_365,U_364] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_366),U_364))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_366),U_365))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_365),U_364)) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

fof(f_177_3,plain,
    ! [U_364,U_365,U_366] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_366),U_364))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_366),U_365))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_365),U_364)) ),
    inference(definitional_conversion,[status(esa)],[f_177_2]) ).

cnf(f_177_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_366),U_364))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_366),U_365))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_365),U_364)) ),
    inference(clausify,[status(thm)],[f_177_3]) ).

fof(f_178_1,plain,
    ! [A,B_1,F,X_2] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,B_1),image_2131964411e_bool(F,A)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
      | B_1 != hAPP_H356885323e_bool(F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_124_image__eqI]) ).

fof(f_178_2,plain,
    ! [U_370,U_369,U_368,U_367] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_369),image_2131964411e_bool(U_368,U_370)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_367),U_370))
      | U_369 != hAPP_H356885323e_bool(U_368,U_367) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

fof(f_178_3,plain,
    ! [U_367,U_368,U_369,U_370] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_369),image_2131964411e_bool(U_368,U_370)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_367),U_370))
      | U_369 != hAPP_H356885323e_bool(U_368,U_367) ),
    inference(definitional_conversion,[status(esa)],[f_178_2]) ).

cnf(f_178_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_369),image_2131964411e_bool(U_368,U_370)))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_367),U_370))
    | U_369 != hAPP_H356885323e_bool(U_368,U_367) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

fof(f_179_1,plain,
    ! [A,B_1,F,X_2] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,B_1),image_1828608335e_bool(F,A)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
      | B_1 != hAPP_H1049623551e_bool(F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_125_image__eqI]) ).

fof(f_179_2,plain,
    ! [U_374,U_373,U_372,U_371] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_373),image_1828608335e_bool(U_372,U_374)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_371),U_374))
      | U_373 != hAPP_H1049623551e_bool(U_372,U_371) ),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

fof(f_179_3,plain,
    ! [U_372,U_371,U_373,U_374] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_373),image_1828608335e_bool(U_372,U_374)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_371),U_374))
      | U_373 != hAPP_H1049623551e_bool(U_372,U_371) ),
    inference(definitional_conversion,[status(esa)],[f_179_2]) ).

cnf(f_179_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_373),image_1828608335e_bool(U_372,U_374)))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_371),U_374))
    | U_373 != hAPP_H1049623551e_bool(U_372,U_371) ),
    inference(clausify,[status(thm)],[f_179_3]) ).

fof(f_180_1,plain,
    ! [A,B_1,F,X_2] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,B_1),image_47868345e_bool(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
      | B_1 != hAPP_p61793385e_bool(F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_126_image__eqI]) ).

fof(f_180_2,plain,
    ! [U_378,U_377,U_376,U_375] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_377),image_47868345e_bool(U_376,U_378)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_375),U_378))
      | U_377 != hAPP_p61793385e_bool(U_376,U_375) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

fof(f_180_3,plain,
    ! [U_376,U_375,U_377,U_378] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_377),image_47868345e_bool(U_376,U_378)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_375),U_378))
      | U_377 != hAPP_p61793385e_bool(U_376,U_375) ),
    inference(definitional_conversion,[status(esa)],[f_180_2]) ).

cnf(f_180_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_377),image_47868345e_bool(U_376,U_378)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_375),U_378))
    | U_377 != hAPP_p61793385e_bool(U_376,U_375) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

fof(f_181_1,plain,
    ! [A,B_1,F,X_2] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,B_1),image_70449425e_bool(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
      | B_1 != hAPP_p442853985e_bool(F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_127_image__eqI]) ).

fof(f_181_2,plain,
    ! [U_382,U_381,U_380,U_379] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_381),image_70449425e_bool(U_380,U_382)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_379),U_382))
      | U_381 != hAPP_p442853985e_bool(U_380,U_379) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

fof(f_181_3,plain,
    ! [U_380,U_379,U_381,U_382] :
      ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_381),image_70449425e_bool(U_380,U_382)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_379),U_382))
      | U_381 != hAPP_p442853985e_bool(U_380,U_379) ),
    inference(definitional_conversion,[status(esa)],[f_181_2]) ).

cnf(f_181_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_381),image_70449425e_bool(U_380,U_382)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_379),U_382))
    | U_381 != hAPP_p442853985e_bool(U_380,U_379) ),
    inference(clausify,[status(thm)],[f_181_3]) ).

fof(f_182_1,plain,
    ! [A,B_1,F,X_2] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_516545147_state(F,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
      | B_1 != hAPP_f888949707_state(F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_128_image__eqI]) ).

fof(f_182_2,plain,
    ! [U_386,U_385,U_384,U_383] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_385),image_516545147_state(U_384,U_386)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_383),U_386))
      | U_385 != hAPP_f888949707_state(U_384,U_383) ),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

fof(f_182_3,plain,
    ! [U_384,U_383,U_385,U_386] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_385),image_516545147_state(U_384,U_386)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_383),U_386))
      | U_385 != hAPP_f888949707_state(U_384,U_383) ),
    inference(definitional_conversion,[status(esa)],[f_182_2]) ).

cnf(f_182_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_385),image_516545147_state(U_384,U_386)))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_383),U_386))
    | U_385 != hAPP_f888949707_state(U_384,U_383) ),
    inference(clausify,[status(thm)],[f_182_3]) ).

fof(f_183_1,plain,
    ! [A,B_1,F,X_2] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_18964633_state(F,A)))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_2),A))
      | B_1 != hAPP_f1387463497_state(F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_129_image__eqI]) ).

fof(f_183_2,plain,
    ! [U_390,U_389,U_388,U_387] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_389),image_18964633_state(U_388,U_390)))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_387),U_390))
      | U_389 != hAPP_f1387463497_state(U_388,U_387) ),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

fof(f_183_3,plain,
    ! [U_388,U_387,U_389,U_390] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_389),image_18964633_state(U_388,U_390)))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_387),U_390))
      | U_389 != hAPP_f1387463497_state(U_388,U_387) ),
    inference(definitional_conversion,[status(esa)],[f_183_2]) ).

cnf(f_183_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_389),image_18964633_state(U_388,U_390)))
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_387),U_390))
    | U_389 != hAPP_f1387463497_state(U_388,U_387) ),
    inference(clausify,[status(thm)],[f_183_3]) ).

fof(f_184_1,plain,
    ! [A,B_1,F,X_2] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_54689091_pname(F,A)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
      | B_1 != hAPP_H1621176307_pname(F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_130_image__eqI]) ).

fof(f_184_2,plain,
    ! [U_394,U_393,U_392,U_391] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_393),image_54689091_pname(U_392,U_394)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_391),U_394))
      | U_393 != hAPP_H1621176307_pname(U_392,U_391) ),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

fof(f_184_3,plain,
    ! [U_391,U_392,U_393,U_394] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_393),image_54689091_pname(U_392,U_394)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_391),U_394))
      | U_393 != hAPP_H1621176307_pname(U_392,U_391) ),
    inference(definitional_conversion,[status(esa)],[f_184_2]) ).

cnf(f_184_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_393),image_54689091_pname(U_392,U_394)))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_391),U_394))
    | U_393 != hAPP_H1621176307_pname(U_392,U_391) ),
    inference(clausify,[status(thm)],[f_184_3]) ).

fof(f_185_1,plain,
    ! [A,B_1,F,X_2] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_pname_pname(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
      | B_1 != hAPP_pname_pname(F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_131_image__eqI]) ).

fof(f_185_2,plain,
    ! [U_398,U_397,U_396,U_395] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_397),image_pname_pname(U_396,U_398)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_395),U_398))
      | U_397 != hAPP_pname_pname(U_396,U_395) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

fof(f_185_3,plain,
    ! [U_396,U_395,U_397,U_398] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_397),image_pname_pname(U_396,U_398)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_395),U_398))
      | U_397 != hAPP_pname_pname(U_396,U_395) ),
    inference(definitional_conversion,[status(esa)],[f_185_2]) ).

cnf(f_185_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_397),image_pname_pname(U_396,U_398)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_395),U_398))
    | U_397 != hAPP_pname_pname(U_396,U_395) ),
    inference(clausify,[status(thm)],[f_185_3]) ).

fof(f_186_1,plain,
    ! [A,B_1,F,X_2] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_1283814551_pname(F,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
      | B_1 != hAPP_f1297739591_pname(F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_132_image__eqI]) ).

fof(f_186_2,plain,
    ! [U_402,U_401,U_400,U_399] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_401),image_1283814551_pname(U_400,U_402)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_399),U_402))
      | U_401 != hAPP_f1297739591_pname(U_400,U_399) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

fof(f_186_3,plain,
    ! [U_399,U_400,U_401,U_402] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_401),image_1283814551_pname(U_400,U_402)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_399),U_402))
      | U_401 != hAPP_f1297739591_pname(U_400,U_399) ),
    inference(definitional_conversion,[status(esa)],[f_186_2]) ).

cnf(f_186_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_401),image_1283814551_pname(U_400,U_402)))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_399),U_402))
    | U_401 != hAPP_f1297739591_pname(U_400,U_399) ),
    inference(clausify,[status(thm)],[f_186_3]) ).

fof(f_187_1,plain,
    ! [A,B_1,F,X_2] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),image_187965177_pname(F,A)))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_2),A))
      | B_1 != hAPP_f560369737_pname(F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_133_image__eqI]) ).

fof(f_187_2,plain,
    ! [U_406,U_405,U_404,U_403] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_405),image_187965177_pname(U_404,U_406)))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_403),U_406))
      | U_405 != hAPP_f560369737_pname(U_404,U_403) ),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

fof(f_187_3,plain,
    ! [U_403,U_404,U_405,U_406] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_405),image_187965177_pname(U_404,U_406)))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_403),U_406))
      | U_405 != hAPP_f560369737_pname(U_404,U_403) ),
    inference(definitional_conversion,[status(esa)],[f_187_2]) ).

cnf(f_187_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_405),image_187965177_pname(U_404,U_406)))
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_403),U_406))
    | U_405 != hAPP_f560369737_pname(U_404,U_403) ),
    inference(clausify,[status(thm)],[f_187_3]) ).

fof(f_188_1,plain,
    ! [A,B_1,F,X_2] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_2003357581_state(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
      | B_1 != hAPP_p1422361149_state(F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_134_image__eqI]) ).

fof(f_188_2,plain,
    ! [U_410,U_409,U_408,U_407] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_409),image_2003357581_state(U_408,U_410)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_407),U_410))
      | U_409 != hAPP_p1422361149_state(U_408,U_407) ),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

fof(f_188_3,plain,
    ! [U_408,U_407,U_409,U_410] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_409),image_2003357581_state(U_408,U_410)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_407),U_410))
      | U_409 != hAPP_p1422361149_state(U_408,U_407) ),
    inference(definitional_conversion,[status(esa)],[f_188_2]) ).

cnf(f_188_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_409),image_2003357581_state(U_408,U_410)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_407),U_410))
    | U_409 != hAPP_p1422361149_state(U_408,U_407) ),
    inference(clausify,[status(thm)],[f_188_3]) ).

fof(f_189_1,plain,
    ! [A_2,A] :
      ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_2),A))
      | A != bot_bo1649642514l_bool ),
    inference(fof_nnf,[status(thm)],[fact_135_equals0D]) ).

fof(f_189_2,plain,
    ! [U_412,U_411] :
      ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_412),U_411))
      | U_411 != bot_bo1649642514l_bool ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

fof(f_189_3,plain,
    ! [U_412,U_411] :
      ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_412),U_411))
      | U_411 != bot_bo1649642514l_bool ),
    inference(definitional_conversion,[status(esa)],[f_189_2]) ).

cnf(f_189_4,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_412),U_411))
    | U_411 != bot_bo1649642514l_bool ),
    inference(clausify,[status(thm)],[f_189_3]) ).

fof(f_190_1,plain,
    ! [A_2,A] :
      ( ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_2),A))
      | A != bot_bo535777328l_bool ),
    inference(fof_nnf,[status(thm)],[fact_136_equals0D]) ).

fof(f_190_2,plain,
    ! [U_414,U_413] :
      ( ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_414),U_413))
      | U_413 != bot_bo535777328l_bool ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

fof(f_190_3,plain,
    ! [U_413,U_414] :
      ( ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_414),U_413))
      | U_413 != bot_bo535777328l_bool ),
    inference(definitional_conversion,[status(esa)],[f_190_2]) ).

cnf(f_190_4,plain,
    ( ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_414),U_413))
    | U_413 != bot_bo535777328l_bool ),
    inference(clausify,[status(thm)],[f_190_3]) ).

fof(f_191_1,plain,
    ! [A_2,A] :
      ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A))
      | A != bot_bo620288102e_bool ),
    inference(fof_nnf,[status(thm)],[fact_137_equals0D]) ).

fof(f_191_2,plain,
    ! [U_416,U_415] :
      ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_416),U_415))
      | U_415 != bot_bo620288102e_bool ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

fof(f_191_3,plain,
    ! [U_415,U_416] :
      ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_416),U_415))
      | U_415 != bot_bo620288102e_bool ),
    inference(definitional_conversion,[status(esa)],[f_191_2]) ).

cnf(f_191_4,plain,
    ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_416),U_415))
    | U_415 != bot_bo620288102e_bool ),
    inference(clausify,[status(thm)],[f_191_3]) ).

fof(f_192_1,plain,
    ! [A_2,A] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
      | A != bot_bo844097828e_bool ),
    inference(fof_nnf,[status(thm)],[fact_138_equals0D]) ).

fof(f_192_2,plain,
    ! [U_418,U_417] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_418),U_417))
      | U_417 != bot_bo844097828e_bool ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

fof(f_192_3,plain,
    ! [U_417,U_418] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_418),U_417))
      | U_417 != bot_bo844097828e_bool ),
    inference(definitional_conversion,[status(esa)],[f_192_2]) ).

cnf(f_192_4,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_418),U_417))
    | U_417 != bot_bo844097828e_bool ),
    inference(clausify,[status(thm)],[f_192_3]) ).

fof(f_193_1,plain,
    ! [P_1] :
      ( ( collec1613912337l_bool(P_1) = bot_bo1537088220l_bool
        | ? [X_1] :
            ( hBOOL(hAPP_f1935102916l_bool(P_1,X_1))
            & is_fun1661590463l_bool(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_f1935102916l_bool(P_1,X_1))
            | ~ is_fun1661590463l_bool(X_1) )
        | collec1613912337l_bool(P_1) != bot_bo1537088220l_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_139_Collect__empty__eq]) ).

fof(f_193_2,plain,
    ! [U_421] :
      ( ( collec1613912337l_bool(U_421) = bot_bo1537088220l_bool
        | ? [U_420] :
            ( hBOOL(hAPP_f1935102916l_bool(U_421,U_420))
            & is_fun1661590463l_bool(U_420) ) )
      & ( ! [U_419] :
            ( ~ hBOOL(hAPP_f1935102916l_bool(U_421,U_419))
            | ~ is_fun1661590463l_bool(U_419) )
        | collec1613912337l_bool(U_421) != bot_bo1537088220l_bool ) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

fof(f_193_3,plain,
    ( ! [U_423] :
        ( collec1613912337l_bool(U_423) = bot_bo1537088220l_bool
        | ? [U_420] :
            ( hBOOL(hAPP_f1935102916l_bool(U_423,U_420))
            & is_fun1661590463l_bool(U_420) ) )
    & ! [U_422] :
        ( ! [U_419] :
            ( ~ hBOOL(hAPP_f1935102916l_bool(U_422,U_419))
            | ~ is_fun1661590463l_bool(U_419) )
        | collec1613912337l_bool(U_422) != bot_bo1537088220l_bool ) ),
    inference(miniscope,[status(thm)],[f_193_2]) ).

fof(f_193_4,plain,
    ( ! [U_423] :
        ( collec1613912337l_bool(U_423) = bot_bo1537088220l_bool
        | ( hBOOL(hAPP_f1935102916l_bool(U_423,sK1(U_423)))
          & is_fun1661590463l_bool(sK1(U_423)) ) )
    & ! [U_422] :
        ( ! [U_419] :
            ( ~ hBOOL(hAPP_f1935102916l_bool(U_422,U_419))
            | ~ is_fun1661590463l_bool(U_419) )
        | collec1613912337l_bool(U_422) != bot_bo1537088220l_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_420,sK1(U_423))],[f_193_3]) ).

fof(f_193_5,plain,
    ( ! [U_423] :
        ( hBOOL(hAPP_f1935102916l_bool(U_423,sK1(U_423)))
        | ~ sP17(U_423) )
    & ! [U_423] :
        ( is_fun1661590463l_bool(sK1(U_423))
        | ~ sP17(U_423) )
    & ! [U_423] :
        ( collec1613912337l_bool(U_423) = bot_bo1537088220l_bool
        | sP17(U_423) )
    & ! [U_419,U_422] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(U_422,U_419))
        | ~ is_fun1661590463l_bool(U_419)
        | collec1613912337l_bool(U_422) != bot_bo1537088220l_bool ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_193_4]) ).

cnf(f_193_6,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(U_422,U_419))
    | ~ is_fun1661590463l_bool(U_419)
    | collec1613912337l_bool(U_422) != bot_bo1537088220l_bool ),
    inference(clausify,[status(thm)],[f_193_5]) ).

cnf(f_193_7,plain,
    ( collec1613912337l_bool(U_423) = bot_bo1537088220l_bool
    | sP17(U_423) ),
    inference(clausify,[status(thm)],[f_193_5]) ).

cnf(f_193_8,plain,
    ( is_fun1661590463l_bool(sK1(U_423))
    | ~ sP17(U_423) ),
    inference(clausify,[status(thm)],[f_193_5]) ).

cnf(f_193_9,plain,
    ( hBOOL(hAPP_f1935102916l_bool(U_423,sK1(U_423)))
    | ~ sP17(U_423) ),
    inference(clausify,[status(thm)],[f_193_5]) ).

fof(f_194_1,plain,
    ! [P_1] :
      ( ( collec488126193l_bool(P_1) = bot_bo1761158942l_bool
        | ? [X_1] : hBOOL(hAPP_f166538662l_bool(P_1,X_1)) )
      & ( ! [X_1] : ~ hBOOL(hAPP_f166538662l_bool(P_1,X_1))
        | collec488126193l_bool(P_1) != bot_bo1761158942l_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_140_Collect__empty__eq]) ).

fof(f_194_2,plain,
    ! [U_426] :
      ( ( collec488126193l_bool(U_426) = bot_bo1761158942l_bool
        | ? [U_425] : hBOOL(hAPP_f166538662l_bool(U_426,U_425)) )
      & ( ! [U_424] : ~ hBOOL(hAPP_f166538662l_bool(U_426,U_424))
        | collec488126193l_bool(U_426) != bot_bo1761158942l_bool ) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

fof(f_194_3,plain,
    ( ! [U_428] :
        ( collec488126193l_bool(U_428) = bot_bo1761158942l_bool
        | ? [U_425] : hBOOL(hAPP_f166538662l_bool(U_428,U_425)) )
    & ! [U_427] :
        ( ! [U_424] : ~ hBOOL(hAPP_f166538662l_bool(U_427,U_424))
        | collec488126193l_bool(U_427) != bot_bo1761158942l_bool ) ),
    inference(miniscope,[status(thm)],[f_194_2]) ).

fof(f_194_4,plain,
    ( ! [U_428] :
        ( collec488126193l_bool(U_428) = bot_bo1761158942l_bool
        | hBOOL(hAPP_f166538662l_bool(U_428,sK2(U_428))) )
    & ! [U_427] :
        ( ! [U_424] : ~ hBOOL(hAPP_f166538662l_bool(U_427,U_424))
        | collec488126193l_bool(U_427) != bot_bo1761158942l_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_425,sK2(U_428))],[f_194_3]) ).

fof(f_194_5,plain,
    ( ! [U_428] :
        ( collec488126193l_bool(U_428) = bot_bo1761158942l_bool
        | hBOOL(hAPP_f166538662l_bool(U_428,sK2(U_428))) )
    & ! [U_424,U_427] :
        ( ~ hBOOL(hAPP_f166538662l_bool(U_427,U_424))
        | collec488126193l_bool(U_427) != bot_bo1761158942l_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_194_4]) ).

cnf(f_194_6,plain,
    ( ~ hBOOL(hAPP_f166538662l_bool(U_427,U_424))
    | collec488126193l_bool(U_427) != bot_bo1761158942l_bool ),
    inference(clausify,[status(thm)],[f_194_5]) ).

cnf(f_194_7,plain,
    ( collec488126193l_bool(U_428) = bot_bo1761158942l_bool
    | hBOOL(hAPP_f166538662l_bool(U_428,sK2(U_428))) ),
    inference(clausify,[status(thm)],[f_194_5]) ).

fof(f_195_1,plain,
    ! [P_1] :
      ( ( collec1823980261e_bool(P_1) = bot_bo535777328l_bool
        | ? [X_1] : hBOOL(hAPP_f971112728l_bool(P_1,X_1)) )
      & ( ! [X_1] : ~ hBOOL(hAPP_f971112728l_bool(P_1,X_1))
        | collec1823980261e_bool(P_1) != bot_bo535777328l_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_141_Collect__empty__eq]) ).

fof(f_195_2,plain,
    ! [U_431] :
      ( ( collec1823980261e_bool(U_431) = bot_bo535777328l_bool
        | ? [U_430] : hBOOL(hAPP_f971112728l_bool(U_431,U_430)) )
      & ( ! [U_429] : ~ hBOOL(hAPP_f971112728l_bool(U_431,U_429))
        | collec1823980261e_bool(U_431) != bot_bo535777328l_bool ) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

fof(f_195_3,plain,
    ( ! [U_433] :
        ( collec1823980261e_bool(U_433) = bot_bo535777328l_bool
        | ? [U_430] : hBOOL(hAPP_f971112728l_bool(U_433,U_430)) )
    & ! [U_432] :
        ( ! [U_429] : ~ hBOOL(hAPP_f971112728l_bool(U_432,U_429))
        | collec1823980261e_bool(U_432) != bot_bo535777328l_bool ) ),
    inference(miniscope,[status(thm)],[f_195_2]) ).

fof(f_195_4,plain,
    ( ! [U_433] :
        ( collec1823980261e_bool(U_433) = bot_bo535777328l_bool
        | hBOOL(hAPP_f971112728l_bool(U_433,sK3(U_433))) )
    & ! [U_432] :
        ( ! [U_429] : ~ hBOOL(hAPP_f971112728l_bool(U_432,U_429))
        | collec1823980261e_bool(U_432) != bot_bo535777328l_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_430,sK3(U_433))],[f_195_3]) ).

fof(f_195_5,plain,
    ( ! [U_433] :
        ( collec1823980261e_bool(U_433) = bot_bo535777328l_bool
        | hBOOL(hAPP_f971112728l_bool(U_433,sK3(U_433))) )
    & ! [U_429,U_432] :
        ( ~ hBOOL(hAPP_f971112728l_bool(U_432,U_429))
        | collec1823980261e_bool(U_432) != bot_bo535777328l_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_195_4]) ).

cnf(f_195_6,plain,
    ( ~ hBOOL(hAPP_f971112728l_bool(U_432,U_429))
    | collec1823980261e_bool(U_432) != bot_bo535777328l_bool ),
    inference(clausify,[status(thm)],[f_195_5]) ).

cnf(f_195_7,plain,
    ( collec1823980261e_bool(U_433) = bot_bo535777328l_bool
    | hBOOL(hAPP_f971112728l_bool(U_433,sK3(U_433))) ),
    inference(clausify,[status(thm)],[f_195_5]) ).

fof(f_196_1,plain,
    ! [P_1] :
      ( ( collec1974731493e_bool(P_1) = bot_bo1649642514l_bool
        | ? [X_1] :
            ( hBOOL(hAPP_f1664156314l_bool(P_1,X_1))
            & is_fun_pname_bool(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,X_1))
            | ~ is_fun_pname_bool(X_1) )
        | collec1974731493e_bool(P_1) != bot_bo1649642514l_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_142_Collect__empty__eq]) ).

fof(f_196_2,plain,
    ! [U_436] :
      ( ( collec1974731493e_bool(U_436) = bot_bo1649642514l_bool
        | ? [U_435] :
            ( hBOOL(hAPP_f1664156314l_bool(U_436,U_435))
            & is_fun_pname_bool(U_435) ) )
      & ( ! [U_434] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(U_436,U_434))
            | ~ is_fun_pname_bool(U_434) )
        | collec1974731493e_bool(U_436) != bot_bo1649642514l_bool ) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

fof(f_196_3,plain,
    ( ! [U_438] :
        ( collec1974731493e_bool(U_438) = bot_bo1649642514l_bool
        | ? [U_435] :
            ( hBOOL(hAPP_f1664156314l_bool(U_438,U_435))
            & is_fun_pname_bool(U_435) ) )
    & ! [U_437] :
        ( ! [U_434] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(U_437,U_434))
            | ~ is_fun_pname_bool(U_434) )
        | collec1974731493e_bool(U_437) != bot_bo1649642514l_bool ) ),
    inference(miniscope,[status(thm)],[f_196_2]) ).

fof(f_196_4,plain,
    ( ! [U_438] :
        ( collec1974731493e_bool(U_438) = bot_bo1649642514l_bool
        | ( hBOOL(hAPP_f1664156314l_bool(U_438,sK4(U_438)))
          & is_fun_pname_bool(sK4(U_438)) ) )
    & ! [U_437] :
        ( ! [U_434] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(U_437,U_434))
            | ~ is_fun_pname_bool(U_434) )
        | collec1974731493e_bool(U_437) != bot_bo1649642514l_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_435,sK4(U_438))],[f_196_3]) ).

fof(f_196_5,plain,
    ( ! [U_438] :
        ( hBOOL(hAPP_f1664156314l_bool(U_438,sK4(U_438)))
        | ~ sP18(U_438) )
    & ! [U_438] :
        ( is_fun_pname_bool(sK4(U_438))
        | ~ sP18(U_438) )
    & ! [U_438] :
        ( collec1974731493e_bool(U_438) = bot_bo1649642514l_bool
        | sP18(U_438) )
    & ! [U_434,U_437] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(U_437,U_434))
        | ~ is_fun_pname_bool(U_434)
        | collec1974731493e_bool(U_437) != bot_bo1649642514l_bool ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_196_4]) ).

cnf(f_196_6,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(U_437,U_434))
    | ~ is_fun_pname_bool(U_434)
    | collec1974731493e_bool(U_437) != bot_bo1649642514l_bool ),
    inference(clausify,[status(thm)],[f_196_5]) ).

cnf(f_196_7,plain,
    ( collec1974731493e_bool(U_438) = bot_bo1649642514l_bool
    | sP18(U_438) ),
    inference(clausify,[status(thm)],[f_196_5]) ).

cnf(f_196_8,plain,
    ( is_fun_pname_bool(sK4(U_438))
    | ~ sP18(U_438) ),
    inference(clausify,[status(thm)],[f_196_5]) ).

cnf(f_196_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_438,sK4(U_438)))
    | ~ sP18(U_438) ),
    inference(clausify,[status(thm)],[f_196_5]) ).

fof(f_197_1,plain,
    ! [P_1] :
      ( ( collec307967673_state(P_1) = bot_bo620288102e_bool
        | ? [X_1] : hBOOL(hAPP_H78829294e_bool(P_1,X_1)) )
      & ( ! [X_1] : ~ hBOOL(hAPP_H78829294e_bool(P_1,X_1))
        | collec307967673_state(P_1) != bot_bo620288102e_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_143_Collect__empty__eq]) ).

fof(f_197_2,plain,
    ! [U_441] :
      ( ( collec307967673_state(U_441) = bot_bo620288102e_bool
        | ? [U_440] : hBOOL(hAPP_H78829294e_bool(U_441,U_440)) )
      & ( ! [U_439] : ~ hBOOL(hAPP_H78829294e_bool(U_441,U_439))
        | collec307967673_state(U_441) != bot_bo620288102e_bool ) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

fof(f_197_3,plain,
    ( ! [U_443] :
        ( collec307967673_state(U_443) = bot_bo620288102e_bool
        | ? [U_440] : hBOOL(hAPP_H78829294e_bool(U_443,U_440)) )
    & ! [U_442] :
        ( ! [U_439] : ~ hBOOL(hAPP_H78829294e_bool(U_442,U_439))
        | collec307967673_state(U_442) != bot_bo620288102e_bool ) ),
    inference(miniscope,[status(thm)],[f_197_2]) ).

fof(f_197_4,plain,
    ( ! [U_443] :
        ( collec307967673_state(U_443) = bot_bo620288102e_bool
        | hBOOL(hAPP_H78829294e_bool(U_443,sK5(U_443))) )
    & ! [U_442] :
        ( ! [U_439] : ~ hBOOL(hAPP_H78829294e_bool(U_442,U_439))
        | collec307967673_state(U_442) != bot_bo620288102e_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_440,sK5(U_443))],[f_197_3]) ).

fof(f_197_5,plain,
    ( ! [U_443] :
        ( collec307967673_state(U_443) = bot_bo620288102e_bool
        | hBOOL(hAPP_H78829294e_bool(U_443,sK5(U_443))) )
    & ! [U_439,U_442] :
        ( ~ hBOOL(hAPP_H78829294e_bool(U_442,U_439))
        | collec307967673_state(U_442) != bot_bo620288102e_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_197_4]) ).

cnf(f_197_6,plain,
    ( ~ hBOOL(hAPP_H78829294e_bool(U_442,U_439))
    | collec307967673_state(U_442) != bot_bo620288102e_bool ),
    inference(clausify,[status(thm)],[f_197_5]) ).

cnf(f_197_7,plain,
    ( collec307967673_state(U_443) = bot_bo620288102e_bool
    | hBOOL(hAPP_H78829294e_bool(U_443,sK5(U_443))) ),
    inference(clausify,[status(thm)],[f_197_5]) ).

fof(f_198_1,plain,
    ! [P_1] :
      ( ( collect_pname(P_1) = bot_bo844097828e_bool
        | ? [X_1] :
            ( hBOOL(hAPP_pname_bool(P_1,X_1))
            & is_pname(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_pname_bool(P_1,X_1))
            | ~ is_pname(X_1) )
        | collect_pname(P_1) != bot_bo844097828e_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_144_Collect__empty__eq]) ).

fof(f_198_2,plain,
    ! [U_446] :
      ( ( collect_pname(U_446) = bot_bo844097828e_bool
        | ? [U_445] :
            ( hBOOL(hAPP_pname_bool(U_446,U_445))
            & is_pname(U_445) ) )
      & ( ! [U_444] :
            ( ~ hBOOL(hAPP_pname_bool(U_446,U_444))
            | ~ is_pname(U_444) )
        | collect_pname(U_446) != bot_bo844097828e_bool ) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

fof(f_198_3,plain,
    ( ! [U_448] :
        ( collect_pname(U_448) = bot_bo844097828e_bool
        | ? [U_445] :
            ( hBOOL(hAPP_pname_bool(U_448,U_445))
            & is_pname(U_445) ) )
    & ! [U_447] :
        ( ! [U_444] :
            ( ~ hBOOL(hAPP_pname_bool(U_447,U_444))
            | ~ is_pname(U_444) )
        | collect_pname(U_447) != bot_bo844097828e_bool ) ),
    inference(miniscope,[status(thm)],[f_198_2]) ).

fof(f_198_4,plain,
    ( ! [U_448] :
        ( collect_pname(U_448) = bot_bo844097828e_bool
        | ( hBOOL(hAPP_pname_bool(U_448,sK6(U_448)))
          & is_pname(sK6(U_448)) ) )
    & ! [U_447] :
        ( ! [U_444] :
            ( ~ hBOOL(hAPP_pname_bool(U_447,U_444))
            | ~ is_pname(U_444) )
        | collect_pname(U_447) != bot_bo844097828e_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_445,sK6(U_448))],[f_198_3]) ).

fof(f_198_5,plain,
    ( ! [U_448] :
        ( hBOOL(hAPP_pname_bool(U_448,sK6(U_448)))
        | ~ sP19(U_448) )
    & ! [U_448] :
        ( is_pname(sK6(U_448))
        | ~ sP19(U_448) )
    & ! [U_448] :
        ( collect_pname(U_448) = bot_bo844097828e_bool
        | sP19(U_448) )
    & ! [U_444,U_447] :
        ( ~ hBOOL(hAPP_pname_bool(U_447,U_444))
        | ~ is_pname(U_444)
        | collect_pname(U_447) != bot_bo844097828e_bool ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_198_4]) ).

cnf(f_198_6,plain,
    ( ~ hBOOL(hAPP_pname_bool(U_447,U_444))
    | ~ is_pname(U_444)
    | collect_pname(U_447) != bot_bo844097828e_bool ),
    inference(clausify,[status(thm)],[f_198_5]) ).

cnf(f_198_7,plain,
    ( collect_pname(U_448) = bot_bo844097828e_bool
    | sP19(U_448) ),
    inference(clausify,[status(thm)],[f_198_5]) ).

cnf(f_198_8,plain,
    ( is_pname(sK6(U_448))
    | ~ sP19(U_448) ),
    inference(clausify,[status(thm)],[f_198_5]) ).

cnf(f_198_9,plain,
    ( hBOOL(hAPP_pname_bool(U_448,sK6(U_448)))
    | ~ sP19(U_448) ),
    inference(clausify,[status(thm)],[f_198_5]) ).

fof(f_199_1,plain,
    ! [C_1] : ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,C_1),bot_bo1649642514l_bool)),
    inference(fof_nnf,[status(thm)],[fact_145_empty__iff]) ).

fof(f_199_2,plain,
    ! [U_449] : ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_449),bot_bo1649642514l_bool)),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

fof(f_199_3,plain,
    ! [U_449] : ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_449),bot_bo1649642514l_bool)),
    inference(definitional_conversion,[status(esa)],[f_199_2]) ).

cnf(f_199_4,plain,
    ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_449),bot_bo1649642514l_bool)),
    inference(clausify,[status(thm)],[f_199_3]) ).

fof(f_200_1,plain,
    ! [C_1] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,C_1),bot_bo535777328l_bool)),
    inference(fof_nnf,[status(thm)],[fact_146_empty__iff]) ).

fof(f_200_2,plain,
    ! [U_450] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_450),bot_bo535777328l_bool)),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

fof(f_200_3,plain,
    ! [U_450] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_450),bot_bo535777328l_bool)),
    inference(definitional_conversion,[status(esa)],[f_200_2]) ).

cnf(f_200_4,plain,
    ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_450),bot_bo535777328l_bool)),
    inference(clausify,[status(thm)],[f_200_3]) ).

fof(f_201_1,plain,
    ! [C_1] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,C_1),bot_bo620288102e_bool)),
    inference(fof_nnf,[status(thm)],[fact_147_empty__iff]) ).

fof(f_201_2,plain,
    ! [U_451] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_451),bot_bo620288102e_bool)),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

fof(f_201_3,plain,
    ! [U_451] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_451),bot_bo620288102e_bool)),
    inference(definitional_conversion,[status(esa)],[f_201_2]) ).

cnf(f_201_4,plain,
    ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_451),bot_bo620288102e_bool)),
    inference(clausify,[status(thm)],[f_201_3]) ).

fof(f_202_1,plain,
    ! [C_1] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),bot_bo844097828e_bool)),
    inference(fof_nnf,[status(thm)],[fact_148_empty__iff]) ).

fof(f_202_2,plain,
    ! [U_452] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_452),bot_bo844097828e_bool)),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

fof(f_202_3,plain,
    ! [U_452] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_452),bot_bo844097828e_bool)),
    inference(definitional_conversion,[status(esa)],[f_202_2]) ).

cnf(f_202_4,plain,
    ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_452),bot_bo844097828e_bool)),
    inference(clausify,[status(thm)],[f_202_3]) ).

fof(f_203_1,plain,
    ! [P_1] :
      ( ( bot_bo1537088220l_bool = collec1613912337l_bool(P_1)
        | ? [X_1] :
            ( hBOOL(hAPP_f1935102916l_bool(P_1,X_1))
            & is_fun1661590463l_bool(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_f1935102916l_bool(P_1,X_1))
            | ~ is_fun1661590463l_bool(X_1) )
        | bot_bo1537088220l_bool != collec1613912337l_bool(P_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_149_empty__Collect__eq]) ).

fof(f_203_2,plain,
    ! [U_455] :
      ( ( bot_bo1537088220l_bool = collec1613912337l_bool(U_455)
        | ? [U_454] :
            ( hBOOL(hAPP_f1935102916l_bool(U_455,U_454))
            & is_fun1661590463l_bool(U_454) ) )
      & ( ! [U_453] :
            ( ~ hBOOL(hAPP_f1935102916l_bool(U_455,U_453))
            | ~ is_fun1661590463l_bool(U_453) )
        | bot_bo1537088220l_bool != collec1613912337l_bool(U_455) ) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

fof(f_203_3,plain,
    ( ! [U_457] :
        ( bot_bo1537088220l_bool = collec1613912337l_bool(U_457)
        | ? [U_454] :
            ( hBOOL(hAPP_f1935102916l_bool(U_457,U_454))
            & is_fun1661590463l_bool(U_454) ) )
    & ! [U_456] :
        ( ! [U_453] :
            ( ~ hBOOL(hAPP_f1935102916l_bool(U_456,U_453))
            | ~ is_fun1661590463l_bool(U_453) )
        | bot_bo1537088220l_bool != collec1613912337l_bool(U_456) ) ),
    inference(miniscope,[status(thm)],[f_203_2]) ).

fof(f_203_4,plain,
    ( ! [U_457] :
        ( bot_bo1537088220l_bool = collec1613912337l_bool(U_457)
        | ( hBOOL(hAPP_f1935102916l_bool(U_457,sK7(U_457)))
          & is_fun1661590463l_bool(sK7(U_457)) ) )
    & ! [U_456] :
        ( ! [U_453] :
            ( ~ hBOOL(hAPP_f1935102916l_bool(U_456,U_453))
            | ~ is_fun1661590463l_bool(U_453) )
        | bot_bo1537088220l_bool != collec1613912337l_bool(U_456) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_454,sK7(U_457))],[f_203_3]) ).

fof(f_203_5,plain,
    ( ! [U_457] :
        ( hBOOL(hAPP_f1935102916l_bool(U_457,sK7(U_457)))
        | ~ sP20(U_457) )
    & ! [U_457] :
        ( is_fun1661590463l_bool(sK7(U_457))
        | ~ sP20(U_457) )
    & ! [U_457] :
        ( bot_bo1537088220l_bool = collec1613912337l_bool(U_457)
        | sP20(U_457) )
    & ! [U_453,U_456] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(U_456,U_453))
        | ~ is_fun1661590463l_bool(U_453)
        | bot_bo1537088220l_bool != collec1613912337l_bool(U_456) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_203_4]) ).

cnf(f_203_6,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(U_456,U_453))
    | ~ is_fun1661590463l_bool(U_453)
    | bot_bo1537088220l_bool != collec1613912337l_bool(U_456) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

cnf(f_203_7,plain,
    ( bot_bo1537088220l_bool = collec1613912337l_bool(U_457)
    | sP20(U_457) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

cnf(f_203_8,plain,
    ( is_fun1661590463l_bool(sK7(U_457))
    | ~ sP20(U_457) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

cnf(f_203_9,plain,
    ( hBOOL(hAPP_f1935102916l_bool(U_457,sK7(U_457)))
    | ~ sP20(U_457) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

fof(f_204_1,plain,
    ! [P_1] :
      ( ( bot_bo1761158942l_bool = collec488126193l_bool(P_1)
        | ? [X_1] : hBOOL(hAPP_f166538662l_bool(P_1,X_1)) )
      & ( ! [X_1] : ~ hBOOL(hAPP_f166538662l_bool(P_1,X_1))
        | bot_bo1761158942l_bool != collec488126193l_bool(P_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_150_empty__Collect__eq]) ).

fof(f_204_2,plain,
    ! [U_460] :
      ( ( bot_bo1761158942l_bool = collec488126193l_bool(U_460)
        | ? [U_459] : hBOOL(hAPP_f166538662l_bool(U_460,U_459)) )
      & ( ! [U_458] : ~ hBOOL(hAPP_f166538662l_bool(U_460,U_458))
        | bot_bo1761158942l_bool != collec488126193l_bool(U_460) ) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

fof(f_204_3,plain,
    ( ! [U_462] :
        ( bot_bo1761158942l_bool = collec488126193l_bool(U_462)
        | ? [U_459] : hBOOL(hAPP_f166538662l_bool(U_462,U_459)) )
    & ! [U_461] :
        ( ! [U_458] : ~ hBOOL(hAPP_f166538662l_bool(U_461,U_458))
        | bot_bo1761158942l_bool != collec488126193l_bool(U_461) ) ),
    inference(miniscope,[status(thm)],[f_204_2]) ).

fof(f_204_4,plain,
    ( ! [U_462] :
        ( bot_bo1761158942l_bool = collec488126193l_bool(U_462)
        | hBOOL(hAPP_f166538662l_bool(U_462,sK8(U_462))) )
    & ! [U_461] :
        ( ! [U_458] : ~ hBOOL(hAPP_f166538662l_bool(U_461,U_458))
        | bot_bo1761158942l_bool != collec488126193l_bool(U_461) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_459,sK8(U_462))],[f_204_3]) ).

fof(f_204_5,plain,
    ( ! [U_462] :
        ( bot_bo1761158942l_bool = collec488126193l_bool(U_462)
        | hBOOL(hAPP_f166538662l_bool(U_462,sK8(U_462))) )
    & ! [U_458,U_461] :
        ( ~ hBOOL(hAPP_f166538662l_bool(U_461,U_458))
        | bot_bo1761158942l_bool != collec488126193l_bool(U_461) ) ),
    inference(definitional_conversion,[status(esa)],[f_204_4]) ).

cnf(f_204_6,plain,
    ( ~ hBOOL(hAPP_f166538662l_bool(U_461,U_458))
    | bot_bo1761158942l_bool != collec488126193l_bool(U_461) ),
    inference(clausify,[status(thm)],[f_204_5]) ).

cnf(f_204_7,plain,
    ( bot_bo1761158942l_bool = collec488126193l_bool(U_462)
    | hBOOL(hAPP_f166538662l_bool(U_462,sK8(U_462))) ),
    inference(clausify,[status(thm)],[f_204_5]) ).

fof(f_205_1,plain,
    ! [P_1] :
      ( ( bot_bo535777328l_bool = collec1823980261e_bool(P_1)
        | ? [X_1] : hBOOL(hAPP_f971112728l_bool(P_1,X_1)) )
      & ( ! [X_1] : ~ hBOOL(hAPP_f971112728l_bool(P_1,X_1))
        | bot_bo535777328l_bool != collec1823980261e_bool(P_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_151_empty__Collect__eq]) ).

fof(f_205_2,plain,
    ! [U_465] :
      ( ( bot_bo535777328l_bool = collec1823980261e_bool(U_465)
        | ? [U_464] : hBOOL(hAPP_f971112728l_bool(U_465,U_464)) )
      & ( ! [U_463] : ~ hBOOL(hAPP_f971112728l_bool(U_465,U_463))
        | bot_bo535777328l_bool != collec1823980261e_bool(U_465) ) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

fof(f_205_3,plain,
    ( ! [U_467] :
        ( bot_bo535777328l_bool = collec1823980261e_bool(U_467)
        | ? [U_464] : hBOOL(hAPP_f971112728l_bool(U_467,U_464)) )
    & ! [U_466] :
        ( ! [U_463] : ~ hBOOL(hAPP_f971112728l_bool(U_466,U_463))
        | bot_bo535777328l_bool != collec1823980261e_bool(U_466) ) ),
    inference(miniscope,[status(thm)],[f_205_2]) ).

fof(f_205_4,plain,
    ( ! [U_467] :
        ( bot_bo535777328l_bool = collec1823980261e_bool(U_467)
        | hBOOL(hAPP_f971112728l_bool(U_467,sK9(U_467))) )
    & ! [U_466] :
        ( ! [U_463] : ~ hBOOL(hAPP_f971112728l_bool(U_466,U_463))
        | bot_bo535777328l_bool != collec1823980261e_bool(U_466) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_464,sK9(U_467))],[f_205_3]) ).

fof(f_205_5,plain,
    ( ! [U_467] :
        ( bot_bo535777328l_bool = collec1823980261e_bool(U_467)
        | hBOOL(hAPP_f971112728l_bool(U_467,sK9(U_467))) )
    & ! [U_463,U_466] :
        ( ~ hBOOL(hAPP_f971112728l_bool(U_466,U_463))
        | bot_bo535777328l_bool != collec1823980261e_bool(U_466) ) ),
    inference(definitional_conversion,[status(esa)],[f_205_4]) ).

cnf(f_205_6,plain,
    ( ~ hBOOL(hAPP_f971112728l_bool(U_466,U_463))
    | bot_bo535777328l_bool != collec1823980261e_bool(U_466) ),
    inference(clausify,[status(thm)],[f_205_5]) ).

cnf(f_205_7,plain,
    ( bot_bo535777328l_bool = collec1823980261e_bool(U_467)
    | hBOOL(hAPP_f971112728l_bool(U_467,sK9(U_467))) ),
    inference(clausify,[status(thm)],[f_205_5]) ).

fof(f_206_1,plain,
    ! [P_1] :
      ( ( bot_bo1649642514l_bool = collec1974731493e_bool(P_1)
        | ? [X_1] :
            ( hBOOL(hAPP_f1664156314l_bool(P_1,X_1))
            & is_fun_pname_bool(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,X_1))
            | ~ is_fun_pname_bool(X_1) )
        | bot_bo1649642514l_bool != collec1974731493e_bool(P_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_152_empty__Collect__eq]) ).

fof(f_206_2,plain,
    ! [U_470] :
      ( ( bot_bo1649642514l_bool = collec1974731493e_bool(U_470)
        | ? [U_469] :
            ( hBOOL(hAPP_f1664156314l_bool(U_470,U_469))
            & is_fun_pname_bool(U_469) ) )
      & ( ! [U_468] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(U_470,U_468))
            | ~ is_fun_pname_bool(U_468) )
        | bot_bo1649642514l_bool != collec1974731493e_bool(U_470) ) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

fof(f_206_3,plain,
    ( ! [U_472] :
        ( bot_bo1649642514l_bool = collec1974731493e_bool(U_472)
        | ? [U_469] :
            ( hBOOL(hAPP_f1664156314l_bool(U_472,U_469))
            & is_fun_pname_bool(U_469) ) )
    & ! [U_471] :
        ( ! [U_468] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(U_471,U_468))
            | ~ is_fun_pname_bool(U_468) )
        | bot_bo1649642514l_bool != collec1974731493e_bool(U_471) ) ),
    inference(miniscope,[status(thm)],[f_206_2]) ).

fof(f_206_4,plain,
    ( ! [U_472] :
        ( bot_bo1649642514l_bool = collec1974731493e_bool(U_472)
        | ( hBOOL(hAPP_f1664156314l_bool(U_472,sK10(U_472)))
          & is_fun_pname_bool(sK10(U_472)) ) )
    & ! [U_471] :
        ( ! [U_468] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(U_471,U_468))
            | ~ is_fun_pname_bool(U_468) )
        | bot_bo1649642514l_bool != collec1974731493e_bool(U_471) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_469,sK10(U_472))],[f_206_3]) ).

fof(f_206_5,plain,
    ( ! [U_472] :
        ( hBOOL(hAPP_f1664156314l_bool(U_472,sK10(U_472)))
        | ~ sP21(U_472) )
    & ! [U_472] :
        ( is_fun_pname_bool(sK10(U_472))
        | ~ sP21(U_472) )
    & ! [U_472] :
        ( bot_bo1649642514l_bool = collec1974731493e_bool(U_472)
        | sP21(U_472) )
    & ! [U_468,U_471] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(U_471,U_468))
        | ~ is_fun_pname_bool(U_468)
        | bot_bo1649642514l_bool != collec1974731493e_bool(U_471) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_206_4]) ).

cnf(f_206_6,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(U_471,U_468))
    | ~ is_fun_pname_bool(U_468)
    | bot_bo1649642514l_bool != collec1974731493e_bool(U_471) ),
    inference(clausify,[status(thm)],[f_206_5]) ).

cnf(f_206_7,plain,
    ( bot_bo1649642514l_bool = collec1974731493e_bool(U_472)
    | sP21(U_472) ),
    inference(clausify,[status(thm)],[f_206_5]) ).

cnf(f_206_8,plain,
    ( is_fun_pname_bool(sK10(U_472))
    | ~ sP21(U_472) ),
    inference(clausify,[status(thm)],[f_206_5]) ).

cnf(f_206_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_472,sK10(U_472)))
    | ~ sP21(U_472) ),
    inference(clausify,[status(thm)],[f_206_5]) ).

fof(f_207_1,plain,
    ! [P_1] :
      ( ( bot_bo620288102e_bool = collec307967673_state(P_1)
        | ? [X_1] : hBOOL(hAPP_H78829294e_bool(P_1,X_1)) )
      & ( ! [X_1] : ~ hBOOL(hAPP_H78829294e_bool(P_1,X_1))
        | bot_bo620288102e_bool != collec307967673_state(P_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_153_empty__Collect__eq]) ).

fof(f_207_2,plain,
    ! [U_475] :
      ( ( bot_bo620288102e_bool = collec307967673_state(U_475)
        | ? [U_474] : hBOOL(hAPP_H78829294e_bool(U_475,U_474)) )
      & ( ! [U_473] : ~ hBOOL(hAPP_H78829294e_bool(U_475,U_473))
        | bot_bo620288102e_bool != collec307967673_state(U_475) ) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

fof(f_207_3,plain,
    ( ! [U_477] :
        ( bot_bo620288102e_bool = collec307967673_state(U_477)
        | ? [U_474] : hBOOL(hAPP_H78829294e_bool(U_477,U_474)) )
    & ! [U_476] :
        ( ! [U_473] : ~ hBOOL(hAPP_H78829294e_bool(U_476,U_473))
        | bot_bo620288102e_bool != collec307967673_state(U_476) ) ),
    inference(miniscope,[status(thm)],[f_207_2]) ).

fof(f_207_4,plain,
    ( ! [U_477] :
        ( bot_bo620288102e_bool = collec307967673_state(U_477)
        | hBOOL(hAPP_H78829294e_bool(U_477,sK11(U_477))) )
    & ! [U_476] :
        ( ! [U_473] : ~ hBOOL(hAPP_H78829294e_bool(U_476,U_473))
        | bot_bo620288102e_bool != collec307967673_state(U_476) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_474,sK11(U_477))],[f_207_3]) ).

fof(f_207_5,plain,
    ( ! [U_477] :
        ( bot_bo620288102e_bool = collec307967673_state(U_477)
        | hBOOL(hAPP_H78829294e_bool(U_477,sK11(U_477))) )
    & ! [U_473,U_476] :
        ( ~ hBOOL(hAPP_H78829294e_bool(U_476,U_473))
        | bot_bo620288102e_bool != collec307967673_state(U_476) ) ),
    inference(definitional_conversion,[status(esa)],[f_207_4]) ).

cnf(f_207_6,plain,
    ( ~ hBOOL(hAPP_H78829294e_bool(U_476,U_473))
    | bot_bo620288102e_bool != collec307967673_state(U_476) ),
    inference(clausify,[status(thm)],[f_207_5]) ).

cnf(f_207_7,plain,
    ( bot_bo620288102e_bool = collec307967673_state(U_477)
    | hBOOL(hAPP_H78829294e_bool(U_477,sK11(U_477))) ),
    inference(clausify,[status(thm)],[f_207_5]) ).

fof(f_208_1,plain,
    ! [P_1] :
      ( ( bot_bo844097828e_bool = collect_pname(P_1)
        | ? [X_1] :
            ( hBOOL(hAPP_pname_bool(P_1,X_1))
            & is_pname(X_1) ) )
      & ( ! [X_1] :
            ( ~ hBOOL(hAPP_pname_bool(P_1,X_1))
            | ~ is_pname(X_1) )
        | bot_bo844097828e_bool != collect_pname(P_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_154_empty__Collect__eq]) ).

fof(f_208_2,plain,
    ! [U_480] :
      ( ( bot_bo844097828e_bool = collect_pname(U_480)
        | ? [U_479] :
            ( hBOOL(hAPP_pname_bool(U_480,U_479))
            & is_pname(U_479) ) )
      & ( ! [U_478] :
            ( ~ hBOOL(hAPP_pname_bool(U_480,U_478))
            | ~ is_pname(U_478) )
        | bot_bo844097828e_bool != collect_pname(U_480) ) ),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

fof(f_208_3,plain,
    ( ! [U_482] :
        ( bot_bo844097828e_bool = collect_pname(U_482)
        | ? [U_479] :
            ( hBOOL(hAPP_pname_bool(U_482,U_479))
            & is_pname(U_479) ) )
    & ! [U_481] :
        ( ! [U_478] :
            ( ~ hBOOL(hAPP_pname_bool(U_481,U_478))
            | ~ is_pname(U_478) )
        | bot_bo844097828e_bool != collect_pname(U_481) ) ),
    inference(miniscope,[status(thm)],[f_208_2]) ).

fof(f_208_4,plain,
    ( ! [U_482] :
        ( bot_bo844097828e_bool = collect_pname(U_482)
        | ( hBOOL(hAPP_pname_bool(U_482,sK12(U_482)))
          & is_pname(sK12(U_482)) ) )
    & ! [U_481] :
        ( ! [U_478] :
            ( ~ hBOOL(hAPP_pname_bool(U_481,U_478))
            | ~ is_pname(U_478) )
        | bot_bo844097828e_bool != collect_pname(U_481) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_479,sK12(U_482))],[f_208_3]) ).

fof(f_208_5,plain,
    ( ! [U_482] :
        ( hBOOL(hAPP_pname_bool(U_482,sK12(U_482)))
        | ~ sP22(U_482) )
    & ! [U_482] :
        ( is_pname(sK12(U_482))
        | ~ sP22(U_482) )
    & ! [U_482] :
        ( bot_bo844097828e_bool = collect_pname(U_482)
        | sP22(U_482) )
    & ! [U_478,U_481] :
        ( ~ hBOOL(hAPP_pname_bool(U_481,U_478))
        | ~ is_pname(U_478)
        | bot_bo844097828e_bool != collect_pname(U_481) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_208_4]) ).

cnf(f_208_6,plain,
    ( ~ hBOOL(hAPP_pname_bool(U_481,U_478))
    | ~ is_pname(U_478)
    | bot_bo844097828e_bool != collect_pname(U_481) ),
    inference(clausify,[status(thm)],[f_208_5]) ).

cnf(f_208_7,plain,
    ( bot_bo844097828e_bool = collect_pname(U_482)
    | sP22(U_482) ),
    inference(clausify,[status(thm)],[f_208_5]) ).

cnf(f_208_8,plain,
    ( is_pname(sK12(U_482))
    | ~ sP22(U_482) ),
    inference(clausify,[status(thm)],[f_208_5]) ).

cnf(f_208_9,plain,
    ( hBOOL(hAPP_pname_bool(U_482,sK12(U_482)))
    | ~ sP22(U_482) ),
    inference(clausify,[status(thm)],[f_208_5]) ).

fof(f_209_1,plain,
    ! [A] :
      ( ( ( ? [X_1] :
              ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
              & is_fun_pname_bool(X_1) )
          | A = bot_bo1649642514l_bool )
        & ( A != bot_bo1649642514l_bool
          | ! [X_1] :
              ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
              | ~ is_fun_pname_bool(X_1) ) ) )
      | ~ is_fun1661590463l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_155_ex__in__conv]) ).

fof(f_209_2,plain,
    ! [U_485] :
      ( ( ( ? [U_484] :
              ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_484),U_485))
              & is_fun_pname_bool(U_484) )
          | U_485 = bot_bo1649642514l_bool )
        & ( U_485 != bot_bo1649642514l_bool
          | ! [U_483] :
              ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_483),U_485))
              | ~ is_fun_pname_bool(U_483) ) ) )
      | ~ is_fun1661590463l_bool(U_485) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

fof(f_209_3,plain,
    ! [U_485] :
      ( ( ( ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK13(U_485)),U_485))
            & is_fun_pname_bool(sK13(U_485)) )
          | U_485 = bot_bo1649642514l_bool )
        & ( U_485 != bot_bo1649642514l_bool
          | ! [U_483] :
              ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_483),U_485))
              | ~ is_fun_pname_bool(U_483) ) ) )
      | ~ is_fun1661590463l_bool(U_485) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_484,sK13(U_485))],[f_209_2]) ).

fof(f_209_4,plain,
    ( ! [U_485] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK13(U_485)),U_485))
        | ~ sP23(U_485) )
    & ! [U_485] :
        ( is_fun_pname_bool(sK13(U_485))
        | ~ sP23(U_485) )
    & ! [U_483,U_485] :
        ( sP23(U_485)
        | U_485 = bot_bo1649642514l_bool
        | ~ sP24(U_483,U_485) )
    & ! [U_483,U_485] :
        ( U_485 != bot_bo1649642514l_bool
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_483),U_485))
        | ~ is_fun_pname_bool(U_483)
        | ~ sP24(U_483,U_485) )
    & ! [U_483,U_485] :
        ( sP24(U_483,U_485)
        | ~ is_fun1661590463l_bool(U_485) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23,sP24])],[f_209_3]) ).

cnf(f_209_5,plain,
    ( sP24(U_483,U_485)
    | ~ is_fun1661590463l_bool(U_485) ),
    inference(clausify,[status(thm)],[f_209_4]) ).

cnf(f_209_6,plain,
    ( U_485 != bot_bo1649642514l_bool
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_483),U_485))
    | ~ is_fun_pname_bool(U_483)
    | ~ sP24(U_483,U_485) ),
    inference(clausify,[status(thm)],[f_209_4]) ).

cnf(f_209_7,plain,
    ( sP23(U_485)
    | U_485 = bot_bo1649642514l_bool
    | ~ sP24(U_483,U_485) ),
    inference(clausify,[status(thm)],[f_209_4]) ).

cnf(f_209_8,plain,
    ( is_fun_pname_bool(sK13(U_485))
    | ~ sP23(U_485) ),
    inference(clausify,[status(thm)],[f_209_4]) ).

cnf(f_209_9,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK13(U_485)),U_485))
    | ~ sP23(U_485) ),
    inference(clausify,[status(thm)],[f_209_4]) ).

fof(f_210_1,plain,
    ! [A] :
      ( ( ? [X_1] : hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_1),A))
        | A = bot_bo535777328l_bool )
      & ( A != bot_bo535777328l_bool
        | ! [X_1] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_156_ex__in__conv]) ).

fof(f_210_2,plain,
    ! [U_488] :
      ( ( ? [U_487] : hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_487),U_488))
        | U_488 = bot_bo535777328l_bool )
      & ( U_488 != bot_bo535777328l_bool
        | ! [U_486] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_486),U_488)) ) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

fof(f_210_3,plain,
    ( ! [U_490] :
        ( ? [U_487] : hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_487),U_490))
        | U_490 = bot_bo535777328l_bool )
    & ! [U_489] :
        ( U_489 != bot_bo535777328l_bool
        | ! [U_486] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_486),U_489)) ) ),
    inference(miniscope,[status(thm)],[f_210_2]) ).

fof(f_210_4,plain,
    ( ! [U_490] :
        ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK14(U_490)),U_490))
        | U_490 = bot_bo535777328l_bool )
    & ! [U_489] :
        ( U_489 != bot_bo535777328l_bool
        | ! [U_486] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_486),U_489)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_487,sK14(U_490))],[f_210_3]) ).

fof(f_210_5,plain,
    ( ! [U_490] :
        ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK14(U_490)),U_490))
        | U_490 = bot_bo535777328l_bool )
    & ! [U_489,U_486] :
        ( U_489 != bot_bo535777328l_bool
        | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_486),U_489)) ) ),
    inference(definitional_conversion,[status(esa)],[f_210_4]) ).

cnf(f_210_6,plain,
    ( U_489 != bot_bo535777328l_bool
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_486),U_489)) ),
    inference(clausify,[status(thm)],[f_210_5]) ).

cnf(f_210_7,plain,
    ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK14(U_490)),U_490))
    | U_490 = bot_bo535777328l_bool ),
    inference(clausify,[status(thm)],[f_210_5]) ).

fof(f_211_1,plain,
    ! [A] :
      ( ( ? [X_1] : hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),A))
        | A = bot_bo620288102e_bool )
      & ( A != bot_bo620288102e_bool
        | ! [X_1] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_157_ex__in__conv]) ).

fof(f_211_2,plain,
    ! [U_493] :
      ( ( ? [U_492] : hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_492),U_493))
        | U_493 = bot_bo620288102e_bool )
      & ( U_493 != bot_bo620288102e_bool
        | ! [U_491] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_491),U_493)) ) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

fof(f_211_3,plain,
    ( ! [U_495] :
        ( ? [U_492] : hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_492),U_495))
        | U_495 = bot_bo620288102e_bool )
    & ! [U_494] :
        ( U_494 != bot_bo620288102e_bool
        | ! [U_491] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_491),U_494)) ) ),
    inference(miniscope,[status(thm)],[f_211_2]) ).

fof(f_211_4,plain,
    ( ! [U_495] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK15(U_495)),U_495))
        | U_495 = bot_bo620288102e_bool )
    & ! [U_494] :
        ( U_494 != bot_bo620288102e_bool
        | ! [U_491] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_491),U_494)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_492,sK15(U_495))],[f_211_3]) ).

fof(f_211_5,plain,
    ( ! [U_495] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK15(U_495)),U_495))
        | U_495 = bot_bo620288102e_bool )
    & ! [U_491,U_494] :
        ( U_494 != bot_bo620288102e_bool
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_491),U_494)) ) ),
    inference(definitional_conversion,[status(esa)],[f_211_4]) ).

cnf(f_211_6,plain,
    ( U_494 != bot_bo620288102e_bool
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_491),U_494)) ),
    inference(clausify,[status(thm)],[f_211_5]) ).

cnf(f_211_7,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK15(U_495)),U_495))
    | U_495 = bot_bo620288102e_bool ),
    inference(clausify,[status(thm)],[f_211_5]) ).

fof(f_212_1,plain,
    ! [A] :
      ( ( ( ? [X_1] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
              & is_pname(X_1) )
          | A = bot_bo844097828e_bool )
        & ( A != bot_bo844097828e_bool
          | ! [X_1] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
              | ~ is_pname(X_1) ) ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_158_ex__in__conv]) ).

fof(f_212_2,plain,
    ! [U_498] :
      ( ( ( ? [U_497] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_497),U_498))
              & is_pname(U_497) )
          | U_498 = bot_bo844097828e_bool )
        & ( U_498 != bot_bo844097828e_bool
          | ! [U_496] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_496),U_498))
              | ~ is_pname(U_496) ) ) )
      | ~ is_fun_pname_bool(U_498) ),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

fof(f_212_3,plain,
    ! [U_498] :
      ( ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK16(U_498)),U_498))
            & is_pname(sK16(U_498)) )
          | U_498 = bot_bo844097828e_bool )
        & ( U_498 != bot_bo844097828e_bool
          | ! [U_496] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_496),U_498))
              | ~ is_pname(U_496) ) ) )
      | ~ is_fun_pname_bool(U_498) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_497,sK16(U_498))],[f_212_2]) ).

fof(f_212_4,plain,
    ( ! [U_498] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK16(U_498)),U_498))
        | ~ sP25(U_498) )
    & ! [U_498] :
        ( is_pname(sK16(U_498))
        | ~ sP25(U_498) )
    & ! [U_496,U_498] :
        ( sP25(U_498)
        | U_498 = bot_bo844097828e_bool
        | ~ sP26(U_496,U_498) )
    & ! [U_496,U_498] :
        ( U_498 != bot_bo844097828e_bool
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_496),U_498))
        | ~ is_pname(U_496)
        | ~ sP26(U_496,U_498) )
    & ! [U_496,U_498] :
        ( sP26(U_496,U_498)
        | ~ is_fun_pname_bool(U_498) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25,sP26])],[f_212_3]) ).

cnf(f_212_5,plain,
    ( sP26(U_496,U_498)
    | ~ is_fun_pname_bool(U_498) ),
    inference(clausify,[status(thm)],[f_212_4]) ).

cnf(f_212_6,plain,
    ( U_498 != bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_496),U_498))
    | ~ is_pname(U_496)
    | ~ sP26(U_496,U_498) ),
    inference(clausify,[status(thm)],[f_212_4]) ).

cnf(f_212_7,plain,
    ( sP25(U_498)
    | U_498 = bot_bo844097828e_bool
    | ~ sP26(U_496,U_498) ),
    inference(clausify,[status(thm)],[f_212_4]) ).

cnf(f_212_8,plain,
    ( is_pname(sK16(U_498))
    | ~ sP25(U_498) ),
    inference(clausify,[status(thm)],[f_212_4]) ).

cnf(f_212_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK16(U_498)),U_498))
    | ~ sP25(U_498) ),
    inference(clausify,[status(thm)],[f_212_4]) ).

fof(f_213_1,plain,
    ! [A] :
      ( ( ( ! [X_1] :
              ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
              | ~ is_fun_pname_bool(X_1) )
          | A != bot_bo1649642514l_bool )
        & ( A = bot_bo1649642514l_bool
          | ? [X_1] :
              ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
              & is_fun_pname_bool(X_1) ) ) )
      | ~ is_fun1661590463l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_159_all__not__in__conv]) ).

fof(f_213_2,plain,
    ! [U_501] :
      ( ( ( ! [U_500] :
              ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_500),U_501))
              | ~ is_fun_pname_bool(U_500) )
          | U_501 != bot_bo1649642514l_bool )
        & ( U_501 = bot_bo1649642514l_bool
          | ? [U_499] :
              ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_499),U_501))
              & is_fun_pname_bool(U_499) ) ) )
      | ~ is_fun1661590463l_bool(U_501) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

fof(f_213_3,plain,
    ! [U_501] :
      ( ( ( ! [U_500] :
              ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_500),U_501))
              | ~ is_fun_pname_bool(U_500) )
          | U_501 != bot_bo1649642514l_bool )
        & ( U_501 = bot_bo1649642514l_bool
          | ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK17(U_501)),U_501))
            & is_fun_pname_bool(sK17(U_501)) ) ) )
      | ~ is_fun1661590463l_bool(U_501) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_499,sK17(U_501))],[f_213_2]) ).

fof(f_213_4,plain,
    ( ! [U_501] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK17(U_501)),U_501))
        | ~ sP27(U_501) )
    & ! [U_501] :
        ( is_fun_pname_bool(sK17(U_501))
        | ~ sP27(U_501) )
    & ! [U_501,U_500] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_500),U_501))
        | ~ is_fun_pname_bool(U_500)
        | U_501 != bot_bo1649642514l_bool
        | ~ sP28(U_501,U_500) )
    & ! [U_501,U_500] :
        ( U_501 = bot_bo1649642514l_bool
        | sP27(U_501)
        | ~ sP28(U_501,U_500) )
    & ! [U_501,U_500] :
        ( sP28(U_501,U_500)
        | ~ is_fun1661590463l_bool(U_501) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27,sP28])],[f_213_3]) ).

cnf(f_213_5,plain,
    ( sP28(U_501,U_500)
    | ~ is_fun1661590463l_bool(U_501) ),
    inference(clausify,[status(thm)],[f_213_4]) ).

cnf(f_213_6,plain,
    ( U_501 = bot_bo1649642514l_bool
    | sP27(U_501)
    | ~ sP28(U_501,U_500) ),
    inference(clausify,[status(thm)],[f_213_4]) ).

cnf(f_213_7,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_500),U_501))
    | ~ is_fun_pname_bool(U_500)
    | U_501 != bot_bo1649642514l_bool
    | ~ sP28(U_501,U_500) ),
    inference(clausify,[status(thm)],[f_213_4]) ).

cnf(f_213_8,plain,
    ( is_fun_pname_bool(sK17(U_501))
    | ~ sP27(U_501) ),
    inference(clausify,[status(thm)],[f_213_4]) ).

cnf(f_213_9,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK17(U_501)),U_501))
    | ~ sP27(U_501) ),
    inference(clausify,[status(thm)],[f_213_4]) ).

fof(f_214_1,plain,
    ! [A] :
      ( ( ! [X_1] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_1),A))
        | A != bot_bo535777328l_bool )
      & ( A = bot_bo535777328l_bool
        | ? [X_1] : hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_160_all__not__in__conv]) ).

fof(f_214_2,plain,
    ! [U_504] :
      ( ( ! [U_503] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_503),U_504))
        | U_504 != bot_bo535777328l_bool )
      & ( U_504 = bot_bo535777328l_bool
        | ? [U_502] : hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_502),U_504)) ) ),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

fof(f_214_3,plain,
    ( ! [U_506] :
        ( ! [U_503] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_503),U_506))
        | U_506 != bot_bo535777328l_bool )
    & ! [U_505] :
        ( U_505 = bot_bo535777328l_bool
        | ? [U_502] : hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_502),U_505)) ) ),
    inference(miniscope,[status(thm)],[f_214_2]) ).

fof(f_214_4,plain,
    ( ! [U_506] :
        ( ! [U_503] : ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_503),U_506))
        | U_506 != bot_bo535777328l_bool )
    & ! [U_505] :
        ( U_505 = bot_bo535777328l_bool
        | hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK18(U_505)),U_505)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_502,sK18(U_505))],[f_214_3]) ).

fof(f_214_5,plain,
    ( ! [U_506,U_503] :
        ( ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_503),U_506))
        | U_506 != bot_bo535777328l_bool )
    & ! [U_505] :
        ( U_505 = bot_bo535777328l_bool
        | hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK18(U_505)),U_505)) ) ),
    inference(definitional_conversion,[status(esa)],[f_214_4]) ).

cnf(f_214_6,plain,
    ( U_505 = bot_bo535777328l_bool
    | hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK18(U_505)),U_505)) ),
    inference(clausify,[status(thm)],[f_214_5]) ).

cnf(f_214_7,plain,
    ( ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_503),U_506))
    | U_506 != bot_bo535777328l_bool ),
    inference(clausify,[status(thm)],[f_214_5]) ).

fof(f_215_1,plain,
    ! [A] :
      ( ( ! [X_1] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),A))
        | A != bot_bo620288102e_bool )
      & ( A = bot_bo620288102e_bool
        | ? [X_1] : hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_161_all__not__in__conv]) ).

fof(f_215_2,plain,
    ! [U_509] :
      ( ( ! [U_508] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_508),U_509))
        | U_509 != bot_bo620288102e_bool )
      & ( U_509 = bot_bo620288102e_bool
        | ? [U_507] : hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_507),U_509)) ) ),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

fof(f_215_3,plain,
    ( ! [U_511] :
        ( ! [U_508] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_508),U_511))
        | U_511 != bot_bo620288102e_bool )
    & ! [U_510] :
        ( U_510 = bot_bo620288102e_bool
        | ? [U_507] : hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_507),U_510)) ) ),
    inference(miniscope,[status(thm)],[f_215_2]) ).

fof(f_215_4,plain,
    ( ! [U_511] :
        ( ! [U_508] : ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_508),U_511))
        | U_511 != bot_bo620288102e_bool )
    & ! [U_510] :
        ( U_510 = bot_bo620288102e_bool
        | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK19(U_510)),U_510)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_507,sK19(U_510))],[f_215_3]) ).

fof(f_215_5,plain,
    ( ! [U_508,U_511] :
        ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_508),U_511))
        | U_511 != bot_bo620288102e_bool )
    & ! [U_510] :
        ( U_510 = bot_bo620288102e_bool
        | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK19(U_510)),U_510)) ) ),
    inference(definitional_conversion,[status(esa)],[f_215_4]) ).

cnf(f_215_6,plain,
    ( U_510 = bot_bo620288102e_bool
    | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK19(U_510)),U_510)) ),
    inference(clausify,[status(thm)],[f_215_5]) ).

cnf(f_215_7,plain,
    ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_508),U_511))
    | U_511 != bot_bo620288102e_bool ),
    inference(clausify,[status(thm)],[f_215_5]) ).

fof(f_216_1,plain,
    ! [A] :
      ( ( ( ! [X_1] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
              | ~ is_pname(X_1) )
          | A != bot_bo844097828e_bool )
        & ( A = bot_bo844097828e_bool
          | ? [X_1] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
              & is_pname(X_1) ) ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_162_all__not__in__conv]) ).

fof(f_216_2,plain,
    ! [U_514] :
      ( ( ( ! [U_513] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_513),U_514))
              | ~ is_pname(U_513) )
          | U_514 != bot_bo844097828e_bool )
        & ( U_514 = bot_bo844097828e_bool
          | ? [U_512] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_512),U_514))
              & is_pname(U_512) ) ) )
      | ~ is_fun_pname_bool(U_514) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

fof(f_216_3,plain,
    ! [U_514] :
      ( ( ( ! [U_513] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_513),U_514))
              | ~ is_pname(U_513) )
          | U_514 != bot_bo844097828e_bool )
        & ( U_514 = bot_bo844097828e_bool
          | ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK20(U_514)),U_514))
            & is_pname(sK20(U_514)) ) ) )
      | ~ is_fun_pname_bool(U_514) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_512,sK20(U_514))],[f_216_2]) ).

fof(f_216_4,plain,
    ( ! [U_514] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK20(U_514)),U_514))
        | ~ sP29(U_514) )
    & ! [U_514] :
        ( is_pname(sK20(U_514))
        | ~ sP29(U_514) )
    & ! [U_513,U_514] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_513),U_514))
        | ~ is_pname(U_513)
        | U_514 != bot_bo844097828e_bool
        | ~ sP30(U_513,U_514) )
    & ! [U_513,U_514] :
        ( U_514 = bot_bo844097828e_bool
        | sP29(U_514)
        | ~ sP30(U_513,U_514) )
    & ! [U_513,U_514] :
        ( sP30(U_513,U_514)
        | ~ is_fun_pname_bool(U_514) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29,sP30])],[f_216_3]) ).

cnf(f_216_5,plain,
    ( sP30(U_513,U_514)
    | ~ is_fun_pname_bool(U_514) ),
    inference(clausify,[status(thm)],[f_216_4]) ).

cnf(f_216_6,plain,
    ( U_514 = bot_bo844097828e_bool
    | sP29(U_514)
    | ~ sP30(U_513,U_514) ),
    inference(clausify,[status(thm)],[f_216_4]) ).

cnf(f_216_7,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_513),U_514))
    | ~ is_pname(U_513)
    | U_514 != bot_bo844097828e_bool
    | ~ sP30(U_513,U_514) ),
    inference(clausify,[status(thm)],[f_216_4]) ).

cnf(f_216_8,plain,
    ( is_pname(sK20(U_514))
    | ~ sP29(U_514) ),
    inference(clausify,[status(thm)],[f_216_4]) ).

cnf(f_216_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK20(U_514)),U_514))
    | ~ sP29(U_514) ),
    inference(clausify,[status(thm)],[f_216_4]) ).

fof(f_217_1,plain,
    bot_bo1761158942l_bool = collec488126193l_bool(cOMBK_482404831l_bool(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_163_empty__def]) ).

fof(f_217_2,plain,
    bot_bo1761158942l_bool = collec488126193l_bool(cOMBK_482404831l_bool(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_217_1]) ).

cnf(f_217_3,plain,
    bot_bo1761158942l_bool = collec488126193l_bool(cOMBK_482404831l_bool(fFalse)),
    inference(clausify,[status(thm)],[f_217_2]) ).

fof(f_218_1,plain,
    bot_bo535777328l_bool = collec1823980261e_bool(cOMBK_129401207e_bool(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_164_empty__def]) ).

fof(f_218_2,plain,
    bot_bo535777328l_bool = collec1823980261e_bool(cOMBK_129401207e_bool(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_218_1]) ).

cnf(f_218_3,plain,
    bot_bo535777328l_bool = collec1823980261e_bool(cOMBK_129401207e_bool(fFalse)),
    inference(clausify,[status(thm)],[f_218_2]) ).

fof(f_219_1,plain,
    bot_bo1649642514l_bool = collec1974731493e_bool(cOMBK_1857069011e_bool(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_165_empty__def]) ).

fof(f_219_2,plain,
    bot_bo1649642514l_bool = collec1974731493e_bool(cOMBK_1857069011e_bool(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_219_1]) ).

cnf(f_219_3,plain,
    bot_bo1649642514l_bool = collec1974731493e_bool(cOMBK_1857069011e_bool(fFalse)),
    inference(clausify,[status(thm)],[f_219_2]) ).

fof(f_220_1,plain,
    bot_bo620288102e_bool = collec307967673_state(cOMBK_659609255_state(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_166_empty__def]) ).

fof(f_220_2,plain,
    bot_bo620288102e_bool = collec307967673_state(cOMBK_659609255_state(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_220_1]) ).

cnf(f_220_3,plain,
    bot_bo620288102e_bool = collec307967673_state(cOMBK_659609255_state(fFalse)),
    inference(clausify,[status(thm)],[f_220_2]) ).

fof(f_221_1,plain,
    bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_167_empty__def]) ).

fof(f_221_2,plain,
    bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_221_1]) ).

cnf(f_221_3,plain,
    bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)),
    inference(clausify,[status(thm)],[f_221_2]) ).

fof(f_222_1,plain,
    ! [A_2,A] :
      ( insert_pname(A_2,A) = A
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_168_insert__absorb]) ).

fof(f_222_2,plain,
    ! [U_516,U_515] :
      ( insert_pname(U_516,U_515) = U_515
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_516),U_515))
      | ~ is_fun_pname_bool(U_515) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

fof(f_222_3,plain,
    ! [U_515,U_516] :
      ( insert_pname(U_516,U_515) = U_515
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_516),U_515))
      | ~ is_fun_pname_bool(U_515) ),
    inference(definitional_conversion,[status(esa)],[f_222_2]) ).

cnf(f_222_4,plain,
    ( insert_pname(U_516,U_515) = U_515
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_516),U_515))
    | ~ is_fun_pname_bool(U_515) ),
    inference(clausify,[status(thm)],[f_222_3]) ).

fof(f_223_1,plain,
    ! [A_2,A] :
      ( insert1415133716_state(A_2,A) = A
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_169_insert__absorb]) ).

fof(f_223_2,plain,
    ! [U_518,U_517] :
      ( insert1415133716_state(U_518,U_517) = U_517
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_518),U_517)) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

fof(f_223_3,plain,
    ! [U_517,U_518] :
      ( insert1415133716_state(U_518,U_517) = U_517
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_518),U_517)) ),
    inference(definitional_conversion,[status(esa)],[f_223_2]) ).

cnf(f_223_4,plain,
    ( insert1415133716_state(U_518,U_517) = U_517
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_518),U_517)) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

fof(f_224_1,plain,
    ! [B_1,A_2,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,B)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B)) ),
    inference(fof_nnf,[status(thm)],[fact_170_insertI2]) ).

fof(f_224_2,plain,
    ! [U_521,U_520,U_519] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_520),insert_pname(U_521,U_519)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_520),U_519)) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

fof(f_224_3,plain,
    ! [U_519,U_520,U_521] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_520),insert_pname(U_521,U_519)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_520),U_519)) ),
    inference(definitional_conversion,[status(esa)],[f_224_2]) ).

cnf(f_224_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_520),insert_pname(U_521,U_519)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_520),U_519)) ),
    inference(clausify,[status(thm)],[f_224_3]) ).

fof(f_225_1,plain,
    ! [B_1,A_2,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,B)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),B)) ),
    inference(fof_nnf,[status(thm)],[fact_171_insertI2]) ).

fof(f_225_2,plain,
    ! [U_524,U_523,U_522] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_523),insert1415133716_state(U_524,U_522)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_523),U_522)) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

fof(f_225_3,plain,
    ! [U_522,U_523,U_524] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_523),insert1415133716_state(U_524,U_522)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_523),U_522)) ),
    inference(definitional_conversion,[status(esa)],[f_225_2]) ).

cnf(f_225_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_523),insert1415133716_state(U_524,U_522)))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_523),U_522)) ),
    inference(clausify,[status(thm)],[f_225_3]) ).

fof(f_226_1,plain,
    ! [B,X_2,A] :
      ( ( ( insert_pname(X_2,A) = insert_pname(X_2,B)
          | A != B )
        & ( A = B
          | insert_pname(X_2,A) != insert_pname(X_2,B) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
      | ~ is_fun_pname_bool(A)
      | ~ is_fun_pname_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_172_insert__ident]) ).

fof(f_226_2,plain,
    ! [U_527,U_526,U_525] :
      ( ( ( insert_pname(U_526,U_525) = insert_pname(U_526,U_527)
          | U_525 != U_527 )
        & ( U_525 = U_527
          | insert_pname(U_526,U_525) != insert_pname(U_526,U_527) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_526),U_527))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_526),U_525))
      | ~ is_fun_pname_bool(U_525)
      | ~ is_fun_pname_bool(U_527) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

fof(f_226_3,plain,
    ( ! [U_525,U_526,U_527] :
        ( insert_pname(U_526,U_525) = insert_pname(U_526,U_527)
        | U_525 != U_527
        | ~ sP31(U_525,U_526,U_527) )
    & ! [U_525,U_526,U_527] :
        ( U_525 = U_527
        | insert_pname(U_526,U_525) != insert_pname(U_526,U_527)
        | ~ sP31(U_525,U_526,U_527) )
    & ! [U_525,U_526,U_527] :
        ( sP31(U_525,U_526,U_527)
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_526),U_527))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_526),U_525))
        | ~ is_fun_pname_bool(U_525)
        | ~ is_fun_pname_bool(U_527) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31])],[f_226_2]) ).

cnf(f_226_4,plain,
    ( sP31(U_525,U_526,U_527)
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_526),U_527))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_526),U_525))
    | ~ is_fun_pname_bool(U_525)
    | ~ is_fun_pname_bool(U_527) ),
    inference(clausify,[status(thm)],[f_226_3]) ).

cnf(f_226_5,plain,
    ( U_525 = U_527
    | insert_pname(U_526,U_525) != insert_pname(U_526,U_527)
    | ~ sP31(U_525,U_526,U_527) ),
    inference(clausify,[status(thm)],[f_226_3]) ).

cnf(f_226_6,plain,
    ( insert_pname(U_526,U_525) = insert_pname(U_526,U_527)
    | U_525 != U_527
    | ~ sP31(U_525,U_526,U_527) ),
    inference(clausify,[status(thm)],[f_226_3]) ).

fof(f_227_1,plain,
    ! [B,X_2,A] :
      ( ( ( insert1415133716_state(X_2,A) = insert1415133716_state(X_2,B)
          | A != B )
        & ( A = B
          | insert1415133716_state(X_2,A) != insert1415133716_state(X_2,B) ) )
      | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B))
      | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_173_insert__ident]) ).

fof(f_227_2,plain,
    ! [U_530,U_529,U_528] :
      ( ( ( insert1415133716_state(U_529,U_528) = insert1415133716_state(U_529,U_530)
          | U_528 != U_530 )
        & ( U_528 = U_530
          | insert1415133716_state(U_529,U_528) != insert1415133716_state(U_529,U_530) ) )
      | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_529),U_530))
      | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_529),U_528)) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

fof(f_227_3,plain,
    ( ! [U_530,U_529,U_528] :
        ( insert1415133716_state(U_529,U_528) = insert1415133716_state(U_529,U_530)
        | U_528 != U_530
        | ~ sP32(U_530,U_529,U_528) )
    & ! [U_530,U_529,U_528] :
        ( U_528 = U_530
        | insert1415133716_state(U_529,U_528) != insert1415133716_state(U_529,U_530)
        | ~ sP32(U_530,U_529,U_528) )
    & ! [U_530,U_529,U_528] :
        ( sP32(U_530,U_529,U_528)
        | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_529),U_530))
        | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_529),U_528)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32])],[f_227_2]) ).

cnf(f_227_4,plain,
    ( sP32(U_530,U_529,U_528)
    | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_529),U_530))
    | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_529),U_528)) ),
    inference(clausify,[status(thm)],[f_227_3]) ).

cnf(f_227_5,plain,
    ( U_528 = U_530
    | insert1415133716_state(U_529,U_528) != insert1415133716_state(U_529,U_530)
    | ~ sP32(U_530,U_529,U_528) ),
    inference(clausify,[status(thm)],[f_227_3]) ).

cnf(f_227_6,plain,
    ( insert1415133716_state(U_529,U_528) = insert1415133716_state(U_529,U_530)
    | U_528 != U_530
    | ~ sP32(U_530,U_529,U_528) ),
    inference(clausify,[status(thm)],[f_227_3]) ).

fof(f_228_1,plain,
    ! [Y_2,A,X_2] :
      ( ( ( hBOOL(hAPP_pname_bool(insert_pname(Y_2,A),X_2))
          | ( ~ hBOOL(hAPP_pname_bool(A,X_2))
            & Y_2 != X_2 ) )
        & ( hBOOL(hAPP_pname_bool(A,X_2))
          | Y_2 = X_2
          | ~ hBOOL(hAPP_pname_bool(insert_pname(Y_2,A),X_2)) ) )
      | ~ is_pname(X_2)
      | ~ is_pname(Y_2) ),
    inference(fof_nnf,[status(thm)],[fact_174_insert__code]) ).

fof(f_228_2,plain,
    ! [U_533,U_532,U_531] :
      ( ( ( hBOOL(hAPP_pname_bool(insert_pname(U_533,U_532),U_531))
          | ( ~ hBOOL(hAPP_pname_bool(U_532,U_531))
            & U_533 != U_531 ) )
        & ( hBOOL(hAPP_pname_bool(U_532,U_531))
          | U_533 = U_531
          | ~ hBOOL(hAPP_pname_bool(insert_pname(U_533,U_532),U_531)) ) )
      | ~ is_pname(U_531)
      | ~ is_pname(U_533) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

fof(f_228_3,plain,
    ( ! [U_532,U_533,U_531] :
        ( ~ hBOOL(hAPP_pname_bool(U_532,U_531))
        | ~ sP33(U_532,U_533,U_531) )
    & ! [U_532,U_533,U_531] :
        ( U_533 != U_531
        | ~ sP33(U_532,U_533,U_531) )
    & ! [U_532,U_533,U_531] :
        ( hBOOL(hAPP_pname_bool(insert_pname(U_533,U_532),U_531))
        | sP33(U_532,U_533,U_531)
        | ~ sP34(U_532,U_533,U_531) )
    & ! [U_532,U_533,U_531] :
        ( hBOOL(hAPP_pname_bool(U_532,U_531))
        | U_533 = U_531
        | ~ hBOOL(hAPP_pname_bool(insert_pname(U_533,U_532),U_531))
        | ~ sP34(U_532,U_533,U_531) )
    & ! [U_532,U_533,U_531] :
        ( sP34(U_532,U_533,U_531)
        | ~ is_pname(U_531)
        | ~ is_pname(U_533) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33,sP34])],[f_228_2]) ).

cnf(f_228_4,plain,
    ( sP34(U_532,U_533,U_531)
    | ~ is_pname(U_531)
    | ~ is_pname(U_533) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_5,plain,
    ( hBOOL(hAPP_pname_bool(U_532,U_531))
    | U_533 = U_531
    | ~ hBOOL(hAPP_pname_bool(insert_pname(U_533,U_532),U_531))
    | ~ sP34(U_532,U_533,U_531) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_6,plain,
    ( hBOOL(hAPP_pname_bool(insert_pname(U_533,U_532),U_531))
    | sP33(U_532,U_533,U_531)
    | ~ sP34(U_532,U_533,U_531) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_7,plain,
    ( U_533 != U_531
    | ~ sP33(U_532,U_533,U_531) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_8,plain,
    ( ~ hBOOL(hAPP_pname_bool(U_532,U_531))
    | ~ sP33(U_532,U_533,U_531) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

fof(f_229_1,plain,
    ! [Y_2,A,X_2] :
      ( ( hBOOL(hAPP_H78829294e_bool(insert1415133716_state(Y_2,A),X_2))
        | ( ~ hBOOL(hAPP_H78829294e_bool(A,X_2))
          & Y_2 != X_2 ) )
      & ( hBOOL(hAPP_H78829294e_bool(A,X_2))
        | Y_2 = X_2
        | ~ hBOOL(hAPP_H78829294e_bool(insert1415133716_state(Y_2,A),X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_175_insert__code]) ).

fof(f_229_2,plain,
    ! [U_536,U_535,U_534] :
      ( ( hBOOL(hAPP_H78829294e_bool(insert1415133716_state(U_536,U_535),U_534))
        | ( ~ hBOOL(hAPP_H78829294e_bool(U_535,U_534))
          & U_536 != U_534 ) )
      & ( hBOOL(hAPP_H78829294e_bool(U_535,U_534))
        | U_536 = U_534
        | ~ hBOOL(hAPP_H78829294e_bool(insert1415133716_state(U_536,U_535),U_534)) ) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

fof(f_229_3,plain,
    ( ! [U_542,U_540,U_538] :
        ( hBOOL(hAPP_H78829294e_bool(insert1415133716_state(U_542,U_540),U_538))
        | ( ~ hBOOL(hAPP_H78829294e_bool(U_540,U_538))
          & U_542 != U_538 ) )
    & ! [U_541,U_539,U_537] :
        ( hBOOL(hAPP_H78829294e_bool(U_539,U_537))
        | U_541 = U_537
        | ~ hBOOL(hAPP_H78829294e_bool(insert1415133716_state(U_541,U_539),U_537)) ) ),
    inference(miniscope,[status(thm)],[f_229_2]) ).

fof(f_229_4,plain,
    ( ! [U_540,U_538,U_542] :
        ( ~ hBOOL(hAPP_H78829294e_bool(U_540,U_538))
        | ~ sP35(U_540,U_538,U_542) )
    & ! [U_540,U_538,U_542] :
        ( U_542 != U_538
        | ~ sP35(U_540,U_538,U_542) )
    & ! [U_540,U_538,U_542] :
        ( hBOOL(hAPP_H78829294e_bool(insert1415133716_state(U_542,U_540),U_538))
        | sP35(U_540,U_538,U_542) )
    & ! [U_539,U_537,U_541] :
        ( hBOOL(hAPP_H78829294e_bool(U_539,U_537))
        | U_541 = U_537
        | ~ hBOOL(hAPP_H78829294e_bool(insert1415133716_state(U_541,U_539),U_537)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35])],[f_229_3]) ).

cnf(f_229_5,plain,
    ( hBOOL(hAPP_H78829294e_bool(U_539,U_537))
    | U_541 = U_537
    | ~ hBOOL(hAPP_H78829294e_bool(insert1415133716_state(U_541,U_539),U_537)) ),
    inference(clausify,[status(thm)],[f_229_4]) ).

cnf(f_229_6,plain,
    ( hBOOL(hAPP_H78829294e_bool(insert1415133716_state(U_542,U_540),U_538))
    | sP35(U_540,U_538,U_542) ),
    inference(clausify,[status(thm)],[f_229_4]) ).

cnf(f_229_7,plain,
    ( U_542 != U_538
    | ~ sP35(U_540,U_538,U_542) ),
    inference(clausify,[status(thm)],[f_229_4]) ).

cnf(f_229_8,plain,
    ( ~ hBOOL(hAPP_H78829294e_bool(U_540,U_538))
    | ~ sP35(U_540,U_538,U_542) ),
    inference(clausify,[status(thm)],[f_229_4]) ).

fof(f_230_1,plain,
    ! [A_2,B_1,A] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,A)))
          | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
            & A_2 != B_1 ) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
          | A_2 = B_1
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(B_1,A))) ) )
      | ~ is_pname(B_1)
      | ~ is_pname(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_176_insert__iff]) ).

fof(f_230_2,plain,
    ! [U_545,U_544,U_543] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),insert_pname(U_544,U_543)))
          | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),U_543))
            & U_545 != U_544 ) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),U_543))
          | U_545 = U_544
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),insert_pname(U_544,U_543))) ) )
      | ~ is_pname(U_544)
      | ~ is_pname(U_545) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

fof(f_230_3,plain,
    ! [U_545,U_544] :
      ( ( ! [U_547] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),insert_pname(U_544,U_547)))
            | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),U_547))
              & U_545 != U_544 ) )
        & ! [U_546] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),U_546))
            | U_545 = U_544
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),insert_pname(U_544,U_546))) ) )
      | ~ is_pname(U_544)
      | ~ is_pname(U_545) ),
    inference(miniscope,[status(thm)],[f_230_2]) ).

fof(f_230_4,plain,
    ( ! [U_544,U_545,U_547] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),U_547))
        | ~ sP36(U_544,U_545,U_547) )
    & ! [U_544,U_545,U_547] :
        ( U_545 != U_544
        | ~ sP36(U_544,U_545,U_547) )
    & ! [U_544,U_545,U_546,U_547] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),insert_pname(U_544,U_547)))
        | sP36(U_544,U_545,U_547)
        | ~ sP37(U_544,U_545,U_546,U_547) )
    & ! [U_544,U_545,U_546,U_547] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),U_546))
        | U_545 = U_544
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),insert_pname(U_544,U_546)))
        | ~ sP37(U_544,U_545,U_546,U_547) )
    & ! [U_544,U_545,U_546,U_547] :
        ( sP37(U_544,U_545,U_546,U_547)
        | ~ is_pname(U_544)
        | ~ is_pname(U_545) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36,sP37])],[f_230_3]) ).

cnf(f_230_5,plain,
    ( sP37(U_544,U_545,U_546,U_547)
    | ~ is_pname(U_544)
    | ~ is_pname(U_545) ),
    inference(clausify,[status(thm)],[f_230_4]) ).

cnf(f_230_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),U_546))
    | U_545 = U_544
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),insert_pname(U_544,U_546)))
    | ~ sP37(U_544,U_545,U_546,U_547) ),
    inference(clausify,[status(thm)],[f_230_4]) ).

cnf(f_230_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),insert_pname(U_544,U_547)))
    | sP36(U_544,U_545,U_547)
    | ~ sP37(U_544,U_545,U_546,U_547) ),
    inference(clausify,[status(thm)],[f_230_4]) ).

cnf(f_230_8,plain,
    ( U_545 != U_544
    | ~ sP36(U_544,U_545,U_547) ),
    inference(clausify,[status(thm)],[f_230_4]) ).

cnf(f_230_9,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_545),U_547))
    | ~ sP36(U_544,U_545,U_547) ),
    inference(clausify,[status(thm)],[f_230_4]) ).

fof(f_231_1,plain,
    ! [A_2,B_1,A] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,A)))
        | ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A))
          & A_2 != B_1 ) )
      & ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),A))
        | A_2 = B_1
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(B_1,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_177_insert__iff]) ).

fof(f_231_2,plain,
    ! [U_550,U_549,U_548] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_550),insert1415133716_state(U_549,U_548)))
        | ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_550),U_548))
          & U_550 != U_549 ) )
      & ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_550),U_548))
        | U_550 = U_549
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_550),insert1415133716_state(U_549,U_548))) ) ),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

fof(f_231_3,plain,
    ( ! [U_556,U_554,U_552] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_556),insert1415133716_state(U_554,U_552)))
        | ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_556),U_552))
          & U_556 != U_554 ) )
    & ! [U_555,U_553,U_551] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_555),U_551))
        | U_555 = U_553
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_555),insert1415133716_state(U_553,U_551))) ) ),
    inference(miniscope,[status(thm)],[f_231_2]) ).

fof(f_231_4,plain,
    ( ! [U_554,U_556,U_552] :
        ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_556),U_552))
        | ~ sP38(U_554,U_556,U_552) )
    & ! [U_554,U_556,U_552] :
        ( U_556 != U_554
        | ~ sP38(U_554,U_556,U_552) )
    & ! [U_554,U_556,U_552] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_556),insert1415133716_state(U_554,U_552)))
        | sP38(U_554,U_556,U_552) )
    & ! [U_551,U_555,U_553] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_555),U_551))
        | U_555 = U_553
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_555),insert1415133716_state(U_553,U_551))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38])],[f_231_3]) ).

cnf(f_231_5,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_555),U_551))
    | U_555 = U_553
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_555),insert1415133716_state(U_553,U_551))) ),
    inference(clausify,[status(thm)],[f_231_4]) ).

cnf(f_231_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_556),insert1415133716_state(U_554,U_552)))
    | sP38(U_554,U_556,U_552) ),
    inference(clausify,[status(thm)],[f_231_4]) ).

cnf(f_231_7,plain,
    ( U_556 != U_554
    | ~ sP38(U_554,U_556,U_552) ),
    inference(clausify,[status(thm)],[f_231_4]) ).

cnf(f_231_8,plain,
    ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_556),U_552))
    | ~ sP38(U_554,U_556,U_552) ),
    inference(clausify,[status(thm)],[f_231_4]) ).

fof(f_232_1,plain,
    ! [X_2,Y_2,A] : insert_pname(X_2,insert_pname(Y_2,A)) = insert_pname(Y_2,insert_pname(X_2,A)),
    inference(fof_nnf,[status(thm)],[fact_178_insert__commute]) ).

fof(f_232_2,plain,
    ! [U_559,U_558,U_557] : insert_pname(U_559,insert_pname(U_558,U_557)) = insert_pname(U_558,insert_pname(U_559,U_557)),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

fof(f_232_3,plain,
    ! [U_557,U_559,U_558] : insert_pname(U_559,insert_pname(U_558,U_557)) = insert_pname(U_558,insert_pname(U_559,U_557)),
    inference(definitional_conversion,[status(esa)],[f_232_2]) ).

cnf(f_232_4,plain,
    insert_pname(U_559,insert_pname(U_558,U_557)) = insert_pname(U_558,insert_pname(U_559,U_557)),
    inference(clausify,[status(thm)],[f_232_3]) ).

fof(f_233_1,plain,
    ! [X_2,Y_2,A] : insert1415133716_state(X_2,insert1415133716_state(Y_2,A)) = insert1415133716_state(Y_2,insert1415133716_state(X_2,A)),
    inference(fof_nnf,[status(thm)],[fact_179_insert__commute]) ).

fof(f_233_2,plain,
    ! [U_562,U_561,U_560] : insert1415133716_state(U_562,insert1415133716_state(U_561,U_560)) = insert1415133716_state(U_561,insert1415133716_state(U_562,U_560)),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

fof(f_233_3,plain,
    ! [U_560,U_561,U_562] : insert1415133716_state(U_562,insert1415133716_state(U_561,U_560)) = insert1415133716_state(U_561,insert1415133716_state(U_562,U_560)),
    inference(definitional_conversion,[status(esa)],[f_233_2]) ).

cnf(f_233_4,plain,
    insert1415133716_state(U_562,insert1415133716_state(U_561,U_560)) = insert1415133716_state(U_561,insert1415133716_state(U_562,U_560)),
    inference(clausify,[status(thm)],[f_233_3]) ).

fof(f_234_1,plain,
    ! [X_2,A] : insert_pname(X_2,insert_pname(X_2,A)) = insert_pname(X_2,A),
    inference(fof_nnf,[status(thm)],[fact_180_insert__absorb2]) ).

fof(f_234_2,plain,
    ! [U_564,U_563] : insert_pname(U_564,insert_pname(U_564,U_563)) = insert_pname(U_564,U_563),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

fof(f_234_3,plain,
    ! [U_563,U_564] : insert_pname(U_564,insert_pname(U_564,U_563)) = insert_pname(U_564,U_563),
    inference(definitional_conversion,[status(esa)],[f_234_2]) ).

cnf(f_234_4,plain,
    insert_pname(U_564,insert_pname(U_564,U_563)) = insert_pname(U_564,U_563),
    inference(clausify,[status(thm)],[f_234_3]) ).

fof(f_235_1,plain,
    ! [X_2,A] : insert1415133716_state(X_2,insert1415133716_state(X_2,A)) = insert1415133716_state(X_2,A),
    inference(fof_nnf,[status(thm)],[fact_181_insert__absorb2]) ).

fof(f_235_2,plain,
    ! [U_566,U_565] : insert1415133716_state(U_566,insert1415133716_state(U_566,U_565)) = insert1415133716_state(U_566,U_565),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

fof(f_235_3,plain,
    ! [U_565,U_566] : insert1415133716_state(U_566,insert1415133716_state(U_566,U_565)) = insert1415133716_state(U_566,U_565),
    inference(definitional_conversion,[status(esa)],[f_235_2]) ).

cnf(f_235_4,plain,
    insert1415133716_state(U_566,insert1415133716_state(U_566,U_565)) = insert1415133716_state(U_566,U_565),
    inference(clausify,[status(thm)],[f_235_3]) ).

fof(f_236_1,plain,
    ! [A_2,P_1] : insert_pname(A_2,collect_pname(P_1)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2))),P_1)),
    inference(fof_nnf,[status(thm)],[fact_182_insert__Collect]) ).

fof(f_236_2,plain,
    ! [U_568,U_567] : insert_pname(U_568,collect_pname(U_567)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_568))),U_567)),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

fof(f_236_3,plain,
    ! [U_567,U_568] : insert_pname(U_568,collect_pname(U_567)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_568))),U_567)),
    inference(definitional_conversion,[status(esa)],[f_236_2]) ).

cnf(f_236_4,plain,
    insert_pname(U_568,collect_pname(U_567)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_568))),U_567)),
    inference(clausify,[status(thm)],[f_236_3]) ).

fof(f_237_1,plain,
    ! [A_2,P_1] : insert1415133716_state(A_2,collec307967673_state(P_1)) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fimplies,cOMBB_2144135922_state(fNot,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2))),P_1)),
    inference(fof_nnf,[status(thm)],[fact_183_insert__Collect]) ).

fof(f_237_2,plain,
    ! [U_570,U_569] : insert1415133716_state(U_570,collec307967673_state(U_569)) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fimplies,cOMBB_2144135922_state(fNot,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_570))),U_569)),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

fof(f_237_3,plain,
    ! [U_569,U_570] : insert1415133716_state(U_570,collec307967673_state(U_569)) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fimplies,cOMBB_2144135922_state(fNot,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_570))),U_569)),
    inference(definitional_conversion,[status(esa)],[f_237_2]) ).

cnf(f_237_4,plain,
    insert1415133716_state(U_570,collec307967673_state(U_569)) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fimplies,cOMBB_2144135922_state(fNot,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_570))),U_569)),
    inference(clausify,[status(thm)],[f_237_3]) ).

fof(f_238_1,plain,
    ! [A_2,P_1] : insert1325755072e_bool(A_2,collec1974731493e_bool(P_1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2))),P_1)),
    inference(fof_nnf,[status(thm)],[fact_184_insert__Collect]) ).

fof(f_238_2,plain,
    ! [U_572,U_571] : insert1325755072e_bool(U_572,collec1974731493e_bool(U_571)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_572))),U_571)),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

fof(f_238_3,plain,
    ! [U_571,U_572] : insert1325755072e_bool(U_572,collec1974731493e_bool(U_571)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_572))),U_571)),
    inference(definitional_conversion,[status(esa)],[f_238_2]) ).

cnf(f_238_4,plain,
    insert1325755072e_bool(U_572,collec1974731493e_bool(U_571)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_572))),U_571)),
    inference(clausify,[status(thm)],[f_238_3]) ).

fof(f_239_1,plain,
    ! [A_2,P_1] : insert1556680138e_bool(A_2,collec1823980261e_bool(P_1)) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fimplies,cOMBB_1522210668e_bool(fNot,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2))),P_1)),
    inference(fof_nnf,[status(thm)],[fact_185_insert__Collect]) ).

fof(f_239_2,plain,
    ! [U_574,U_573] : insert1556680138e_bool(U_574,collec1823980261e_bool(U_573)) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fimplies,cOMBB_1522210668e_bool(fNot,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_574))),U_573)),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

fof(f_239_3,plain,
    ! [U_573,U_574] : insert1556680138e_bool(U_574,collec1823980261e_bool(U_573)) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fimplies,cOMBB_1522210668e_bool(fNot,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_574))),U_573)),
    inference(definitional_conversion,[status(esa)],[f_239_2]) ).

cnf(f_239_4,plain,
    insert1556680138e_bool(U_574,collec1823980261e_bool(U_573)) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fimplies,cOMBB_1522210668e_bool(fNot,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_574))),U_573)),
    inference(clausify,[status(thm)],[f_239_3]) ).

fof(f_240_1,plain,
    ! [A_2,B] : insert_pname(A_2,B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B))),
    inference(fof_nnf,[status(thm)],[fact_186_insert__compr]) ).

fof(f_240_2,plain,
    ! [U_576,U_575] : insert_pname(U_576,U_575) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_576)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_575))),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

fof(f_240_3,plain,
    ! [U_575,U_576] : insert_pname(U_576,U_575) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_576)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_575))),
    inference(definitional_conversion,[status(esa)],[f_240_2]) ).

cnf(f_240_4,plain,
    insert_pname(U_576,U_575) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_576)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_575))),
    inference(clausify,[status(thm)],[f_240_3]) ).

fof(f_241_1,plain,
    ! [A_2,B] : insert1415133716_state(A_2,B) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),B))),
    inference(fof_nnf,[status(thm)],[fact_187_insert__compr]) ).

fof(f_241_2,plain,
    ! [U_578,U_577] : insert1415133716_state(U_578,U_577) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_578)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),U_577))),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

fof(f_241_3,plain,
    ! [U_577,U_578] : insert1415133716_state(U_578,U_577) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_578)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),U_577))),
    inference(definitional_conversion,[status(esa)],[f_241_2]) ).

cnf(f_241_4,plain,
    insert1415133716_state(U_578,U_577) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_578)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),U_577))),
    inference(clausify,[status(thm)],[f_241_3]) ).

fof(f_242_1,plain,
    ! [A_2,B] : insert1325755072e_bool(A_2,B) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),B))),
    inference(fof_nnf,[status(thm)],[fact_188_insert__compr]) ).

fof(f_242_2,plain,
    ! [U_580,U_579] : insert1325755072e_bool(U_580,U_579) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_580)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_579))),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

fof(f_242_3,plain,
    ! [U_579,U_580] : insert1325755072e_bool(U_580,U_579) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_580)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_579))),
    inference(definitional_conversion,[status(esa)],[f_242_2]) ).

cnf(f_242_4,plain,
    insert1325755072e_bool(U_580,U_579) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_580)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_579))),
    inference(clausify,[status(thm)],[f_242_3]) ).

fof(f_243_1,plain,
    ! [A_2,B] : insert1556680138e_bool(A_2,B) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),B))),
    inference(fof_nnf,[status(thm)],[fact_189_insert__compr]) ).

fof(f_243_2,plain,
    ! [U_582,U_581] : insert1556680138e_bool(U_582,U_581) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_582)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),U_581))),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

fof(f_243_3,plain,
    ! [U_581,U_582] : insert1556680138e_bool(U_582,U_581) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_582)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),U_581))),
    inference(definitional_conversion,[status(esa)],[f_243_2]) ).

cnf(f_243_4,plain,
    insert1556680138e_bool(U_582,U_581) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_582)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),U_581))),
    inference(clausify,[status(thm)],[f_243_3]) ).

fof(f_244_1,plain,
    ! [A_2,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),insert_pname(A_2,B))),
    inference(fof_nnf,[status(thm)],[fact_190_insertI1]) ).

fof(f_244_2,plain,
    ! [U_584,U_583] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_584),insert_pname(U_584,U_583))),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

fof(f_244_3,plain,
    ! [U_583,U_584] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_584),insert_pname(U_584,U_583))),
    inference(definitional_conversion,[status(esa)],[f_244_2]) ).

cnf(f_244_4,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_584),insert_pname(U_584,U_583))),
    inference(clausify,[status(thm)],[f_244_3]) ).

fof(f_245_1,plain,
    ! [A_2,B] : hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_2),insert1415133716_state(A_2,B))),
    inference(fof_nnf,[status(thm)],[fact_191_insertI1]) ).

fof(f_245_2,plain,
    ! [U_586,U_585] : hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_586),insert1415133716_state(U_586,U_585))),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ! [U_585,U_586] : hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_586),insert1415133716_state(U_586,U_585))),
    inference(definitional_conversion,[status(esa)],[f_245_2]) ).

cnf(f_245_4,plain,
    hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_586),insert1415133716_state(U_586,U_585))),
    inference(clausify,[status(thm)],[f_245_3]) ).

fof(f_246_1,plain,
    ! [A,B] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) )
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_192_equalityE]) ).

fof(f_246_2,plain,
    ! [U_588,U_587] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_587),U_588))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_588),U_587)) )
      | U_588 != U_587 ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

fof(f_246_3,plain,
    ( ! [U_587,U_588] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_587),U_588))
        | ~ sP39(U_587,U_588) )
    & ! [U_587,U_588] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_588),U_587))
        | ~ sP39(U_587,U_588) )
    & ! [U_587,U_588] :
        ( sP39(U_587,U_588)
        | U_588 != U_587 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39])],[f_246_2]) ).

cnf(f_246_4,plain,
    ( sP39(U_587,U_588)
    | U_588 != U_587 ),
    inference(clausify,[status(thm)],[f_246_3]) ).

cnf(f_246_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_588),U_587))
    | ~ sP39(U_587,U_588) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

cnf(f_246_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_587),U_588))
    | ~ sP39(U_587,U_588) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

fof(f_247_1,plain,
    ! [A,B] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A))
        & hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) )
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_193_equalityE]) ).

fof(f_247_2,plain,
    ! [U_590,U_589] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_589),U_590))
        & hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_590),U_589)) )
      | U_590 != U_589 ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

fof(f_247_3,plain,
    ( ! [U_589,U_590] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_589),U_590))
        | ~ sP40(U_589,U_590) )
    & ! [U_589,U_590] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_590),U_589))
        | ~ sP40(U_589,U_590) )
    & ! [U_589,U_590] :
        ( sP40(U_589,U_590)
        | U_590 != U_589 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_247_2]) ).

cnf(f_247_4,plain,
    ( sP40(U_589,U_590)
    | U_590 != U_589 ),
    inference(clausify,[status(thm)],[f_247_3]) ).

cnf(f_247_5,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_590),U_589))
    | ~ sP40(U_589,U_590) ),
    inference(clausify,[status(thm)],[f_247_3]) ).

cnf(f_247_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_589),U_590))
    | ~ sP40(U_589,U_590) ),
    inference(clausify,[status(thm)],[f_247_3]) ).

fof(f_248_1,plain,
    ! [C_2,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C_2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C_2))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_194_subset__trans]) ).

fof(f_248_2,plain,
    ! [U_593,U_592,U_591] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_592),U_593))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_591),U_593))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_592),U_591)) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

fof(f_248_3,plain,
    ! [U_591,U_592,U_593] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_592),U_593))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_591),U_593))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_592),U_591)) ),
    inference(definitional_conversion,[status(esa)],[f_248_2]) ).

cnf(f_248_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_592),U_593))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_591),U_593))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_592),U_591)) ),
    inference(clausify,[status(thm)],[f_248_3]) ).

fof(f_249_1,plain,
    ! [C_2,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),C_2))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),C_2))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_195_subset__trans]) ).

fof(f_249_2,plain,
    ! [U_596,U_595,U_594] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_595),U_596))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_594),U_596))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_595),U_594)) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

fof(f_249_3,plain,
    ! [U_595,U_594,U_596] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_595),U_596))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_594),U_596))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_595),U_594)) ),
    inference(definitional_conversion,[status(esa)],[f_249_2]) ).

cnf(f_249_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_595),U_596))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_594),U_596))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_595),U_594)) ),
    inference(clausify,[status(thm)],[f_249_3]) ).

fof(f_250_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_196_set__mp]) ).

fof(f_250_2,plain,
    ! [U_599,U_598,U_597] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_599),U_597))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_599),U_598))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_598),U_597)) ),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

fof(f_250_3,plain,
    ! [U_597,U_598,U_599] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_599),U_597))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_599),U_598))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_598),U_597)) ),
    inference(definitional_conversion,[status(esa)],[f_250_2]) ).

cnf(f_250_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_599),U_597))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_599),U_598))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_598),U_597)) ),
    inference(clausify,[status(thm)],[f_250_3]) ).

fof(f_251_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_197_set__mp]) ).

fof(f_251_2,plain,
    ! [U_602,U_601,U_600] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_602),U_600))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_602),U_601))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_601),U_600)) ),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

fof(f_251_3,plain,
    ! [U_601,U_600,U_602] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_602),U_600))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_602),U_601))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_601),U_600)) ),
    inference(definitional_conversion,[status(esa)],[f_251_2]) ).

cnf(f_251_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_602),U_600))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_602),U_601))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_601),U_600)) ),
    inference(clausify,[status(thm)],[f_251_3]) ).

fof(f_252_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_198_set__rev__mp]) ).

fof(f_252_2,plain,
    ! [U_605,U_604,U_603] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_604),U_605))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_603),U_605))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_604),U_603)) ),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

fof(f_252_3,plain,
    ! [U_603,U_604,U_605] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_604),U_605))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_603),U_605))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_604),U_603)) ),
    inference(definitional_conversion,[status(esa)],[f_252_2]) ).

cnf(f_252_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_604),U_605))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_603),U_605))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_604),U_603)) ),
    inference(clausify,[status(thm)],[f_252_3]) ).

fof(f_253_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_199_set__rev__mp]) ).

fof(f_253_2,plain,
    ! [U_608,U_607,U_606] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_607),U_608))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_606),U_608))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_607),U_606)) ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

fof(f_253_3,plain,
    ! [U_606,U_607,U_608] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_607),U_608))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_606),U_608))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_607),U_606)) ),
    inference(definitional_conversion,[status(esa)],[f_253_2]) ).

cnf(f_253_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_607),U_608))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_606),U_608))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_607),U_606)) ),
    inference(clausify,[status(thm)],[f_253_3]) ).

fof(f_254_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_200_in__mono]) ).

fof(f_254_2,plain,
    ! [U_611,U_610,U_609] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_611),U_609))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_611),U_610))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_610),U_609)) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

fof(f_254_3,plain,
    ! [U_609,U_610,U_611] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_611),U_609))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_611),U_610))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_610),U_609)) ),
    inference(definitional_conversion,[status(esa)],[f_254_2]) ).

cnf(f_254_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_611),U_609))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_611),U_610))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_610),U_609)) ),
    inference(clausify,[status(thm)],[f_254_3]) ).

fof(f_255_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_201_in__mono]) ).

fof(f_255_2,plain,
    ! [U_614,U_613,U_612] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_614),U_612))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_614),U_613))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_613),U_612)) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

fof(f_255_3,plain,
    ! [U_613,U_612,U_614] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_614),U_612))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_614),U_613))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_613),U_612)) ),
    inference(definitional_conversion,[status(esa)],[f_255_2]) ).

cnf(f_255_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_614),U_612))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_614),U_613))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_613),U_612)) ),
    inference(clausify,[status(thm)],[f_255_3]) ).

fof(f_256_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_202_equalityD2]) ).

fof(f_256_2,plain,
    ! [U_616,U_615] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_615),U_616))
      | U_616 != U_615 ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

fof(f_256_3,plain,
    ! [U_615,U_616] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_615),U_616))
      | U_616 != U_615 ),
    inference(definitional_conversion,[status(esa)],[f_256_2]) ).

cnf(f_256_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_615),U_616))
    | U_616 != U_615 ),
    inference(clausify,[status(thm)],[f_256_3]) ).

fof(f_257_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_203_equalityD2]) ).

fof(f_257_2,plain,
    ! [U_618,U_617] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_617),U_618))
      | U_618 != U_617 ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

fof(f_257_3,plain,
    ! [U_617,U_618] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_617),U_618))
      | U_618 != U_617 ),
    inference(definitional_conversion,[status(esa)],[f_257_2]) ).

cnf(f_257_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_617),U_618))
    | U_618 != U_617 ),
    inference(clausify,[status(thm)],[f_257_3]) ).

fof(f_258_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_204_equalityD1]) ).

fof(f_258_2,plain,
    ! [U_620,U_619] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_620),U_619))
      | U_620 != U_619 ),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

fof(f_258_3,plain,
    ! [U_620,U_619] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_620),U_619))
      | U_620 != U_619 ),
    inference(definitional_conversion,[status(esa)],[f_258_2]) ).

cnf(f_258_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_620),U_619))
    | U_620 != U_619 ),
    inference(clausify,[status(thm)],[f_258_3]) ).

fof(f_259_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_205_equalityD1]) ).

fof(f_259_2,plain,
    ! [U_622,U_621] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_622),U_621))
      | U_622 != U_621 ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

fof(f_259_3,plain,
    ! [U_621,U_622] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_622),U_621))
      | U_622 != U_621 ),
    inference(definitional_conversion,[status(esa)],[f_259_2]) ).

cnf(f_259_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_622),U_621))
    | U_622 != U_621 ),
    inference(clausify,[status(thm)],[f_259_3]) ).

fof(f_260_1,plain,
    ! [A,B] :
      ( ( ( A = B
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) )
        & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) )
          | A != B ) )
      | ~ is_fun_pname_bool(B)
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_206_set__eq__subset]) ).

fof(f_260_2,plain,
    ! [U_624,U_623] :
      ( ( ( U_624 = U_623
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_623),U_624))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_624),U_623)) )
        & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_623),U_624))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_624),U_623)) )
          | U_624 != U_623 ) )
      | ~ is_fun_pname_bool(U_623)
      | ~ is_fun_pname_bool(U_624) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

fof(f_260_3,plain,
    ( ! [U_623,U_624] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_623),U_624))
        | ~ sP41(U_623,U_624) )
    & ! [U_623,U_624] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_624),U_623))
        | ~ sP41(U_623,U_624) )
    & ! [U_623,U_624] :
        ( U_624 = U_623
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_623),U_624))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_624),U_623))
        | ~ sP42(U_623,U_624) )
    & ! [U_623,U_624] :
        ( sP41(U_623,U_624)
        | U_624 != U_623
        | ~ sP42(U_623,U_624) )
    & ! [U_623,U_624] :
        ( sP42(U_623,U_624)
        | ~ is_fun_pname_bool(U_623)
        | ~ is_fun_pname_bool(U_624) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41,sP42])],[f_260_2]) ).

cnf(f_260_4,plain,
    ( sP42(U_623,U_624)
    | ~ is_fun_pname_bool(U_623)
    | ~ is_fun_pname_bool(U_624) ),
    inference(clausify,[status(thm)],[f_260_3]) ).

cnf(f_260_5,plain,
    ( sP41(U_623,U_624)
    | U_624 != U_623
    | ~ sP42(U_623,U_624) ),
    inference(clausify,[status(thm)],[f_260_3]) ).

cnf(f_260_6,plain,
    ( U_624 = U_623
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_623),U_624))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_624),U_623))
    | ~ sP42(U_623,U_624) ),
    inference(clausify,[status(thm)],[f_260_3]) ).

cnf(f_260_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_624),U_623))
    | ~ sP41(U_623,U_624) ),
    inference(clausify,[status(thm)],[f_260_3]) ).

cnf(f_260_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_623),U_624))
    | ~ sP41(U_623,U_624) ),
    inference(clausify,[status(thm)],[f_260_3]) ).

fof(f_261_1,plain,
    ! [A,B] :
      ( ( A = B
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) )
      & ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),A))
          & hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) )
        | A != B ) ),
    inference(fof_nnf,[status(thm)],[fact_207_set__eq__subset]) ).

fof(f_261_2,plain,
    ! [U_626,U_625] :
      ( ( U_626 = U_625
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_625),U_626))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_626),U_625)) )
      & ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_625),U_626))
          & hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_626),U_625)) )
        | U_626 != U_625 ) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

fof(f_261_3,plain,
    ( ! [U_630,U_628] :
        ( U_630 = U_628
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_628),U_630))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_630),U_628)) )
    & ! [U_629,U_627] :
        ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_627),U_629))
          & hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_629),U_627)) )
        | U_629 != U_627 ) ),
    inference(miniscope,[status(thm)],[f_261_2]) ).

fof(f_261_4,plain,
    ( ! [U_629,U_627] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_627),U_629))
        | ~ sP43(U_629,U_627) )
    & ! [U_629,U_627] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_629),U_627))
        | ~ sP43(U_629,U_627) )
    & ! [U_630,U_628] :
        ( U_630 = U_628
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_628),U_630))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_630),U_628)) )
    & ! [U_629,U_627] :
        ( sP43(U_629,U_627)
        | U_629 != U_627 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43])],[f_261_3]) ).

cnf(f_261_5,plain,
    ( sP43(U_629,U_627)
    | U_629 != U_627 ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_6,plain,
    ( U_630 = U_628
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_628),U_630))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_630),U_628)) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_7,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_629),U_627))
    | ~ sP43(U_629,U_627) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_8,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_627),U_629))
    | ~ sP43(U_629,U_627) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

fof(f_262_1,plain,
    ! [A] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),A)),
    inference(fof_nnf,[status(thm)],[fact_208_subset__refl]) ).

fof(f_262_2,plain,
    ! [U_631] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_631),U_631)),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

fof(f_262_3,plain,
    ! [U_631] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_631),U_631)),
    inference(definitional_conversion,[status(esa)],[f_262_2]) ).

cnf(f_262_4,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_631),U_631)),
    inference(clausify,[status(thm)],[f_262_3]) ).

fof(f_263_1,plain,
    ! [A] : hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),A)),
    inference(fof_nnf,[status(thm)],[fact_209_subset__refl]) ).

fof(f_263_2,plain,
    ! [U_632] : hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_632),U_632)),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

fof(f_263_3,plain,
    ! [U_632] : hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_632),U_632)),
    inference(definitional_conversion,[status(esa)],[f_263_2]) ).

cnf(f_263_4,plain,
    hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_632),U_632)),
    inference(clausify,[status(thm)],[f_263_3]) ).

fof(f_264_1,plain,
    ! [B_1,F,X_2,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_2003357581_state(F,A)))
      | B_1 != hAPP_p1422361149_state(F,X_2)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_210_rev__image__eqI]) ).

fof(f_264_2,plain,
    ! [U_636,U_635,U_634,U_633] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_636),image_2003357581_state(U_635,U_633)))
      | U_636 != hAPP_p1422361149_state(U_635,U_634)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_634),U_633)) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

fof(f_264_3,plain,
    ! [U_633,U_634,U_635,U_636] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_636),image_2003357581_state(U_635,U_633)))
      | U_636 != hAPP_p1422361149_state(U_635,U_634)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_634),U_633)) ),
    inference(definitional_conversion,[status(esa)],[f_264_2]) ).

cnf(f_264_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_636),image_2003357581_state(U_635,U_633)))
    | U_636 != hAPP_p1422361149_state(U_635,U_634)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_634),U_633)) ),
    inference(clausify,[status(thm)],[f_264_3]) ).

fof(f_265_1,plain,
    ! [F,X_2,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,hAPP_p1422361149_state(F,X_2)),image_2003357581_state(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_211_imageI]) ).

fof(f_265_2,plain,
    ! [U_639,U_638,U_637] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,hAPP_p1422361149_state(U_639,U_638)),image_2003357581_state(U_639,U_637)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_638),U_637)) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

fof(f_265_3,plain,
    ! [U_638,U_637,U_639] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,hAPP_p1422361149_state(U_639,U_638)),image_2003357581_state(U_639,U_637)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_638),U_637)) ),
    inference(definitional_conversion,[status(esa)],[f_265_2]) ).

cnf(f_265_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,hAPP_p1422361149_state(U_639,U_638)),image_2003357581_state(U_639,U_637)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_638),U_637)) ),
    inference(clausify,[status(thm)],[f_265_3]) ).

fof(f_266_1,plain,
    ! [Z,F,A] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,Z),image_2003357581_state(F,A)))
        | ! [X_1] :
            ( Z != hAPP_p1422361149_state(F,X_1)
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
            | ~ is_pname(X_1) ) )
      & ( ? [X_1] :
            ( Z = hAPP_p1422361149_state(F,X_1)
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
            & is_pname(X_1) )
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,Z),image_2003357581_state(F,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_212_image__iff]) ).

fof(f_266_2,plain,
    ! [U_644,U_643,U_642] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_644),image_2003357581_state(U_643,U_642)))
        | ! [U_641] :
            ( U_644 != hAPP_p1422361149_state(U_643,U_641)
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_641),U_642))
            | ~ is_pname(U_641) ) )
      & ( ? [U_640] :
            ( U_644 = hAPP_p1422361149_state(U_643,U_640)
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_640),U_642))
            & is_pname(U_640) )
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_644),image_2003357581_state(U_643,U_642))) ) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

fof(f_266_3,plain,
    ( ! [U_650,U_648,U_646] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_650),image_2003357581_state(U_648,U_646)))
        | ! [U_641] :
            ( U_650 != hAPP_p1422361149_state(U_648,U_641)
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_641),U_646))
            | ~ is_pname(U_641) ) )
    & ! [U_649,U_647,U_645] :
        ( ? [U_640] :
            ( U_649 = hAPP_p1422361149_state(U_647,U_640)
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_640),U_645))
            & is_pname(U_640) )
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_649),image_2003357581_state(U_647,U_645))) ) ),
    inference(miniscope,[status(thm)],[f_266_2]) ).

fof(f_266_4,plain,
    ( ! [U_650,U_648,U_646] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_650),image_2003357581_state(U_648,U_646)))
        | ! [U_641] :
            ( U_650 != hAPP_p1422361149_state(U_648,U_641)
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_641),U_646))
            | ~ is_pname(U_641) ) )
    & ! [U_649,U_647,U_645] :
        ( ( U_649 = hAPP_p1422361149_state(U_647,sK21(U_649,U_647,U_645))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK21(U_649,U_647,U_645)),U_645))
          & is_pname(sK21(U_649,U_647,U_645)) )
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_649),image_2003357581_state(U_647,U_645))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_640,sK21(U_649,U_647,U_645))],[f_266_3]) ).

fof(f_266_5,plain,
    ( ! [U_647,U_645,U_649] :
        ( U_649 = hAPP_p1422361149_state(U_647,sK21(U_649,U_647,U_645))
        | ~ sP44(U_647,U_645,U_649) )
    & ! [U_647,U_645,U_649] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK21(U_649,U_647,U_645)),U_645))
        | ~ sP44(U_647,U_645,U_649) )
    & ! [U_647,U_645,U_649] :
        ( is_pname(sK21(U_649,U_647,U_645))
        | ~ sP44(U_647,U_645,U_649) )
    & ! [U_641,U_646,U_648,U_650] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_650),image_2003357581_state(U_648,U_646)))
        | U_650 != hAPP_p1422361149_state(U_648,U_641)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_641),U_646))
        | ~ is_pname(U_641) )
    & ! [U_647,U_645,U_649] :
        ( sP44(U_647,U_645,U_649)
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_649),image_2003357581_state(U_647,U_645))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44])],[f_266_4]) ).

cnf(f_266_6,plain,
    ( sP44(U_647,U_645,U_649)
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_649),image_2003357581_state(U_647,U_645))) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

cnf(f_266_7,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_650),image_2003357581_state(U_648,U_646)))
    | U_650 != hAPP_p1422361149_state(U_648,U_641)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_641),U_646))
    | ~ is_pname(U_641) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

cnf(f_266_8,plain,
    ( is_pname(sK21(U_649,U_647,U_645))
    | ~ sP44(U_647,U_645,U_649) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

cnf(f_266_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK21(U_649,U_647,U_645)),U_645))
    | ~ sP44(U_647,U_645,U_649) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

cnf(f_266_10,plain,
    ( U_649 = hAPP_p1422361149_state(U_647,sK21(U_649,U_647,U_645))
    | ~ sP44(U_647,U_645,U_649) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

fof(f_267_1,plain,
    ! [P_1,Q_1] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,P_1),Q_1))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(P_1))) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(P_1))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,P_1),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_213_finite__Collect__disjI]) ).

fof(f_267_2,plain,
    ! [U_652,U_651] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_652),U_651))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_651)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_652))) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_651)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_652))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_652),U_651)))) ) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

fof(f_267_3,plain,
    ( ! [U_656,U_654] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_656),U_654))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_654)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_656))) )
    & ! [U_655,U_653] :
        ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_653)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_655))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_655),U_653)))) ) ),
    inference(miniscope,[status(thm)],[f_267_2]) ).

fof(f_267_4,plain,
    ( ! [U_655,U_653] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_653)))
        | ~ sP45(U_655,U_653) )
    & ! [U_655,U_653] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_655)))
        | ~ sP45(U_655,U_653) )
    & ! [U_654,U_656] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_656),U_654))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_654)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_656))) )
    & ! [U_655,U_653] :
        ( sP45(U_655,U_653)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_655),U_653)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45])],[f_267_3]) ).

cnf(f_267_5,plain,
    ( sP45(U_655,U_653)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_655),U_653)))) ),
    inference(clausify,[status(thm)],[f_267_4]) ).

cnf(f_267_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_656),U_654))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_654)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_656))) ),
    inference(clausify,[status(thm)],[f_267_4]) ).

cnf(f_267_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_655)))
    | ~ sP45(U_655,U_653) ),
    inference(clausify,[status(thm)],[f_267_4]) ).

cnf(f_267_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_653)))
    | ~ sP45(U_655,U_653) ),
    inference(clausify,[status(thm)],[f_267_4]) ).

fof(f_268_1,plain,
    ! [P_1,Q_1] :
      ( ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,P_1),Q_1))))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(Q_1)))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(P_1))) )
      & ( ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(Q_1)))
          & hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(P_1))) )
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,P_1),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_214_finite__Collect__disjI]) ).

fof(f_268_2,plain,
    ! [U_658,U_657] :
      ( ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,U_658),U_657))))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_657)))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_658))) )
      & ( ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_657)))
          & hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_658))) )
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,U_658),U_657)))) ) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

fof(f_268_3,plain,
    ( ! [U_662,U_660] :
        ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,U_662),U_660))))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_660)))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_662))) )
    & ! [U_661,U_659] :
        ( ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_659)))
          & hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_661))) )
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,U_661),U_659)))) ) ),
    inference(miniscope,[status(thm)],[f_268_2]) ).

fof(f_268_4,plain,
    ( ! [U_661,U_659] :
        ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_659)))
        | ~ sP46(U_661,U_659) )
    & ! [U_661,U_659] :
        ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_661)))
        | ~ sP46(U_661,U_659) )
    & ! [U_660,U_662] :
        ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,U_662),U_660))))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_660)))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_662))) )
    & ! [U_661,U_659] :
        ( sP46(U_661,U_659)
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,U_661),U_659)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_268_3]) ).

cnf(f_268_5,plain,
    ( sP46(U_661,U_659)
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,U_661),U_659)))) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

cnf(f_268_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,U_662),U_660))))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_660)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_662))) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

cnf(f_268_7,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_661)))
    | ~ sP46(U_661,U_659) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

cnf(f_268_8,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,collec307967673_state(U_659)))
    | ~ sP46(U_661,U_659) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

fof(f_269_1,plain,
    ! [P_1,Q_1] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,P_1),Q_1))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(P_1))) )
      & ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(P_1))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,P_1),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_215_finite__Collect__disjI]) ).

fof(f_269_2,plain,
    ! [U_664,U_663] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_664),U_663))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_663)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_664))) )
      & ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_663)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_664))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_664),U_663)))) ) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

fof(f_269_3,plain,
    ( ! [U_668,U_666] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_668),U_666))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_666)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_668))) )
    & ! [U_667,U_665] :
        ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_665)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_667))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_667),U_665)))) ) ),
    inference(miniscope,[status(thm)],[f_269_2]) ).

fof(f_269_4,plain,
    ( ! [U_665,U_667] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_665)))
        | ~ sP47(U_665,U_667) )
    & ! [U_665,U_667] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_667)))
        | ~ sP47(U_665,U_667) )
    & ! [U_666,U_668] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_668),U_666))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_666)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_668))) )
    & ! [U_665,U_667] :
        ( sP47(U_665,U_667)
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_667),U_665)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_269_3]) ).

cnf(f_269_5,plain,
    ( sP47(U_665,U_667)
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_667),U_665)))) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

cnf(f_269_6,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_668),U_666))))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_666)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_668))) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

cnf(f_269_7,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_667)))
    | ~ sP47(U_665,U_667) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

cnf(f_269_8,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_665)))
    | ~ sP47(U_665,U_667) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

fof(f_270_1,plain,
    ! [P_1,Q_1] :
      ( ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,P_1),Q_1))))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(Q_1)))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(P_1))) )
      & ( ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(Q_1)))
          & hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(P_1))) )
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,P_1),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_216_finite__Collect__disjI]) ).

fof(f_270_2,plain,
    ! [U_670,U_669] :
      ( ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,U_670),U_669))))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_669)))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_670))) )
      & ( ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_669)))
          & hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_670))) )
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,U_670),U_669)))) ) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ( ! [U_674,U_672] :
        ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,U_674),U_672))))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_672)))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_674))) )
    & ! [U_673,U_671] :
        ( ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_671)))
          & hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_673))) )
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,U_673),U_671)))) ) ),
    inference(miniscope,[status(thm)],[f_270_2]) ).

fof(f_270_4,plain,
    ( ! [U_671,U_673] :
        ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_671)))
        | ~ sP48(U_671,U_673) )
    & ! [U_671,U_673] :
        ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_673)))
        | ~ sP48(U_671,U_673) )
    & ! [U_672,U_674] :
        ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,U_674),U_672))))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_672)))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_674))) )
    & ! [U_671,U_673] :
        ( sP48(U_671,U_673)
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,U_673),U_671)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_270_3]) ).

cnf(f_270_5,plain,
    ( sP48(U_671,U_673)
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,U_673),U_671)))) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_6,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,U_674),U_672))))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_672)))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_674))) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_7,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_673)))
    | ~ sP48(U_671,U_673) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_8,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,collec1823980261e_bool(U_671)))
    | ~ sP48(U_671,U_673) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

fof(f_271_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_217_insert__compr__raw]) ).

fof(f_271_2,plain,
    ! [U_676,U_675] : insert_pname(U_676,U_675) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_676)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_675))),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

fof(f_271_3,plain,
    ! [U_676,U_675] : insert_pname(U_676,U_675) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_676)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_675))),
    inference(definitional_conversion,[status(esa)],[f_271_2]) ).

cnf(f_271_4,plain,
    insert_pname(U_676,U_675) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_676)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_675))),
    inference(clausify,[status(thm)],[f_271_3]) ).

fof(f_272_1,plain,
    ! [X_1,Xa] : insert1415133716_state(X_1,Xa) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),X_1)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),Xa))),
    inference(fof_nnf,[status(thm)],[fact_218_insert__compr__raw]) ).

fof(f_272_2,plain,
    ! [U_678,U_677] : insert1415133716_state(U_678,U_677) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_678)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),U_677))),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

fof(f_272_3,plain,
    ! [U_678,U_677] : insert1415133716_state(U_678,U_677) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_678)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),U_677))),
    inference(definitional_conversion,[status(esa)],[f_272_2]) ).

cnf(f_272_4,plain,
    insert1415133716_state(U_678,U_677) = collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fdisj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_678)),hAPP_f98417237e_bool(cOMBC_1734175330l_bool(member1338687867_state),U_677))),
    inference(clausify,[status(thm)],[f_272_3]) ).

fof(f_273_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_219_insert__compr__raw]) ).

fof(f_273_2,plain,
    ! [U_680,U_679] : insert1325755072e_bool(U_680,U_679) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_680)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_679))),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

fof(f_273_3,plain,
    ! [U_679,U_680] : insert1325755072e_bool(U_680,U_679) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_680)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_679))),
    inference(definitional_conversion,[status(esa)],[f_273_2]) ).

cnf(f_273_4,plain,
    insert1325755072e_bool(U_680,U_679) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_680)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_679))),
    inference(clausify,[status(thm)],[f_273_3]) ).

fof(f_274_1,plain,
    ! [X_1,Xa] : insert1556680138e_bool(X_1,Xa) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),X_1)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),Xa))),
    inference(fof_nnf,[status(thm)],[fact_220_insert__compr__raw]) ).

fof(f_274_2,plain,
    ! [U_682,U_681] : insert1556680138e_bool(U_682,U_681) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_682)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),U_681))),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ! [U_681,U_682] : insert1556680138e_bool(U_682,U_681) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_682)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),U_681))),
    inference(definitional_conversion,[status(esa)],[f_274_2]) ).

cnf(f_274_4,plain,
    insert1556680138e_bool(U_682,U_681) = collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fdisj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_682)),hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(member2114907555e_bool),U_681))),
    inference(clausify,[status(thm)],[f_274_3]) ).

fof(f_275_1,plain,
    ! [A_2,B_1] :
      ( A_2 = B_1
      | insert_pname(A_2,bot_bo844097828e_bool) != insert_pname(B_1,bot_bo844097828e_bool)
      | ~ is_pname(B_1)
      | ~ is_pname(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_221_singleton__inject]) ).

fof(f_275_2,plain,
    ! [U_684,U_683] :
      ( U_684 = U_683
      | insert_pname(U_684,bot_bo844097828e_bool) != insert_pname(U_683,bot_bo844097828e_bool)
      | ~ is_pname(U_683)
      | ~ is_pname(U_684) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

fof(f_275_3,plain,
    ! [U_684,U_683] :
      ( U_684 = U_683
      | insert_pname(U_684,bot_bo844097828e_bool) != insert_pname(U_683,bot_bo844097828e_bool)
      | ~ is_pname(U_683)
      | ~ is_pname(U_684) ),
    inference(definitional_conversion,[status(esa)],[f_275_2]) ).

cnf(f_275_4,plain,
    ( U_684 = U_683
    | insert_pname(U_684,bot_bo844097828e_bool) != insert_pname(U_683,bot_bo844097828e_bool)
    | ~ is_pname(U_683)
    | ~ is_pname(U_684) ),
    inference(clausify,[status(thm)],[f_275_3]) ).

fof(f_276_1,plain,
    ! [A_2,B_1] :
      ( A_2 = B_1
      | insert1415133716_state(A_2,bot_bo620288102e_bool) != insert1415133716_state(B_1,bot_bo620288102e_bool) ),
    inference(fof_nnf,[status(thm)],[fact_222_singleton__inject]) ).

fof(f_276_2,plain,
    ! [U_686,U_685] :
      ( U_686 = U_685
      | insert1415133716_state(U_686,bot_bo620288102e_bool) != insert1415133716_state(U_685,bot_bo620288102e_bool) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

fof(f_276_3,plain,
    ! [U_685,U_686] :
      ( U_686 = U_685
      | insert1415133716_state(U_686,bot_bo620288102e_bool) != insert1415133716_state(U_685,bot_bo620288102e_bool) ),
    inference(definitional_conversion,[status(esa)],[f_276_2]) ).

cnf(f_276_4,plain,
    ( U_686 = U_685
    | insert1415133716_state(U_686,bot_bo620288102e_bool) != insert1415133716_state(U_685,bot_bo620288102e_bool) ),
    inference(clausify,[status(thm)],[f_276_3]) ).

fof(f_277_1,plain,
    ! [B_1,A_2] :
      ( B_1 = A_2
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_2,bot_bo844097828e_bool)))
      | ~ is_pname(A_2)
      | ~ is_pname(B_1) ),
    inference(fof_nnf,[status(thm)],[fact_223_singletonE]) ).

fof(f_277_2,plain,
    ! [U_688,U_687] :
      ( U_688 = U_687
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_688),insert_pname(U_687,bot_bo844097828e_bool)))
      | ~ is_pname(U_687)
      | ~ is_pname(U_688) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

fof(f_277_3,plain,
    ! [U_687,U_688] :
      ( U_688 = U_687
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_688),insert_pname(U_687,bot_bo844097828e_bool)))
      | ~ is_pname(U_687)
      | ~ is_pname(U_688) ),
    inference(definitional_conversion,[status(esa)],[f_277_2]) ).

cnf(f_277_4,plain,
    ( U_688 = U_687
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_688),insert_pname(U_687,bot_bo844097828e_bool)))
    | ~ is_pname(U_687)
    | ~ is_pname(U_688) ),
    inference(clausify,[status(thm)],[f_277_3]) ).

fof(f_278_1,plain,
    ! [B_1,A_2] :
      ( B_1 = A_2
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),insert1415133716_state(A_2,bot_bo620288102e_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_224_singletonE]) ).

fof(f_278_2,plain,
    ! [U_690,U_689] :
      ( U_690 = U_689
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_690),insert1415133716_state(U_689,bot_bo620288102e_bool))) ),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

fof(f_278_3,plain,
    ! [U_690,U_689] :
      ( U_690 = U_689
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_690),insert1415133716_state(U_689,bot_bo620288102e_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_278_2]) ).

cnf(f_278_4,plain,
    ( U_690 = U_689
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_690),insert1415133716_state(U_689,bot_bo620288102e_bool))) ),
    inference(clausify,[status(thm)],[f_278_3]) ).

fof(f_279_1,plain,
    ! [A_2,B_1,C_1,D_1] :
      ( ( ( insert_pname(A_2,insert_pname(B_1,bot_bo844097828e_bool)) = insert_pname(C_1,insert_pname(D_1,bot_bo844097828e_bool))
          | ( ( B_1 != C_1
              | A_2 != D_1 )
            & ( B_1 != D_1
              | A_2 != C_1 ) ) )
        & ( ( B_1 = C_1
            & A_2 = D_1 )
          | ( B_1 = D_1
            & A_2 = C_1 )
          | insert_pname(A_2,insert_pname(B_1,bot_bo844097828e_bool)) != insert_pname(C_1,insert_pname(D_1,bot_bo844097828e_bool)) ) )
      | ~ is_pname(D_1)
      | ~ is_pname(C_1)
      | ~ is_pname(B_1)
      | ~ is_pname(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_225_doubleton__eq__iff]) ).

fof(f_279_2,plain,
    ! [U_694,U_693,U_692,U_691] :
      ( ( ( insert_pname(U_694,insert_pname(U_693,bot_bo844097828e_bool)) = insert_pname(U_692,insert_pname(U_691,bot_bo844097828e_bool))
          | ( ( U_693 != U_692
              | U_694 != U_691 )
            & ( U_693 != U_691
              | U_694 != U_692 ) ) )
        & ( ( U_693 = U_692
            & U_694 = U_691 )
          | ( U_693 = U_691
            & U_694 = U_692 )
          | insert_pname(U_694,insert_pname(U_693,bot_bo844097828e_bool)) != insert_pname(U_692,insert_pname(U_691,bot_bo844097828e_bool)) ) )
      | ~ is_pname(U_691)
      | ~ is_pname(U_692)
      | ~ is_pname(U_693)
      | ~ is_pname(U_694) ),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

fof(f_279_3,plain,
    ( ! [U_692,U_691,U_693,U_694] :
        ( U_693 != U_692
        | U_694 != U_691
        | ~ sP51(U_692,U_691,U_693,U_694) )
    & ! [U_692,U_691,U_693,U_694] :
        ( U_693 != U_691
        | U_694 != U_692
        | ~ sP51(U_692,U_691,U_693,U_694) )
    & ! [U_692,U_691,U_693,U_694] :
        ( U_693 = U_692
        | ~ sP50(U_692,U_691,U_693,U_694) )
    & ! [U_692,U_691,U_693,U_694] :
        ( U_694 = U_691
        | ~ sP50(U_692,U_691,U_693,U_694) )
    & ! [U_692,U_691,U_693,U_694] :
        ( U_693 = U_691
        | ~ sP49(U_692,U_691,U_693,U_694) )
    & ! [U_692,U_691,U_693,U_694] :
        ( U_694 = U_692
        | ~ sP49(U_692,U_691,U_693,U_694) )
    & ! [U_692,U_691,U_693,U_694] :
        ( insert_pname(U_694,insert_pname(U_693,bot_bo844097828e_bool)) = insert_pname(U_692,insert_pname(U_691,bot_bo844097828e_bool))
        | sP51(U_692,U_691,U_693,U_694)
        | ~ sP52(U_692,U_691,U_693,U_694) )
    & ! [U_692,U_691,U_693,U_694] :
        ( sP50(U_692,U_691,U_693,U_694)
        | sP49(U_692,U_691,U_693,U_694)
        | insert_pname(U_694,insert_pname(U_693,bot_bo844097828e_bool)) != insert_pname(U_692,insert_pname(U_691,bot_bo844097828e_bool))
        | ~ sP52(U_692,U_691,U_693,U_694) )
    & ! [U_692,U_691,U_693,U_694] :
        ( sP52(U_692,U_691,U_693,U_694)
        | ~ is_pname(U_691)
        | ~ is_pname(U_692)
        | ~ is_pname(U_693)
        | ~ is_pname(U_694) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49,sP50,sP51,sP52])],[f_279_2]) ).

cnf(f_279_4,plain,
    ( sP52(U_692,U_691,U_693,U_694)
    | ~ is_pname(U_691)
    | ~ is_pname(U_692)
    | ~ is_pname(U_693)
    | ~ is_pname(U_694) ),
    inference(clausify,[status(thm)],[f_279_3]) ).

cnf(f_279_5,plain,
    ( sP50(U_692,U_691,U_693,U_694)
    | sP49(U_692,U_691,U_693,U_694)
    | insert_pname(U_694,insert_pname(U_693,bot_bo844097828e_bool)) != insert_pname(U_692,insert_pname(U_691,bot_bo844097828e_bool))
    | ~ sP52(U_692,U_691,U_693,U_694) ),
    inference(clausify,[status(thm)],[f_279_3]) ).

cnf(f_279_6,plain,
    ( insert_pname(U_694,insert_pname(U_693,bot_bo844097828e_bool)) = insert_pname(U_692,insert_pname(U_691,bot_bo844097828e_bool))
    | sP51(U_692,U_691,U_693,U_694)
    | ~ sP52(U_692,U_691,U_693,U_694) ),
    inference(clausify,[status(thm)],[f_279_3]) ).

cnf(f_279_7,plain,
    ( U_694 = U_692
    | ~ sP49(U_692,U_691,U_693,U_694) ),
    inference(clausify,[status(thm)],[f_279_3]) ).

cnf(f_279_8,plain,
    ( U_693 = U_691
    | ~ sP49(U_692,U_691,U_693,U_694) ),
    inference(clausify,[status(thm)],[f_279_3]) ).

cnf(f_279_9,plain,
    ( U_694 = U_691
    | ~ sP50(U_692,U_691,U_693,U_694) ),
    inference(clausify,[status(thm)],[f_279_3]) ).

cnf(f_279_10,plain,
    ( U_693 = U_692
    | ~ sP50(U_692,U_691,U_693,U_694) ),
    inference(clausify,[status(thm)],[f_279_3]) ).

cnf(f_279_11,plain,
    ( U_693 != U_691
    | U_694 != U_692
    | ~ sP51(U_692,U_691,U_693,U_694) ),
    inference(clausify,[status(thm)],[f_279_3]) ).

cnf(f_279_12,plain,
    ( U_693 != U_692
    | U_694 != U_691
    | ~ sP51(U_692,U_691,U_693,U_694) ),
    inference(clausify,[status(thm)],[f_279_3]) ).

fof(f_280_1,plain,
    ! [A_2,B_1,C_1,D_1] :
      ( ( insert1415133716_state(A_2,insert1415133716_state(B_1,bot_bo620288102e_bool)) = insert1415133716_state(C_1,insert1415133716_state(D_1,bot_bo620288102e_bool))
        | ( ( B_1 != C_1
            | A_2 != D_1 )
          & ( B_1 != D_1
            | A_2 != C_1 ) ) )
      & ( ( B_1 = C_1
          & A_2 = D_1 )
        | ( B_1 = D_1
          & A_2 = C_1 )
        | insert1415133716_state(A_2,insert1415133716_state(B_1,bot_bo620288102e_bool)) != insert1415133716_state(C_1,insert1415133716_state(D_1,bot_bo620288102e_bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_226_doubleton__eq__iff]) ).

fof(f_280_2,plain,
    ! [U_698,U_697,U_696,U_695] :
      ( ( insert1415133716_state(U_698,insert1415133716_state(U_697,bot_bo620288102e_bool)) = insert1415133716_state(U_696,insert1415133716_state(U_695,bot_bo620288102e_bool))
        | ( ( U_697 != U_696
            | U_698 != U_695 )
          & ( U_697 != U_695
            | U_698 != U_696 ) ) )
      & ( ( U_697 = U_696
          & U_698 = U_695 )
        | ( U_697 = U_695
          & U_698 = U_696 )
        | insert1415133716_state(U_698,insert1415133716_state(U_697,bot_bo620288102e_bool)) != insert1415133716_state(U_696,insert1415133716_state(U_695,bot_bo620288102e_bool)) ) ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

fof(f_280_3,plain,
    ( ! [U_706,U_704,U_702,U_700] :
        ( insert1415133716_state(U_706,insert1415133716_state(U_704,bot_bo620288102e_bool)) = insert1415133716_state(U_702,insert1415133716_state(U_700,bot_bo620288102e_bool))
        | ( ( U_704 != U_702
            | U_706 != U_700 )
          & ( U_704 != U_700
            | U_706 != U_702 ) ) )
    & ! [U_705,U_703,U_701,U_699] :
        ( ( U_703 = U_701
          & U_705 = U_699 )
        | ( U_703 = U_699
          & U_705 = U_701 )
        | insert1415133716_state(U_705,insert1415133716_state(U_703,bot_bo620288102e_bool)) != insert1415133716_state(U_701,insert1415133716_state(U_699,bot_bo620288102e_bool)) ) ),
    inference(miniscope,[status(thm)],[f_280_2]) ).

fof(f_280_4,plain,
    ( ! [U_700,U_704,U_702,U_706] :
        ( U_704 != U_702
        | U_706 != U_700
        | ~ sP55(U_700,U_704,U_702,U_706) )
    & ! [U_700,U_704,U_702,U_706] :
        ( U_704 != U_700
        | U_706 != U_702
        | ~ sP55(U_700,U_704,U_702,U_706) )
    & ! [U_703,U_699,U_705,U_701] :
        ( U_703 = U_701
        | ~ sP54(U_703,U_699,U_705,U_701) )
    & ! [U_703,U_699,U_705,U_701] :
        ( U_705 = U_699
        | ~ sP54(U_703,U_699,U_705,U_701) )
    & ! [U_703,U_699,U_705,U_701] :
        ( U_703 = U_699
        | ~ sP53(U_703,U_699,U_705,U_701) )
    & ! [U_703,U_699,U_705,U_701] :
        ( U_705 = U_701
        | ~ sP53(U_703,U_699,U_705,U_701) )
    & ! [U_700,U_704,U_702,U_706] :
        ( insert1415133716_state(U_706,insert1415133716_state(U_704,bot_bo620288102e_bool)) = insert1415133716_state(U_702,insert1415133716_state(U_700,bot_bo620288102e_bool))
        | sP55(U_700,U_704,U_702,U_706) )
    & ! [U_703,U_699,U_705,U_701] :
        ( sP54(U_703,U_699,U_705,U_701)
        | sP53(U_703,U_699,U_705,U_701)
        | insert1415133716_state(U_705,insert1415133716_state(U_703,bot_bo620288102e_bool)) != insert1415133716_state(U_701,insert1415133716_state(U_699,bot_bo620288102e_bool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53,sP54,sP55])],[f_280_3]) ).

cnf(f_280_5,plain,
    ( sP54(U_703,U_699,U_705,U_701)
    | sP53(U_703,U_699,U_705,U_701)
    | insert1415133716_state(U_705,insert1415133716_state(U_703,bot_bo620288102e_bool)) != insert1415133716_state(U_701,insert1415133716_state(U_699,bot_bo620288102e_bool)) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

cnf(f_280_6,plain,
    ( insert1415133716_state(U_706,insert1415133716_state(U_704,bot_bo620288102e_bool)) = insert1415133716_state(U_702,insert1415133716_state(U_700,bot_bo620288102e_bool))
    | sP55(U_700,U_704,U_702,U_706) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

cnf(f_280_7,plain,
    ( U_705 = U_701
    | ~ sP53(U_703,U_699,U_705,U_701) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

cnf(f_280_8,plain,
    ( U_703 = U_699
    | ~ sP53(U_703,U_699,U_705,U_701) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

cnf(f_280_9,plain,
    ( U_705 = U_699
    | ~ sP54(U_703,U_699,U_705,U_701) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

cnf(f_280_10,plain,
    ( U_703 = U_701
    | ~ sP54(U_703,U_699,U_705,U_701) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

cnf(f_280_11,plain,
    ( U_704 != U_700
    | U_706 != U_702
    | ~ sP55(U_700,U_704,U_702,U_706) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

cnf(f_280_12,plain,
    ( U_704 != U_702
    | U_706 != U_700
    | ~ sP55(U_700,U_704,U_702,U_706) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

fof(f_281_1,plain,
    ! [B_1,A_2] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_2,bot_bo844097828e_bool)))
          | B_1 != A_2 )
        & ( B_1 = A_2
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_1),insert_pname(A_2,bot_bo844097828e_bool))) ) )
      | ~ is_pname(A_2)
      | ~ is_pname(B_1) ),
    inference(fof_nnf,[status(thm)],[fact_227_singleton__iff]) ).

fof(f_281_2,plain,
    ! [U_708,U_707] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_708),insert_pname(U_707,bot_bo844097828e_bool)))
          | U_708 != U_707 )
        & ( U_708 = U_707
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_708),insert_pname(U_707,bot_bo844097828e_bool))) ) )
      | ~ is_pname(U_707)
      | ~ is_pname(U_708) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

fof(f_281_3,plain,
    ( ! [U_707,U_708] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_708),insert_pname(U_707,bot_bo844097828e_bool)))
        | U_708 != U_707
        | ~ sP56(U_707,U_708) )
    & ! [U_707,U_708] :
        ( U_708 = U_707
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_708),insert_pname(U_707,bot_bo844097828e_bool)))
        | ~ sP56(U_707,U_708) )
    & ! [U_707,U_708] :
        ( sP56(U_707,U_708)
        | ~ is_pname(U_707)
        | ~ is_pname(U_708) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56])],[f_281_2]) ).

cnf(f_281_4,plain,
    ( sP56(U_707,U_708)
    | ~ is_pname(U_707)
    | ~ is_pname(U_708) ),
    inference(clausify,[status(thm)],[f_281_3]) ).

cnf(f_281_5,plain,
    ( U_708 = U_707
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_708),insert_pname(U_707,bot_bo844097828e_bool)))
    | ~ sP56(U_707,U_708) ),
    inference(clausify,[status(thm)],[f_281_3]) ).

cnf(f_281_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_708),insert_pname(U_707,bot_bo844097828e_bool)))
    | U_708 != U_707
    | ~ sP56(U_707,U_708) ),
    inference(clausify,[status(thm)],[f_281_3]) ).

fof(f_282_1,plain,
    ! [B_1,A_2] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),insert1415133716_state(A_2,bot_bo620288102e_bool)))
        | B_1 != A_2 )
      & ( B_1 = A_2
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),insert1415133716_state(A_2,bot_bo620288102e_bool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_228_singleton__iff]) ).

fof(f_282_2,plain,
    ! [U_710,U_709] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_710),insert1415133716_state(U_709,bot_bo620288102e_bool)))
        | U_710 != U_709 )
      & ( U_710 = U_709
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_710),insert1415133716_state(U_709,bot_bo620288102e_bool))) ) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

fof(f_282_3,plain,
    ( ! [U_714,U_712] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_714),insert1415133716_state(U_712,bot_bo620288102e_bool)))
        | U_714 != U_712 )
    & ! [U_713,U_711] :
        ( U_713 = U_711
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_713),insert1415133716_state(U_711,bot_bo620288102e_bool))) ) ),
    inference(miniscope,[status(thm)],[f_282_2]) ).

fof(f_282_4,plain,
    ( ! [U_714,U_712] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_714),insert1415133716_state(U_712,bot_bo620288102e_bool)))
        | U_714 != U_712 )
    & ! [U_711,U_713] :
        ( U_713 = U_711
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_713),insert1415133716_state(U_711,bot_bo620288102e_bool))) ) ),
    inference(definitional_conversion,[status(esa)],[f_282_3]) ).

cnf(f_282_5,plain,
    ( U_713 = U_711
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_713),insert1415133716_state(U_711,bot_bo620288102e_bool))) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

cnf(f_282_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_714),insert1415133716_state(U_712,bot_bo620288102e_bool)))
    | U_714 != U_712 ),
    inference(clausify,[status(thm)],[f_282_4]) ).

fof(f_283_1,plain,
    ! [A_2,A] : insert_pname(A_2,A) != bot_bo844097828e_bool,
    inference(fof_nnf,[status(thm)],[fact_229_insert__not__empty]) ).

fof(f_283_2,plain,
    ! [U_716,U_715] : insert_pname(U_716,U_715) != bot_bo844097828e_bool,
    inference(variable_rename,[status(thm)],[f_283_1]) ).

fof(f_283_3,plain,
    ! [U_715,U_716] : insert_pname(U_716,U_715) != bot_bo844097828e_bool,
    inference(definitional_conversion,[status(esa)],[f_283_2]) ).

cnf(f_283_4,plain,
    insert_pname(U_716,U_715) != bot_bo844097828e_bool,
    inference(clausify,[status(thm)],[f_283_3]) ).

fof(f_284_1,plain,
    ! [A_2,A] : insert1415133716_state(A_2,A) != bot_bo620288102e_bool,
    inference(fof_nnf,[status(thm)],[fact_230_insert__not__empty]) ).

fof(f_284_2,plain,
    ! [U_718,U_717] : insert1415133716_state(U_718,U_717) != bot_bo620288102e_bool,
    inference(variable_rename,[status(thm)],[f_284_1]) ).

fof(f_284_3,plain,
    ! [U_717,U_718] : insert1415133716_state(U_718,U_717) != bot_bo620288102e_bool,
    inference(definitional_conversion,[status(esa)],[f_284_2]) ).

cnf(f_284_4,plain,
    insert1415133716_state(U_718,U_717) != bot_bo620288102e_bool,
    inference(clausify,[status(thm)],[f_284_3]) ).

fof(f_285_1,plain,
    ! [A_2,A] : bot_bo844097828e_bool != insert_pname(A_2,A),
    inference(fof_nnf,[status(thm)],[fact_231_empty__not__insert]) ).

fof(f_285_2,plain,
    ! [U_720,U_719] : bot_bo844097828e_bool != insert_pname(U_720,U_719),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

fof(f_285_3,plain,
    ! [U_720,U_719] : bot_bo844097828e_bool != insert_pname(U_720,U_719),
    inference(definitional_conversion,[status(esa)],[f_285_2]) ).

cnf(f_285_4,plain,
    bot_bo844097828e_bool != insert_pname(U_720,U_719),
    inference(clausify,[status(thm)],[f_285_3]) ).

fof(f_286_1,plain,
    ! [A_2,A] : bot_bo620288102e_bool != insert1415133716_state(A_2,A),
    inference(fof_nnf,[status(thm)],[fact_232_empty__not__insert]) ).

fof(f_286_2,plain,
    ! [U_722,U_721] : bot_bo620288102e_bool != insert1415133716_state(U_722,U_721),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

fof(f_286_3,plain,
    ! [U_722,U_721] : bot_bo620288102e_bool != insert1415133716_state(U_722,U_721),
    inference(definitional_conversion,[status(esa)],[f_286_2]) ).

cnf(f_286_4,plain,
    bot_bo620288102e_bool != insert1415133716_state(U_722,U_721),
    inference(clausify,[status(thm)],[f_286_3]) ).

fof(f_287_1,plain,
    ! [A_2,A] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_2,A)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) )
      & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_2,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_233_finite__insert]) ).

fof(f_287_2,plain,
    ! [U_724,U_723] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_724,U_723)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_723)) )
      & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_723))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_724,U_723))) ) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

fof(f_287_3,plain,
    ( ! [U_728,U_726] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_728,U_726)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_726)) )
    & ! [U_727,U_725] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_725))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_727,U_725))) ) ),
    inference(miniscope,[status(thm)],[f_287_2]) ).

fof(f_287_4,plain,
    ( ! [U_726,U_728] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_728,U_726)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_726)) )
    & ! [U_727,U_725] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_725))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_727,U_725))) ) ),
    inference(definitional_conversion,[status(esa)],[f_287_3]) ).

cnf(f_287_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_725))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_727,U_725))) ),
    inference(clausify,[status(thm)],[f_287_4]) ).

cnf(f_287_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_728,U_726)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_726)) ),
    inference(clausify,[status(thm)],[f_287_4]) ).

fof(f_288_1,plain,
    ! [A_2,A] :
      ( ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(A_2,A)))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,A)) )
      & ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,A))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(A_2,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_234_finite__insert]) ).

fof(f_288_2,plain,
    ! [U_730,U_729] :
      ( ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(U_730,U_729)))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_729)) )
      & ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_729))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(U_730,U_729))) ) ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

fof(f_288_3,plain,
    ( ! [U_734,U_732] :
        ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(U_734,U_732)))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_732)) )
    & ! [U_733,U_731] :
        ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_731))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(U_733,U_731))) ) ),
    inference(miniscope,[status(thm)],[f_288_2]) ).

fof(f_288_4,plain,
    ( ! [U_732,U_734] :
        ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(U_734,U_732)))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_732)) )
    & ! [U_733,U_731] :
        ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_731))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(U_733,U_731))) ) ),
    inference(definitional_conversion,[status(esa)],[f_288_3]) ).

cnf(f_288_5,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_731))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(U_733,U_731))) ),
    inference(clausify,[status(thm)],[f_288_4]) ).

cnf(f_288_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,insert1415133716_state(U_734,U_732)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_732)) ),
    inference(clausify,[status(thm)],[f_288_4]) ).

fof(f_289_1,plain,
    ! [A_2,A] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_2,A)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) )
      & ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_2,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_235_finite__insert]) ).

fof(f_289_2,plain,
    ! [U_736,U_735] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_736,U_735)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_735)) )
      & ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_735))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_736,U_735))) ) ),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

fof(f_289_3,plain,
    ( ! [U_740,U_738] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_740,U_738)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_738)) )
    & ! [U_739,U_737] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_737))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_739,U_737))) ) ),
    inference(miniscope,[status(thm)],[f_289_2]) ).

fof(f_289_4,plain,
    ( ! [U_738,U_740] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_740,U_738)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_738)) )
    & ! [U_739,U_737] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_737))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_739,U_737))) ) ),
    inference(definitional_conversion,[status(esa)],[f_289_3]) ).

cnf(f_289_5,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_737))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_739,U_737))) ),
    inference(clausify,[status(thm)],[f_289_4]) ).

cnf(f_289_6,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_740,U_738)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_738)) ),
    inference(clausify,[status(thm)],[f_289_4]) ).

fof(f_290_1,plain,
    ! [A_2,A] :
      ( ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(A_2,A)))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A)) )
      & ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(A_2,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_236_finite__insert]) ).

fof(f_290_2,plain,
    ! [U_742,U_741] :
      ( ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(U_742,U_741)))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_741)) )
      & ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_741))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(U_742,U_741))) ) ),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

fof(f_290_3,plain,
    ( ! [U_746,U_744] :
        ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(U_746,U_744)))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_744)) )
    & ! [U_745,U_743] :
        ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_743))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(U_745,U_743))) ) ),
    inference(miniscope,[status(thm)],[f_290_2]) ).

fof(f_290_4,plain,
    ( ! [U_744,U_746] :
        ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(U_746,U_744)))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_744)) )
    & ! [U_745,U_743] :
        ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_743))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(U_745,U_743))) ) ),
    inference(definitional_conversion,[status(esa)],[f_290_3]) ).

cnf(f_290_5,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_743))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(U_745,U_743))) ),
    inference(clausify,[status(thm)],[f_290_4]) ).

cnf(f_290_6,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,insert1556680138e_bool(U_746,U_744)))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_744)) ),
    inference(clausify,[status(thm)],[f_290_4]) ).

fof(f_291_1,plain,
    ! [A] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),bot_bo844097828e_bool))
          | A != bot_bo844097828e_bool )
        & ( A = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),bot_bo844097828e_bool)) ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_237_subset__empty]) ).

fof(f_291_2,plain,
    ! [U_747] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_747),bot_bo844097828e_bool))
          | U_747 != bot_bo844097828e_bool )
        & ( U_747 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_747),bot_bo844097828e_bool)) ) )
      | ~ is_fun_pname_bool(U_747) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

fof(f_291_3,plain,
    ( ! [U_747] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_747),bot_bo844097828e_bool))
        | U_747 != bot_bo844097828e_bool
        | ~ sP57(U_747) )
    & ! [U_747] :
        ( U_747 = bot_bo844097828e_bool
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_747),bot_bo844097828e_bool))
        | ~ sP57(U_747) )
    & ! [U_747] :
        ( sP57(U_747)
        | ~ is_fun_pname_bool(U_747) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57])],[f_291_2]) ).

cnf(f_291_4,plain,
    ( sP57(U_747)
    | ~ is_fun_pname_bool(U_747) ),
    inference(clausify,[status(thm)],[f_291_3]) ).

cnf(f_291_5,plain,
    ( U_747 = bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_747),bot_bo844097828e_bool))
    | ~ sP57(U_747) ),
    inference(clausify,[status(thm)],[f_291_3]) ).

cnf(f_291_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_747),bot_bo844097828e_bool))
    | U_747 != bot_bo844097828e_bool
    | ~ sP57(U_747) ),
    inference(clausify,[status(thm)],[f_291_3]) ).

fof(f_292_1,plain,
    ! [A] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),bot_bo620288102e_bool))
        | A != bot_bo620288102e_bool )
      & ( A = bot_bo620288102e_bool
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),bot_bo620288102e_bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_238_subset__empty]) ).

fof(f_292_2,plain,
    ! [U_748] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_748),bot_bo620288102e_bool))
        | U_748 != bot_bo620288102e_bool )
      & ( U_748 = bot_bo620288102e_bool
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_748),bot_bo620288102e_bool)) ) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

fof(f_292_3,plain,
    ( ! [U_750] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_750),bot_bo620288102e_bool))
        | U_750 != bot_bo620288102e_bool )
    & ! [U_749] :
        ( U_749 = bot_bo620288102e_bool
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_749),bot_bo620288102e_bool)) ) ),
    inference(miniscope,[status(thm)],[f_292_2]) ).

fof(f_292_4,plain,
    ( ! [U_750] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_750),bot_bo620288102e_bool))
        | U_750 != bot_bo620288102e_bool )
    & ! [U_749] :
        ( U_749 = bot_bo620288102e_bool
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_749),bot_bo620288102e_bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_292_3]) ).

cnf(f_292_5,plain,
    ( U_749 = bot_bo620288102e_bool
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_749),bot_bo620288102e_bool)) ),
    inference(clausify,[status(thm)],[f_292_4]) ).

cnf(f_292_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_750),bot_bo620288102e_bool))
    | U_750 != bot_bo620288102e_bool ),
    inference(clausify,[status(thm)],[f_292_4]) ).

fof(f_293_1,plain,
    ! [F,A] :
      ( ( ( image_2003357581_state(F,A) = bot_bo620288102e_bool
          | A != bot_bo844097828e_bool )
        & ( A = bot_bo844097828e_bool
          | image_2003357581_state(F,A) != bot_bo620288102e_bool ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_239_image__is__empty]) ).

fof(f_293_2,plain,
    ! [U_752,U_751] :
      ( ( ( image_2003357581_state(U_752,U_751) = bot_bo620288102e_bool
          | U_751 != bot_bo844097828e_bool )
        & ( U_751 = bot_bo844097828e_bool
          | image_2003357581_state(U_752,U_751) != bot_bo620288102e_bool ) )
      | ~ is_fun_pname_bool(U_751) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ( ! [U_752,U_751] :
        ( image_2003357581_state(U_752,U_751) = bot_bo620288102e_bool
        | U_751 != bot_bo844097828e_bool
        | ~ sP58(U_752,U_751) )
    & ! [U_752,U_751] :
        ( U_751 = bot_bo844097828e_bool
        | image_2003357581_state(U_752,U_751) != bot_bo620288102e_bool
        | ~ sP58(U_752,U_751) )
    & ! [U_752,U_751] :
        ( sP58(U_752,U_751)
        | ~ is_fun_pname_bool(U_751) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58])],[f_293_2]) ).

cnf(f_293_4,plain,
    ( sP58(U_752,U_751)
    | ~ is_fun_pname_bool(U_751) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

cnf(f_293_5,plain,
    ( U_751 = bot_bo844097828e_bool
    | image_2003357581_state(U_752,U_751) != bot_bo620288102e_bool
    | ~ sP58(U_752,U_751) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

cnf(f_293_6,plain,
    ( image_2003357581_state(U_752,U_751) = bot_bo620288102e_bool
    | U_751 != bot_bo844097828e_bool
    | ~ sP58(U_752,U_751) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

fof(f_294_1,plain,
    ! [F] : image_2003357581_state(F,bot_bo844097828e_bool) = bot_bo620288102e_bool,
    inference(fof_nnf,[status(thm)],[fact_240_image__empty]) ).

fof(f_294_2,plain,
    ! [U_753] : image_2003357581_state(U_753,bot_bo844097828e_bool) = bot_bo620288102e_bool,
    inference(variable_rename,[status(thm)],[f_294_1]) ).

fof(f_294_3,plain,
    ! [U_753] : image_2003357581_state(U_753,bot_bo844097828e_bool) = bot_bo620288102e_bool,
    inference(definitional_conversion,[status(esa)],[f_294_2]) ).

cnf(f_294_4,plain,
    image_2003357581_state(U_753,bot_bo844097828e_bool) = bot_bo620288102e_bool,
    inference(clausify,[status(thm)],[f_294_3]) ).

fof(f_295_1,plain,
    ! [F,A] :
      ( ( ( bot_bo620288102e_bool = image_2003357581_state(F,A)
          | A != bot_bo844097828e_bool )
        & ( A = bot_bo844097828e_bool
          | bot_bo620288102e_bool != image_2003357581_state(F,A) ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_241_empty__is__image]) ).

fof(f_295_2,plain,
    ! [U_755,U_754] :
      ( ( ( bot_bo620288102e_bool = image_2003357581_state(U_755,U_754)
          | U_754 != bot_bo844097828e_bool )
        & ( U_754 = bot_bo844097828e_bool
          | bot_bo620288102e_bool != image_2003357581_state(U_755,U_754) ) )
      | ~ is_fun_pname_bool(U_754) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

fof(f_295_3,plain,
    ( ! [U_755,U_754] :
        ( bot_bo620288102e_bool = image_2003357581_state(U_755,U_754)
        | U_754 != bot_bo844097828e_bool
        | ~ sP59(U_755,U_754) )
    & ! [U_755,U_754] :
        ( U_754 = bot_bo844097828e_bool
        | bot_bo620288102e_bool != image_2003357581_state(U_755,U_754)
        | ~ sP59(U_755,U_754) )
    & ! [U_755,U_754] :
        ( sP59(U_755,U_754)
        | ~ is_fun_pname_bool(U_754) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_295_2]) ).

cnf(f_295_4,plain,
    ( sP59(U_755,U_754)
    | ~ is_fun_pname_bool(U_754) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

cnf(f_295_5,plain,
    ( U_754 = bot_bo844097828e_bool
    | bot_bo620288102e_bool != image_2003357581_state(U_755,U_754)
    | ~ sP59(U_755,U_754) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

cnf(f_295_6,plain,
    ( bot_bo620288102e_bool = image_2003357581_state(U_755,U_754)
    | U_754 != bot_bo844097828e_bool
    | ~ sP59(U_755,U_754) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

fof(f_296_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_242_finite__subset]) ).

fof(f_296_2,plain,
    ! [U_757,U_756] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_757))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_756))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_757),U_756)) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ! [U_757,U_756] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_757))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_756))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_757),U_756)) ),
    inference(definitional_conversion,[status(esa)],[f_296_2]) ).

cnf(f_296_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_757))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_756))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_757),U_756)) ),
    inference(clausify,[status(thm)],[f_296_3]) ).

fof(f_297_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,B))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_243_finite__subset]) ).

fof(f_297_2,plain,
    ! [U_759,U_758] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_759))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_758))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_759),U_758)) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

fof(f_297_3,plain,
    ! [U_759,U_758] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_759))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_758))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_759),U_758)) ),
    inference(definitional_conversion,[status(esa)],[f_297_2]) ).

cnf(f_297_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_759))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_758))
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_759),U_758)) ),
    inference(clausify,[status(thm)],[f_297_3]) ).

fof(f_298_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_244_finite__subset]) ).

fof(f_298_2,plain,
    ! [U_761,U_760] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_761))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_760))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_761),U_760)) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

fof(f_298_3,plain,
    ! [U_761,U_760] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_761))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_760))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_761),U_760)) ),
    inference(definitional_conversion,[status(esa)],[f_298_2]) ).

cnf(f_298_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_761))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_760))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_761),U_760)) ),
    inference(clausify,[status(thm)],[f_298_3]) ).

fof(f_299_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,A))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,B))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_245_finite__subset]) ).

fof(f_299_2,plain,
    ! [U_763,U_762] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_763))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_762))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_763),U_762)) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

fof(f_299_3,plain,
    ! [U_763,U_762] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_763))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_762))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_763),U_762)) ),
    inference(definitional_conversion,[status(esa)],[f_299_2]) ).

cnf(f_299_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_763))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_762))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_763),U_762)) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

fof(f_300_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_246_rev__finite__subset]) ).

fof(f_300_2,plain,
    ! [U_765,U_764] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_765))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_765),U_764))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_764)) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

fof(f_300_3,plain,
    ! [U_764,U_765] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_765))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_765),U_764))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_764)) ),
    inference(definitional_conversion,[status(esa)],[f_300_2]) ).

cnf(f_300_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_765))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_765),U_764))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_764)) ),
    inference(clausify,[status(thm)],[f_300_3]) ).

fof(f_301_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,A))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,A),B))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_247_rev__finite__subset]) ).

fof(f_301_2,plain,
    ! [U_767,U_766] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_767))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_767),U_766))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_766)) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

fof(f_301_3,plain,
    ! [U_766,U_767] :
      ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_767))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_767),U_766))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_766)) ),
    inference(definitional_conversion,[status(esa)],[f_301_2]) ).

cnf(f_301_4,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_767))
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_767),U_766))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_766)) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

fof(f_302_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ),
    inference(fof_nnf,[status(thm)],[fact_248_rev__finite__subset]) ).

fof(f_302_2,plain,
    ! [U_769,U_768] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_769))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_769),U_768))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_768)) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ! [U_769,U_768] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_769))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_769),U_768))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_768)) ),
    inference(definitional_conversion,[status(esa)],[f_302_2]) ).

cnf(f_302_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_769))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_769),U_768))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_768)) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

fof(f_303_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,A))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,B)) ),
    inference(fof_nnf,[status(thm)],[fact_249_rev__finite__subset]) ).

fof(f_303_2,plain,
    ! [U_771,U_770] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_771))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_771),U_770))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_770)) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

fof(f_303_3,plain,
    ! [U_770,U_771] :
      ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_771))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_771),U_770))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_770)) ),
    inference(definitional_conversion,[status(esa)],[f_303_2]) ).

cnf(f_303_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_771))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_771),U_770))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_770)) ),
    inference(clausify,[status(thm)],[f_303_3]) ).

fof(f_304_1,plain,
    ! [A_2,C_2,D] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(A_2,C_2)),insert_pname(A_2,D)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_2),D)) ),
    inference(fof_nnf,[status(thm)],[fact_250_insert__mono]) ).

fof(f_304_2,plain,
    ! [U_774,U_773,U_772] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_774,U_773)),insert_pname(U_774,U_772)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_773),U_772)) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

fof(f_304_3,plain,
    ! [U_773,U_772,U_774] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_774,U_773)),insert_pname(U_774,U_772)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_773),U_772)) ),
    inference(definitional_conversion,[status(esa)],[f_304_2]) ).

cnf(f_304_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_774,U_773)),insert_pname(U_774,U_772)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_773),U_772)) ),
    inference(clausify,[status(thm)],[f_304_3]) ).

fof(f_305_1,plain,
    ! [A_2,C_2,D] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(A_2,C_2)),insert1415133716_state(A_2,D)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,C_2),D)) ),
    inference(fof_nnf,[status(thm)],[fact_251_insert__mono]) ).

fof(f_305_2,plain,
    ! [U_777,U_776,U_775] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(U_777,U_776)),insert1415133716_state(U_777,U_775)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_776),U_775)) ),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

fof(f_305_3,plain,
    ! [U_775,U_776,U_777] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(U_777,U_776)),insert1415133716_state(U_777,U_775)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_776),U_775)) ),
    inference(definitional_conversion,[status(esa)],[f_305_2]) ).

cnf(f_305_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(U_777,U_776)),insert1415133716_state(U_777,U_775)))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_776),U_775)) ),
    inference(clausify,[status(thm)],[f_305_3]) ).

fof(f_306_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
        | ~ hBOOL(hAPP_pname_bool(A,X_2)) )
      & ( hBOOL(hAPP_pname_bool(A,X_2))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_252_mem__def]) ).

fof(f_306_2,plain,
    ! [U_779,U_778] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_779),U_778))
        | ~ hBOOL(hAPP_pname_bool(U_778,U_779)) )
      & ( hBOOL(hAPP_pname_bool(U_778,U_779))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_779),U_778)) ) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ( ! [U_783,U_781] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_783),U_781))
        | ~ hBOOL(hAPP_pname_bool(U_781,U_783)) )
    & ! [U_782,U_780] :
        ( hBOOL(hAPP_pname_bool(U_780,U_782))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_782),U_780)) ) ),
    inference(miniscope,[status(thm)],[f_306_2]) ).

fof(f_306_4,plain,
    ( ! [U_781,U_783] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_783),U_781))
        | ~ hBOOL(hAPP_pname_bool(U_781,U_783)) )
    & ! [U_782,U_780] :
        ( hBOOL(hAPP_pname_bool(U_780,U_782))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_782),U_780)) ) ),
    inference(definitional_conversion,[status(esa)],[f_306_3]) ).

cnf(f_306_5,plain,
    ( hBOOL(hAPP_pname_bool(U_780,U_782))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_782),U_780)) ),
    inference(clausify,[status(thm)],[f_306_4]) ).

cnf(f_306_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_783),U_781))
    | ~ hBOOL(hAPP_pname_bool(U_781,U_783)) ),
    inference(clausify,[status(thm)],[f_306_4]) ).

fof(f_307_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A))
        | ~ hBOOL(hAPP_H78829294e_bool(A,X_2)) )
      & ( hBOOL(hAPP_H78829294e_bool(A,X_2))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_253_mem__def]) ).

fof(f_307_2,plain,
    ! [U_785,U_784] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_785),U_784))
        | ~ hBOOL(hAPP_H78829294e_bool(U_784,U_785)) )
      & ( hBOOL(hAPP_H78829294e_bool(U_784,U_785))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_785),U_784)) ) ),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

fof(f_307_3,plain,
    ( ! [U_789,U_787] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_789),U_787))
        | ~ hBOOL(hAPP_H78829294e_bool(U_787,U_789)) )
    & ! [U_788,U_786] :
        ( hBOOL(hAPP_H78829294e_bool(U_786,U_788))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_788),U_786)) ) ),
    inference(miniscope,[status(thm)],[f_307_2]) ).

fof(f_307_4,plain,
    ( ! [U_787,U_789] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_789),U_787))
        | ~ hBOOL(hAPP_H78829294e_bool(U_787,U_789)) )
    & ! [U_788,U_786] :
        ( hBOOL(hAPP_H78829294e_bool(U_786,U_788))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_788),U_786)) ) ),
    inference(definitional_conversion,[status(esa)],[f_307_3]) ).

cnf(f_307_5,plain,
    ( hBOOL(hAPP_H78829294e_bool(U_786,U_788))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_788),U_786)) ),
    inference(clausify,[status(thm)],[f_307_4]) ).

cnf(f_307_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_789),U_787))
    | ~ hBOOL(hAPP_H78829294e_bool(U_787,U_789)) ),
    inference(clausify,[status(thm)],[f_307_4]) ).

fof(f_308_1,plain,
    ! [P_1] :
      ( collect_pname(P_1) = P_1
      | ~ is_fun_pname_bool(P_1) ),
    inference(fof_nnf,[status(thm)],[fact_254_Collect__def]) ).

fof(f_308_2,plain,
    ! [U_790] :
      ( collect_pname(U_790) = U_790
      | ~ is_fun_pname_bool(U_790) ),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

fof(f_308_3,plain,
    ! [U_790] :
      ( collect_pname(U_790) = U_790
      | ~ is_fun_pname_bool(U_790) ),
    inference(definitional_conversion,[status(esa)],[f_308_2]) ).

cnf(f_308_4,plain,
    ( collect_pname(U_790) = U_790
    | ~ is_fun_pname_bool(U_790) ),
    inference(clausify,[status(thm)],[f_308_3]) ).

fof(f_309_1,plain,
    ! [P_1] : collec307967673_state(P_1) = P_1,
    inference(fof_nnf,[status(thm)],[fact_255_Collect__def]) ).

fof(f_309_2,plain,
    ! [U_791] : collec307967673_state(U_791) = U_791,
    inference(variable_rename,[status(thm)],[f_309_1]) ).

fof(f_309_3,plain,
    ! [U_791] : collec307967673_state(U_791) = U_791,
    inference(definitional_conversion,[status(esa)],[f_309_2]) ).

cnf(f_309_4,plain,
    collec307967673_state(U_791) = U_791,
    inference(clausify,[status(thm)],[f_309_3]) ).

fof(f_310_1,plain,
    ! [P_1] :
      ( collec1974731493e_bool(P_1) = P_1
      | ~ is_fun1661590463l_bool(P_1) ),
    inference(fof_nnf,[status(thm)],[fact_256_Collect__def]) ).

fof(f_310_2,plain,
    ! [U_792] :
      ( collec1974731493e_bool(U_792) = U_792
      | ~ is_fun1661590463l_bool(U_792) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

fof(f_310_3,plain,
    ! [U_792] :
      ( collec1974731493e_bool(U_792) = U_792
      | ~ is_fun1661590463l_bool(U_792) ),
    inference(definitional_conversion,[status(esa)],[f_310_2]) ).

cnf(f_310_4,plain,
    ( collec1974731493e_bool(U_792) = U_792
    | ~ is_fun1661590463l_bool(U_792) ),
    inference(clausify,[status(thm)],[f_310_3]) ).

fof(f_311_1,plain,
    ! [P_1] : collec1823980261e_bool(P_1) = P_1,
    inference(fof_nnf,[status(thm)],[fact_257_Collect__def]) ).

fof(f_311_2,plain,
    ! [U_793] : collec1823980261e_bool(U_793) = U_793,
    inference(variable_rename,[status(thm)],[f_311_1]) ).

fof(f_311_3,plain,
    ! [U_793] : collec1823980261e_bool(U_793) = U_793,
    inference(definitional_conversion,[status(esa)],[f_311_2]) ).

cnf(f_311_4,plain,
    collec1823980261e_bool(U_793) = U_793,
    inference(clausify,[status(thm)],[f_311_3]) ).

fof(f_312_1,plain,
    ! [B_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(B_1,B)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_258_subset__insertI2]) ).

fof(f_312_2,plain,
    ! [U_796,U_795,U_794] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_795),insert_pname(U_796,U_794)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_795),U_794)) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

fof(f_312_3,plain,
    ! [U_794,U_795,U_796] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_795),insert_pname(U_796,U_794)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_795),U_794)) ),
    inference(definitional_conversion,[status(esa)],[f_312_2]) ).

cnf(f_312_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_795),insert_pname(U_796,U_794)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_795),U_794)) ),
    inference(clausify,[status(thm)],[f_312_3]) ).

fof(f_313_1,plain,
    ! [B_1,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),insert1415133716_state(B_1,B)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_259_subset__insertI2]) ).

fof(f_313_2,plain,
    ! [U_799,U_798,U_797] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_798),insert1415133716_state(U_799,U_797)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_798),U_797)) ),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

fof(f_313_3,plain,
    ! [U_797,U_798,U_799] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_798),insert1415133716_state(U_799,U_797)))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_798),U_797)) ),
    inference(definitional_conversion,[status(esa)],[f_313_2]) ).

cnf(f_313_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_798),insert1415133716_state(U_799,U_797)))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_798),U_797)) ),
    inference(clausify,[status(thm)],[f_313_3]) ).

fof(f_314_1,plain,
    ! [B,X_2,A] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,B)))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,B))) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_260_subset__insert]) ).

fof(f_314_2,plain,
    ! [U_802,U_801,U_800] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_800),insert_pname(U_801,U_802)))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_800),U_802)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_800),U_802))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_800),insert_pname(U_801,U_802))) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_801),U_800)) ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

fof(f_314_3,plain,
    ( ! [U_800,U_801,U_802] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_800),insert_pname(U_801,U_802)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_800),U_802))
        | ~ sP60(U_800,U_801,U_802) )
    & ! [U_800,U_801,U_802] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_800),U_802))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_800),insert_pname(U_801,U_802)))
        | ~ sP60(U_800,U_801,U_802) )
    & ! [U_800,U_801,U_802] :
        ( sP60(U_800,U_801,U_802)
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_801),U_800)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60])],[f_314_2]) ).

cnf(f_314_4,plain,
    ( sP60(U_800,U_801,U_802)
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_801),U_800)) ),
    inference(clausify,[status(thm)],[f_314_3]) ).

cnf(f_314_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_800),U_802))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_800),insert_pname(U_801,U_802)))
    | ~ sP60(U_800,U_801,U_802) ),
    inference(clausify,[status(thm)],[f_314_3]) ).

cnf(f_314_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_800),insert_pname(U_801,U_802)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_800),U_802))
    | ~ sP60(U_800,U_801,U_802) ),
    inference(clausify,[status(thm)],[f_314_3]) ).

fof(f_315_1,plain,
    ! [B,X_2,A] :
      ( ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),insert1415133716_state(X_2,B)))
          | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B)) )
        & ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
          | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),insert1415133716_state(X_2,B))) ) )
      | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_261_subset__insert]) ).

fof(f_315_2,plain,
    ! [U_805,U_804,U_803] :
      ( ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_803),insert1415133716_state(U_804,U_805)))
          | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_803),U_805)) )
        & ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_803),U_805))
          | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_803),insert1415133716_state(U_804,U_805))) ) )
      | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_804),U_803)) ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

fof(f_315_3,plain,
    ( ! [U_804,U_805,U_803] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_803),insert1415133716_state(U_804,U_805)))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_803),U_805))
        | ~ sP61(U_804,U_805,U_803) )
    & ! [U_804,U_805,U_803] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_803),U_805))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_803),insert1415133716_state(U_804,U_805)))
        | ~ sP61(U_804,U_805,U_803) )
    & ! [U_804,U_805,U_803] :
        ( sP61(U_804,U_805,U_803)
        | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_804),U_803)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_315_2]) ).

cnf(f_315_4,plain,
    ( sP61(U_804,U_805,U_803)
    | hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_804),U_803)) ),
    inference(clausify,[status(thm)],[f_315_3]) ).

cnf(f_315_5,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_803),U_805))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_803),insert1415133716_state(U_804,U_805)))
    | ~ sP61(U_804,U_805,U_803) ),
    inference(clausify,[status(thm)],[f_315_3]) ).

cnf(f_315_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_803),insert1415133716_state(U_804,U_805)))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_803),U_805))
    | ~ sP61(U_804,U_805,U_803) ),
    inference(clausify,[status(thm)],[f_315_3]) ).

fof(f_316_1,plain,
    ! [X_2,A,B] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_2,A)),B))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_2,A)),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_262_insert__subset]) ).

fof(f_316_2,plain,
    ! [U_808,U_807,U_806] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_808,U_807)),U_806))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_807),U_806))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_808),U_806)) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_807),U_806))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_808),U_806)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_808,U_807)),U_806)) ) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

fof(f_316_3,plain,
    ( ! [U_814,U_812,U_810] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_814,U_812)),U_810))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_812),U_810))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_814),U_810)) )
    & ! [U_813,U_811,U_809] :
        ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_811),U_809))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_813),U_809)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_813,U_811)),U_809)) ) ),
    inference(miniscope,[status(thm)],[f_316_2]) ).

fof(f_316_4,plain,
    ( ! [U_813,U_809,U_811] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_811),U_809))
        | ~ sP62(U_813,U_809,U_811) )
    & ! [U_813,U_809,U_811] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_813),U_809))
        | ~ sP62(U_813,U_809,U_811) )
    & ! [U_814,U_812,U_810] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_814,U_812)),U_810))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_812),U_810))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_814),U_810)) )
    & ! [U_813,U_809,U_811] :
        ( sP62(U_813,U_809,U_811)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_813,U_811)),U_809)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_316_3]) ).

cnf(f_316_5,plain,
    ( sP62(U_813,U_809,U_811)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_813,U_811)),U_809)) ),
    inference(clausify,[status(thm)],[f_316_4]) ).

cnf(f_316_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_814,U_812)),U_810))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_812),U_810))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_814),U_810)) ),
    inference(clausify,[status(thm)],[f_316_4]) ).

cnf(f_316_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_813),U_809))
    | ~ sP62(U_813,U_809,U_811) ),
    inference(clausify,[status(thm)],[f_316_4]) ).

cnf(f_316_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_811),U_809))
    | ~ sP62(U_813,U_809,U_811) ),
    inference(clausify,[status(thm)],[f_316_4]) ).

fof(f_317_1,plain,
    ! [X_2,A,B] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(X_2,A)),B))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B)) )
      & ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
          & hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_2),B)) )
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(X_2,A)),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_263_insert__subset]) ).

fof(f_317_2,plain,
    ! [U_817,U_816,U_815] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(U_817,U_816)),U_815))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_816),U_815))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_817),U_815)) )
      & ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_816),U_815))
          & hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_817),U_815)) )
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(U_817,U_816)),U_815)) ) ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

fof(f_317_3,plain,
    ( ! [U_823,U_821,U_819] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(U_823,U_821)),U_819))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_821),U_819))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_823),U_819)) )
    & ! [U_822,U_820,U_818] :
        ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_820),U_818))
          & hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_822),U_818)) )
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(U_822,U_820)),U_818)) ) ),
    inference(miniscope,[status(thm)],[f_317_2]) ).

fof(f_317_4,plain,
    ( ! [U_820,U_818,U_822] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_820),U_818))
        | ~ sP63(U_820,U_818,U_822) )
    & ! [U_820,U_818,U_822] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_822),U_818))
        | ~ sP63(U_820,U_818,U_822) )
    & ! [U_823,U_821,U_819] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(U_823,U_821)),U_819))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_821),U_819))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_823),U_819)) )
    & ! [U_820,U_818,U_822] :
        ( sP63(U_820,U_818,U_822)
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(U_822,U_820)),U_818)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_317_3]) ).

cnf(f_317_5,plain,
    ( sP63(U_820,U_818,U_822)
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(U_822,U_820)),U_818)) ),
    inference(clausify,[status(thm)],[f_317_4]) ).

cnf(f_317_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,insert1415133716_state(U_823,U_821)),U_819))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_821),U_819))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_823),U_819)) ),
    inference(clausify,[status(thm)],[f_317_4]) ).

cnf(f_317_7,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_822),U_818))
    | ~ sP63(U_820,U_818,U_822) ),
    inference(clausify,[status(thm)],[f_317_4]) ).

cnf(f_317_8,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_820),U_818))
    | ~ sP63(U_820,U_818,U_822) ),
    inference(clausify,[status(thm)],[f_317_4]) ).

fof(f_318_1,plain,
    ! [B,A_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),insert_pname(A_2,B))),
    inference(fof_nnf,[status(thm)],[fact_264_subset__insertI]) ).

fof(f_318_2,plain,
    ! [U_825,U_824] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_825),insert_pname(U_824,U_825))),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ! [U_824,U_825] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_825),insert_pname(U_824,U_825))),
    inference(definitional_conversion,[status(esa)],[f_318_2]) ).

cnf(f_318_4,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_825),insert_pname(U_824,U_825))),
    inference(clausify,[status(thm)],[f_318_3]) ).

fof(f_319_1,plain,
    ! [B,A_2] : hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),insert1415133716_state(A_2,B))),
    inference(fof_nnf,[status(thm)],[fact_265_subset__insertI]) ).

fof(f_319_2,plain,
    ! [U_827,U_826] : hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_827),insert1415133716_state(U_826,U_827))),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

fof(f_319_3,plain,
    ! [U_827,U_826] : hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_827),insert1415133716_state(U_826,U_827))),
    inference(definitional_conversion,[status(esa)],[f_319_2]) ).

cnf(f_319_4,plain,
    hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_827),insert1415133716_state(U_826,U_827))),
    inference(clausify,[status(thm)],[f_319_3]) ).

fof(f_320_1,plain,
    ! [F,X_2,A] :
      ( insert1415133716_state(hAPP_p1422361149_state(F,X_2),image_2003357581_state(F,A)) = image_2003357581_state(F,A)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_266_insert__image]) ).

fof(f_320_2,plain,
    ! [U_830,U_829,U_828] :
      ( insert1415133716_state(hAPP_p1422361149_state(U_830,U_829),image_2003357581_state(U_830,U_828)) = image_2003357581_state(U_830,U_828)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_829),U_828)) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

fof(f_320_3,plain,
    ! [U_828,U_829,U_830] :
      ( insert1415133716_state(hAPP_p1422361149_state(U_830,U_829),image_2003357581_state(U_830,U_828)) = image_2003357581_state(U_830,U_828)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_829),U_828)) ),
    inference(definitional_conversion,[status(esa)],[f_320_2]) ).

cnf(f_320_4,plain,
    ( insert1415133716_state(hAPP_p1422361149_state(U_830,U_829),image_2003357581_state(U_830,U_828)) = image_2003357581_state(U_830,U_828)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_829),U_828)) ),
    inference(clausify,[status(thm)],[f_320_3]) ).

fof(f_321_1,plain,
    ! [F,A_2,B] : image_2003357581_state(F,insert_pname(A_2,B)) = insert1415133716_state(hAPP_p1422361149_state(F,A_2),image_2003357581_state(F,B)),
    inference(fof_nnf,[status(thm)],[fact_267_image__insert]) ).

fof(f_321_2,plain,
    ! [U_833,U_832,U_831] : image_2003357581_state(U_833,insert_pname(U_832,U_831)) = insert1415133716_state(hAPP_p1422361149_state(U_833,U_832),image_2003357581_state(U_833,U_831)),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

fof(f_321_3,plain,
    ! [U_831,U_832,U_833] : image_2003357581_state(U_833,insert_pname(U_832,U_831)) = insert1415133716_state(hAPP_p1422361149_state(U_833,U_832),image_2003357581_state(U_833,U_831)),
    inference(definitional_conversion,[status(esa)],[f_321_2]) ).

cnf(f_321_4,plain,
    image_2003357581_state(U_833,insert_pname(U_832,U_831)) = insert1415133716_state(hAPP_p1422361149_state(U_833,U_832),image_2003357581_state(U_833,U_831)),
    inference(clausify,[status(thm)],[f_321_3]) ).

fof(f_322_1,plain,
    ! [F,A,B] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,image_2003357581_state(F,A)),image_2003357581_state(F,B)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_268_image__mono]) ).

fof(f_322_2,plain,
    ! [U_836,U_835,U_834] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,image_2003357581_state(U_836,U_835)),image_2003357581_state(U_836,U_834)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_835),U_834)) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

fof(f_322_3,plain,
    ! [U_834,U_835,U_836] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,image_2003357581_state(U_836,U_835)),image_2003357581_state(U_836,U_834)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_835),U_834)) ),
    inference(definitional_conversion,[status(esa)],[f_322_2]) ).

cnf(f_322_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,image_2003357581_state(U_836,U_835)),image_2003357581_state(U_836,U_834)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_835),U_834)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

fof(f_323_1,plain,
    ! [B,F,A] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_2003357581_state(F,A)))
        | ! [AA] :
            ( B != image_2003357581_state(F,AA)
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A))
            | ~ is_fun_pname_bool(AA) ) )
      & ( ? [AA] :
            ( B = image_2003357581_state(F,AA)
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A))
            & is_fun_pname_bool(AA) )
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_2003357581_state(F,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_269_subset__image__iff]) ).

fof(f_323_2,plain,
    ! [U_841,U_840,U_839] :
      ( ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_841),image_2003357581_state(U_840,U_839)))
        | ! [U_838] :
            ( U_841 != image_2003357581_state(U_840,U_838)
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_838),U_839))
            | ~ is_fun_pname_bool(U_838) ) )
      & ( ? [U_837] :
            ( U_841 = image_2003357581_state(U_840,U_837)
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_837),U_839))
            & is_fun_pname_bool(U_837) )
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_841),image_2003357581_state(U_840,U_839))) ) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

fof(f_323_3,plain,
    ( ! [U_847,U_845,U_843] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_847),image_2003357581_state(U_845,U_843)))
        | ! [U_838] :
            ( U_847 != image_2003357581_state(U_845,U_838)
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_838),U_843))
            | ~ is_fun_pname_bool(U_838) ) )
    & ! [U_846,U_844,U_842] :
        ( ? [U_837] :
            ( U_846 = image_2003357581_state(U_844,U_837)
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_837),U_842))
            & is_fun_pname_bool(U_837) )
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_846),image_2003357581_state(U_844,U_842))) ) ),
    inference(miniscope,[status(thm)],[f_323_2]) ).

fof(f_323_4,plain,
    ( ! [U_847,U_845,U_843] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_847),image_2003357581_state(U_845,U_843)))
        | ! [U_838] :
            ( U_847 != image_2003357581_state(U_845,U_838)
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_838),U_843))
            | ~ is_fun_pname_bool(U_838) ) )
    & ! [U_846,U_844,U_842] :
        ( ( U_846 = image_2003357581_state(U_844,sK22(U_846,U_844,U_842))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK22(U_846,U_844,U_842)),U_842))
          & is_fun_pname_bool(sK22(U_846,U_844,U_842)) )
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_846),image_2003357581_state(U_844,U_842))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_837,sK22(U_846,U_844,U_842))],[f_323_3]) ).

fof(f_323_5,plain,
    ( ! [U_844,U_842,U_846] :
        ( U_846 = image_2003357581_state(U_844,sK22(U_846,U_844,U_842))
        | ~ sP64(U_844,U_842,U_846) )
    & ! [U_844,U_842,U_846] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK22(U_846,U_844,U_842)),U_842))
        | ~ sP64(U_844,U_842,U_846) )
    & ! [U_844,U_842,U_846] :
        ( is_fun_pname_bool(sK22(U_846,U_844,U_842))
        | ~ sP64(U_844,U_842,U_846) )
    & ! [U_838,U_843,U_845,U_847] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_847),image_2003357581_state(U_845,U_843)))
        | U_847 != image_2003357581_state(U_845,U_838)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_838),U_843))
        | ~ is_fun_pname_bool(U_838) )
    & ! [U_844,U_842,U_846] :
        ( sP64(U_844,U_842,U_846)
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_846),image_2003357581_state(U_844,U_842))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64])],[f_323_4]) ).

cnf(f_323_6,plain,
    ( sP64(U_844,U_842,U_846)
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_846),image_2003357581_state(U_844,U_842))) ),
    inference(clausify,[status(thm)],[f_323_5]) ).

cnf(f_323_7,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_847),image_2003357581_state(U_845,U_843)))
    | U_847 != image_2003357581_state(U_845,U_838)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_838),U_843))
    | ~ is_fun_pname_bool(U_838) ),
    inference(clausify,[status(thm)],[f_323_5]) ).

cnf(f_323_8,plain,
    ( is_fun_pname_bool(sK22(U_846,U_844,U_842))
    | ~ sP64(U_844,U_842,U_846) ),
    inference(clausify,[status(thm)],[f_323_5]) ).

cnf(f_323_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK22(U_846,U_844,U_842)),U_842))
    | ~ sP64(U_844,U_842,U_846) ),
    inference(clausify,[status(thm)],[f_323_5]) ).

cnf(f_323_10,plain,
    ( U_846 = image_2003357581_state(U_844,sK22(U_846,U_844,U_842))
    | ~ sP64(U_844,U_842,U_846) ),
    inference(clausify,[status(thm)],[f_323_5]) ).

fof(f_324_1,plain,
    ! [M,A_2,B_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),dom_pname_com(M)))
      | hAPP_p799580910on_com(M,A_2) != some_com(B_1) ),
    inference(fof_nnf,[status(thm)],[fact_270_domI]) ).

fof(f_324_2,plain,
    ! [U_850,U_849,U_848] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_849),dom_pname_com(U_850)))
      | hAPP_p799580910on_com(U_850,U_849) != some_com(U_848) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

fof(f_324_3,plain,
    ! [U_850,U_849] :
      ( ! [U_848] : hAPP_p799580910on_com(U_850,U_849) != some_com(U_848)
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_849),dom_pname_com(U_850))) ),
    inference(miniscope,[status(thm)],[f_324_2]) ).

fof(f_324_4,plain,
    ! [U_849,U_848,U_850] :
      ( hAPP_p799580910on_com(U_850,U_849) != some_com(U_848)
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_849),dom_pname_com(U_850))) ),
    inference(definitional_conversion,[status(esa)],[f_324_3]) ).

cnf(f_324_5,plain,
    ( hAPP_p799580910on_com(U_850,U_849) != some_com(U_848)
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_849),dom_pname_com(U_850))) ),
    inference(clausify,[status(thm)],[f_324_4]) ).

fof(f_325_1,plain,
    ! [P_1,A_2] :
      ( ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),P_1)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(P_1,A_2)) )
      & ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),P_1)) = insert_pname(A_2,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(P_1,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_271_Collect__conv__if]) ).

fof(f_325_2,plain,
    ! [U_852,U_851] :
      ( ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_851)),U_852)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(U_852,U_851)) )
      & ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_851)),U_852)) = insert_pname(U_851,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(U_852,U_851)) ) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

fof(f_325_3,plain,
    ( ! [U_856,U_854] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_854)),U_856)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(U_856,U_854)) )
    & ! [U_855,U_853] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_853)),U_855)) = insert_pname(U_853,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(U_855,U_853)) ) ),
    inference(miniscope,[status(thm)],[f_325_2]) ).

fof(f_325_4,plain,
    ( ! [U_856,U_854] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_854)),U_856)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(U_856,U_854)) )
    & ! [U_855,U_853] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_853)),U_855)) = insert_pname(U_853,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(U_855,U_853)) ) ),
    inference(definitional_conversion,[status(esa)],[f_325_3]) ).

cnf(f_325_5,plain,
    ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_853)),U_855)) = insert_pname(U_853,bot_bo844097828e_bool)
    | ~ hBOOL(hAPP_pname_bool(U_855,U_853)) ),
    inference(clausify,[status(thm)],[f_325_4]) ).

cnf(f_325_6,plain,
    ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_854)),U_856)) = bot_bo844097828e_bool
    | hBOOL(hAPP_pname_bool(U_856,U_854)) ),
    inference(clausify,[status(thm)],[f_325_4]) ).

fof(f_326_1,plain,
    ! [P_1,A_2] :
      ( ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)),P_1)) = bot_bo620288102e_bool
        | hBOOL(hAPP_H78829294e_bool(P_1,A_2)) )
      & ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)),P_1)) = insert1415133716_state(A_2,bot_bo620288102e_bool)
        | ~ hBOOL(hAPP_H78829294e_bool(P_1,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_272_Collect__conv__if]) ).

fof(f_326_2,plain,
    ! [U_858,U_857] :
      ( ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_857)),U_858)) = bot_bo620288102e_bool
        | hBOOL(hAPP_H78829294e_bool(U_858,U_857)) )
      & ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_857)),U_858)) = insert1415133716_state(U_857,bot_bo620288102e_bool)
        | ~ hBOOL(hAPP_H78829294e_bool(U_858,U_857)) ) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

fof(f_326_3,plain,
    ( ! [U_862,U_860] :
        ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_860)),U_862)) = bot_bo620288102e_bool
        | hBOOL(hAPP_H78829294e_bool(U_862,U_860)) )
    & ! [U_861,U_859] :
        ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_859)),U_861)) = insert1415133716_state(U_859,bot_bo620288102e_bool)
        | ~ hBOOL(hAPP_H78829294e_bool(U_861,U_859)) ) ),
    inference(miniscope,[status(thm)],[f_326_2]) ).

fof(f_326_4,plain,
    ( ! [U_862,U_860] :
        ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_860)),U_862)) = bot_bo620288102e_bool
        | hBOOL(hAPP_H78829294e_bool(U_862,U_860)) )
    & ! [U_861,U_859] :
        ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_859)),U_861)) = insert1415133716_state(U_859,bot_bo620288102e_bool)
        | ~ hBOOL(hAPP_H78829294e_bool(U_861,U_859)) ) ),
    inference(definitional_conversion,[status(esa)],[f_326_3]) ).

cnf(f_326_5,plain,
    ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_859)),U_861)) = insert1415133716_state(U_859,bot_bo620288102e_bool)
    | ~ hBOOL(hAPP_H78829294e_bool(U_861,U_859)) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

cnf(f_326_6,plain,
    ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_860)),U_862)) = bot_bo620288102e_bool
    | hBOOL(hAPP_H78829294e_bool(U_862,U_860)) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

fof(f_327_1,plain,
    ! [P_1,A_2] :
      ( ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)),P_1)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(P_1,A_2)) )
      & ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)),P_1)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(P_1,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_273_Collect__conv__if]) ).

fof(f_327_2,plain,
    ! [U_864,U_863] :
      ( ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_863)),U_864)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(U_864,U_863)) )
      & ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_863)),U_864)) = insert1325755072e_bool(U_863,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_864,U_863)) ) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

fof(f_327_3,plain,
    ( ! [U_868,U_866] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_866)),U_868)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(U_868,U_866)) )
    & ! [U_867,U_865] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_865)),U_867)) = insert1325755072e_bool(U_865,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_867,U_865)) ) ),
    inference(miniscope,[status(thm)],[f_327_2]) ).

fof(f_327_4,plain,
    ( ! [U_866,U_868] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_866)),U_868)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(U_868,U_866)) )
    & ! [U_867,U_865] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_865)),U_867)) = insert1325755072e_bool(U_865,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_867,U_865)) ) ),
    inference(definitional_conversion,[status(esa)],[f_327_3]) ).

cnf(f_327_5,plain,
    ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_865)),U_867)) = insert1325755072e_bool(U_865,bot_bo1649642514l_bool)
    | ~ hBOOL(hAPP_f1664156314l_bool(U_867,U_865)) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_6,plain,
    ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_866)),U_868)) = bot_bo1649642514l_bool
    | hBOOL(hAPP_f1664156314l_bool(U_868,U_866)) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

fof(f_328_1,plain,
    ! [P_1,A_2] :
      ( ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)),P_1)) = bot_bo535777328l_bool
        | hBOOL(hAPP_f971112728l_bool(P_1,A_2)) )
      & ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)),P_1)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool)
        | ~ hBOOL(hAPP_f971112728l_bool(P_1,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_274_Collect__conv__if]) ).

fof(f_328_2,plain,
    ! [U_870,U_869] :
      ( ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_869)),U_870)) = bot_bo535777328l_bool
        | hBOOL(hAPP_f971112728l_bool(U_870,U_869)) )
      & ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_869)),U_870)) = insert1556680138e_bool(U_869,bot_bo535777328l_bool)
        | ~ hBOOL(hAPP_f971112728l_bool(U_870,U_869)) ) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

fof(f_328_3,plain,
    ( ! [U_874,U_872] :
        ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_872)),U_874)) = bot_bo535777328l_bool
        | hBOOL(hAPP_f971112728l_bool(U_874,U_872)) )
    & ! [U_873,U_871] :
        ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_871)),U_873)) = insert1556680138e_bool(U_871,bot_bo535777328l_bool)
        | ~ hBOOL(hAPP_f971112728l_bool(U_873,U_871)) ) ),
    inference(miniscope,[status(thm)],[f_328_2]) ).

fof(f_328_4,plain,
    ( ! [U_872,U_874] :
        ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_872)),U_874)) = bot_bo535777328l_bool
        | hBOOL(hAPP_f971112728l_bool(U_874,U_872)) )
    & ! [U_873,U_871] :
        ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_871)),U_873)) = insert1556680138e_bool(U_871,bot_bo535777328l_bool)
        | ~ hBOOL(hAPP_f971112728l_bool(U_873,U_871)) ) ),
    inference(definitional_conversion,[status(esa)],[f_328_3]) ).

cnf(f_328_5,plain,
    ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_871)),U_873)) = insert1556680138e_bool(U_871,bot_bo535777328l_bool)
    | ~ hBOOL(hAPP_f971112728l_bool(U_873,U_871)) ),
    inference(clausify,[status(thm)],[f_328_4]) ).

cnf(f_328_6,plain,
    ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_872)),U_874)) = bot_bo535777328l_bool
    | hBOOL(hAPP_f971112728l_bool(U_874,U_872)) ),
    inference(clausify,[status(thm)],[f_328_4]) ).

fof(f_329_1,plain,
    ! [P_1,A_2] :
      ( ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_2)),P_1)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(P_1,A_2)) )
      & ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_2)),P_1)) = insert_pname(A_2,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(P_1,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_275_Collect__conv__if2]) ).

fof(f_329_2,plain,
    ! [U_876,U_875] :
      ( ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_875)),U_876)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(U_876,U_875)) )
      & ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_875)),U_876)) = insert_pname(U_875,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(U_876,U_875)) ) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

fof(f_329_3,plain,
    ( ! [U_880,U_878] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_878)),U_880)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(U_880,U_878)) )
    & ! [U_879,U_877] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_877)),U_879)) = insert_pname(U_877,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(U_879,U_877)) ) ),
    inference(miniscope,[status(thm)],[f_329_2]) ).

fof(f_329_4,plain,
    ( ! [U_878,U_880] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_878)),U_880)) = bot_bo844097828e_bool
        | hBOOL(hAPP_pname_bool(U_880,U_878)) )
    & ! [U_879,U_877] :
        ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_877)),U_879)) = insert_pname(U_877,bot_bo844097828e_bool)
        | ~ hBOOL(hAPP_pname_bool(U_879,U_877)) ) ),
    inference(definitional_conversion,[status(esa)],[f_329_3]) ).

cnf(f_329_5,plain,
    ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_877)),U_879)) = insert_pname(U_877,bot_bo844097828e_bool)
    | ~ hBOOL(hAPP_pname_bool(U_879,U_877)) ),
    inference(clausify,[status(thm)],[f_329_4]) ).

cnf(f_329_6,plain,
    ( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,U_878)),U_880)) = bot_bo844097828e_bool
    | hBOOL(hAPP_pname_bool(U_880,U_878)) ),
    inference(clausify,[status(thm)],[f_329_4]) ).

fof(f_330_1,plain,
    ! [P_1,A_2] :
      ( ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,A_2)),P_1)) = bot_bo620288102e_bool
        | hBOOL(hAPP_H78829294e_bool(P_1,A_2)) )
      & ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,A_2)),P_1)) = insert1415133716_state(A_2,bot_bo620288102e_bool)
        | ~ hBOOL(hAPP_H78829294e_bool(P_1,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_276_Collect__conv__if2]) ).

fof(f_330_2,plain,
    ! [U_882,U_881] :
      ( ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,U_881)),U_882)) = bot_bo620288102e_bool
        | hBOOL(hAPP_H78829294e_bool(U_882,U_881)) )
      & ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,U_881)),U_882)) = insert1415133716_state(U_881,bot_bo620288102e_bool)
        | ~ hBOOL(hAPP_H78829294e_bool(U_882,U_881)) ) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

fof(f_330_3,plain,
    ( ! [U_886,U_884] :
        ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,U_884)),U_886)) = bot_bo620288102e_bool
        | hBOOL(hAPP_H78829294e_bool(U_886,U_884)) )
    & ! [U_885,U_883] :
        ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,U_883)),U_885)) = insert1415133716_state(U_883,bot_bo620288102e_bool)
        | ~ hBOOL(hAPP_H78829294e_bool(U_885,U_883)) ) ),
    inference(miniscope,[status(thm)],[f_330_2]) ).

fof(f_330_4,plain,
    ( ! [U_884,U_886] :
        ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,U_884)),U_886)) = bot_bo620288102e_bool
        | hBOOL(hAPP_H78829294e_bool(U_886,U_884)) )
    & ! [U_885,U_883] :
        ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,U_883)),U_885)) = insert1415133716_state(U_883,bot_bo620288102e_bool)
        | ~ hBOOL(hAPP_H78829294e_bool(U_885,U_883)) ) ),
    inference(definitional_conversion,[status(esa)],[f_330_3]) ).

cnf(f_330_5,plain,
    ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,U_883)),U_885)) = insert1415133716_state(U_883,bot_bo620288102e_bool)
    | ~ hBOOL(hAPP_H78829294e_bool(U_885,U_883)) ),
    inference(clausify,[status(thm)],[f_330_4]) ).

cnf(f_330_6,plain,
    ( collec307967673_state(cOMBS_458705923l_bool(cOMBB_962198420_state(fconj,hAPP_H1049623551e_bool(fequal1111551311_state,U_884)),U_886)) = bot_bo620288102e_bool
    | hBOOL(hAPP_H78829294e_bool(U_886,U_884)) ),
    inference(clausify,[status(thm)],[f_330_4]) ).

fof(f_331_1,plain,
    ! [P_1,A_2] :
      ( ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_2)),P_1)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(P_1,A_2)) )
      & ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,A_2)),P_1)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(P_1,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_277_Collect__conv__if2]) ).

fof(f_331_2,plain,
    ! [U_888,U_887] :
      ( ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_887)),U_888)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(U_888,U_887)) )
      & ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_887)),U_888)) = insert1325755072e_bool(U_887,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_888,U_887)) ) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

fof(f_331_3,plain,
    ( ! [U_892,U_890] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_890)),U_892)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(U_892,U_890)) )
    & ! [U_891,U_889] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_889)),U_891)) = insert1325755072e_bool(U_889,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_891,U_889)) ) ),
    inference(miniscope,[status(thm)],[f_331_2]) ).

fof(f_331_4,plain,
    ( ! [U_890,U_892] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_890)),U_892)) = bot_bo1649642514l_bool
        | hBOOL(hAPP_f1664156314l_bool(U_892,U_890)) )
    & ! [U_891,U_889] :
        ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_889)),U_891)) = insert1325755072e_bool(U_889,bot_bo1649642514l_bool)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_891,U_889)) ) ),
    inference(definitional_conversion,[status(esa)],[f_331_3]) ).

cnf(f_331_5,plain,
    ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_889)),U_891)) = insert1325755072e_bool(U_889,bot_bo1649642514l_bool)
    | ~ hBOOL(hAPP_f1664156314l_bool(U_891,U_889)) ),
    inference(clausify,[status(thm)],[f_331_4]) ).

cnf(f_331_6,plain,
    ( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,U_890)),U_892)) = bot_bo1649642514l_bool
    | hBOOL(hAPP_f1664156314l_bool(U_892,U_890)) ),
    inference(clausify,[status(thm)],[f_331_4]) ).

fof(f_332_1,plain,
    ! [P_1,A_2] :
      ( ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,A_2)),P_1)) = bot_bo535777328l_bool
        | hBOOL(hAPP_f971112728l_bool(P_1,A_2)) )
      & ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,A_2)),P_1)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool)
        | ~ hBOOL(hAPP_f971112728l_bool(P_1,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_278_Collect__conv__if2]) ).

fof(f_332_2,plain,
    ! [U_894,U_893] :
      ( ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,U_893)),U_894)) = bot_bo535777328l_bool
        | hBOOL(hAPP_f971112728l_bool(U_894,U_893)) )
      & ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,U_893)),U_894)) = insert1556680138e_bool(U_893,bot_bo535777328l_bool)
        | ~ hBOOL(hAPP_f971112728l_bool(U_894,U_893)) ) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

fof(f_332_3,plain,
    ( ! [U_898,U_896] :
        ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,U_896)),U_898)) = bot_bo535777328l_bool
        | hBOOL(hAPP_f971112728l_bool(U_898,U_896)) )
    & ! [U_897,U_895] :
        ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,U_895)),U_897)) = insert1556680138e_bool(U_895,bot_bo535777328l_bool)
        | ~ hBOOL(hAPP_f971112728l_bool(U_897,U_895)) ) ),
    inference(miniscope,[status(thm)],[f_332_2]) ).

fof(f_332_4,plain,
    ( ! [U_896,U_898] :
        ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,U_896)),U_898)) = bot_bo535777328l_bool
        | hBOOL(hAPP_f971112728l_bool(U_898,U_896)) )
    & ! [U_897,U_895] :
        ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,U_895)),U_897)) = insert1556680138e_bool(U_895,bot_bo535777328l_bool)
        | ~ hBOOL(hAPP_f971112728l_bool(U_897,U_895)) ) ),
    inference(definitional_conversion,[status(esa)],[f_332_3]) ).

cnf(f_332_5,plain,
    ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,U_895)),U_897)) = insert1556680138e_bool(U_895,bot_bo535777328l_bool)
    | ~ hBOOL(hAPP_f971112728l_bool(U_897,U_895)) ),
    inference(clausify,[status(thm)],[f_332_4]) ).

cnf(f_332_6,plain,
    ( collec1823980261e_bool(cOMBS_2066081387l_bool(cOMBB_1585081418e_bool(fconj,hAPP_f72706945l_bool(fequal1311889615e_bool,U_896)),U_898)) = bot_bo535777328l_bool
    | hBOOL(hAPP_f971112728l_bool(U_898,U_896)) ),
    inference(clausify,[status(thm)],[f_332_4]) ).

fof(f_333_1,plain,
    ! [A_2] : collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)) = insert_pname(A_2,bot_bo844097828e_bool),
    inference(fof_nnf,[status(thm)],[fact_279_singleton__conv]) ).

fof(f_333_2,plain,
    ! [U_899] : collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_899)) = insert_pname(U_899,bot_bo844097828e_bool),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

fof(f_333_3,plain,
    ! [U_899] : collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_899)) = insert_pname(U_899,bot_bo844097828e_bool),
    inference(definitional_conversion,[status(esa)],[f_333_2]) ).

cnf(f_333_4,plain,
    collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_899)) = insert_pname(U_899,bot_bo844097828e_bool),
    inference(clausify,[status(thm)],[f_333_3]) ).

fof(f_334_1,plain,
    ! [A_2] : collec307967673_state(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),A_2)) = insert1415133716_state(A_2,bot_bo620288102e_bool),
    inference(fof_nnf,[status(thm)],[fact_280_singleton__conv]) ).

fof(f_334_2,plain,
    ! [U_900] : collec307967673_state(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_900)) = insert1415133716_state(U_900,bot_bo620288102e_bool),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

fof(f_334_3,plain,
    ! [U_900] : collec307967673_state(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_900)) = insert1415133716_state(U_900,bot_bo620288102e_bool),
    inference(definitional_conversion,[status(esa)],[f_334_2]) ).

cnf(f_334_4,plain,
    collec307967673_state(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(fequal1111551311_state),U_900)) = insert1415133716_state(U_900,bot_bo620288102e_bool),
    inference(clausify,[status(thm)],[f_334_3]) ).

fof(f_335_1,plain,
    ! [A_2] : collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_2)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool),
    inference(fof_nnf,[status(thm)],[fact_281_singleton__conv]) ).

fof(f_335_2,plain,
    ! [U_901] : collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_901)) = insert1325755072e_bool(U_901,bot_bo1649642514l_bool),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

fof(f_335_3,plain,
    ! [U_901] : collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_901)) = insert1325755072e_bool(U_901,bot_bo1649642514l_bool),
    inference(definitional_conversion,[status(esa)],[f_335_2]) ).

cnf(f_335_4,plain,
    collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_901)) = insert1325755072e_bool(U_901,bot_bo1649642514l_bool),
    inference(clausify,[status(thm)],[f_335_3]) ).

fof(f_336_1,plain,
    ! [A_2] : collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),A_2)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool),
    inference(fof_nnf,[status(thm)],[fact_282_singleton__conv]) ).

fof(f_336_2,plain,
    ! [U_902] : collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_902)) = insert1556680138e_bool(U_902,bot_bo535777328l_bool),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

fof(f_336_3,plain,
    ! [U_902] : collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_902)) = insert1556680138e_bool(U_902,bot_bo535777328l_bool),
    inference(definitional_conversion,[status(esa)],[f_336_2]) ).

cnf(f_336_4,plain,
    collec1823980261e_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(fequal1311889615e_bool),U_902)) = insert1556680138e_bool(U_902,bot_bo535777328l_bool),
    inference(clausify,[status(thm)],[f_336_3]) ).

fof(f_337_1,plain,
    ! [A_2] : collect_pname(hAPP_p61793385e_bool(fequal_pname,A_2)) = insert_pname(A_2,bot_bo844097828e_bool),
    inference(fof_nnf,[status(thm)],[fact_283_singleton__conv2]) ).

fof(f_337_2,plain,
    ! [U_903] : collect_pname(hAPP_p61793385e_bool(fequal_pname,U_903)) = insert_pname(U_903,bot_bo844097828e_bool),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

fof(f_337_3,plain,
    ! [U_903] : collect_pname(hAPP_p61793385e_bool(fequal_pname,U_903)) = insert_pname(U_903,bot_bo844097828e_bool),
    inference(definitional_conversion,[status(esa)],[f_337_2]) ).

cnf(f_337_4,plain,
    collect_pname(hAPP_p61793385e_bool(fequal_pname,U_903)) = insert_pname(U_903,bot_bo844097828e_bool),
    inference(clausify,[status(thm)],[f_337_3]) ).

fof(f_338_1,plain,
    ! [A_2] : collec307967673_state(hAPP_H1049623551e_bool(fequal1111551311_state,A_2)) = insert1415133716_state(A_2,bot_bo620288102e_bool),
    inference(fof_nnf,[status(thm)],[fact_284_singleton__conv2]) ).

fof(f_338_2,plain,
    ! [U_904] : collec307967673_state(hAPP_H1049623551e_bool(fequal1111551311_state,U_904)) = insert1415133716_state(U_904,bot_bo620288102e_bool),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

fof(f_338_3,plain,
    ! [U_904] : collec307967673_state(hAPP_H1049623551e_bool(fequal1111551311_state,U_904)) = insert1415133716_state(U_904,bot_bo620288102e_bool),
    inference(definitional_conversion,[status(esa)],[f_338_2]) ).

cnf(f_338_4,plain,
    collec307967673_state(hAPP_H1049623551e_bool(fequal1111551311_state,U_904)) = insert1415133716_state(U_904,bot_bo620288102e_bool),
    inference(clausify,[status(thm)],[f_338_3]) ).

fof(f_339_1,plain,
    ! [A_2] : collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,A_2)) = insert1325755072e_bool(A_2,bot_bo1649642514l_bool),
    inference(fof_nnf,[status(thm)],[fact_285_singleton__conv2]) ).

fof(f_339_2,plain,
    ! [U_905] : collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_905)) = insert1325755072e_bool(U_905,bot_bo1649642514l_bool),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

fof(f_339_3,plain,
    ! [U_905] : collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_905)) = insert1325755072e_bool(U_905,bot_bo1649642514l_bool),
    inference(definitional_conversion,[status(esa)],[f_339_2]) ).

cnf(f_339_4,plain,
    collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_905)) = insert1325755072e_bool(U_905,bot_bo1649642514l_bool),
    inference(clausify,[status(thm)],[f_339_3]) ).

fof(f_340_1,plain,
    ! [A_2] : collec1823980261e_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,A_2)) = insert1556680138e_bool(A_2,bot_bo535777328l_bool),
    inference(fof_nnf,[status(thm)],[fact_286_singleton__conv2]) ).

fof(f_340_2,plain,
    ! [U_906] : collec1823980261e_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,U_906)) = insert1556680138e_bool(U_906,bot_bo535777328l_bool),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

fof(f_340_3,plain,
    ! [U_906] : collec1823980261e_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,U_906)) = insert1556680138e_bool(U_906,bot_bo535777328l_bool),
    inference(definitional_conversion,[status(esa)],[f_340_2]) ).

cnf(f_340_4,plain,
    collec1823980261e_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,U_906)) = insert1556680138e_bool(U_906,bot_bo535777328l_bool),
    inference(clausify,[status(thm)],[f_340_3]) ).

fof(f_341_1,plain,
    ! [C_1,G] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,C_1),bot_bo620288102e_bool)))
      | ~ hBOOL(wt(C_1))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(G),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,X_1)),bot_bo620288102e_bool)))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),dom_pname_com(body)))
          & is_pname(X_1) )
      | ~ hBOOL(hoare_165779456gleton) ),
    inference(fof_nnf,[status(thm)],[fact_287_MGF__lemma1]) ).

fof(f_341_2,plain,
    ! [U_909,U_908] :
      ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_908),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,U_909),bot_bo620288102e_bool)))
      | ~ hBOOL(wt(U_909))
      | ? [U_907] :
          ( ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_908),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,U_907)),bot_bo620288102e_bool)))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_907),dom_pname_com(body)))
          & is_pname(U_907) )
      | ~ hBOOL(hoare_165779456gleton) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

fof(f_341_3,plain,
    ( ! [U_909,U_908] :
        ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_908),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,U_909),bot_bo620288102e_bool)))
        | ~ hBOOL(wt(U_909))
        | ? [U_907] :
            ( ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_908),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,U_907)),bot_bo620288102e_bool)))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_907),dom_pname_com(body)))
            & is_pname(U_907) ) )
    | ~ hBOOL(hoare_165779456gleton) ),
    inference(miniscope,[status(thm)],[f_341_2]) ).

fof(f_341_4,plain,
    ( ! [U_909,U_908] :
        ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_908),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,U_909),bot_bo620288102e_bool)))
        | ~ hBOOL(wt(U_909))
        | ( ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_908),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,sK23(U_909,U_908))),bot_bo620288102e_bool)))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK23(U_909,U_908)),dom_pname_com(body)))
          & is_pname(sK23(U_909,U_908)) ) )
    | ~ hBOOL(hoare_165779456gleton) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_907,sK23(U_909,U_908))],[f_341_3]) ).

fof(f_341_5,plain,
    ( ! [U_908,U_909] :
        ( ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_908),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,sK23(U_909,U_908))),bot_bo620288102e_bool)))
        | ~ sP65(U_908,U_909) )
    & ! [U_908,U_909] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK23(U_909,U_908)),dom_pname_com(body)))
        | ~ sP65(U_908,U_909) )
    & ! [U_908,U_909] :
        ( is_pname(sK23(U_909,U_908))
        | ~ sP65(U_908,U_909) )
    & ! [U_908,U_909] :
        ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_908),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,U_909),bot_bo620288102e_bool)))
        | ~ hBOOL(wt(U_909))
        | sP65(U_908,U_909)
        | ~ hBOOL(hoare_165779456gleton) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_341_4]) ).

cnf(f_341_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_908),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,U_909),bot_bo620288102e_bool)))
    | ~ hBOOL(wt(U_909))
    | sP65(U_908,U_909)
    | ~ hBOOL(hoare_165779456gleton) ),
    inference(clausify,[status(thm)],[f_341_5]) ).

cnf(f_341_7,plain,
    ( is_pname(sK23(U_909,U_908))
    | ~ sP65(U_908,U_909) ),
    inference(clausify,[status(thm)],[f_341_5]) ).

cnf(f_341_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK23(U_909,U_908)),dom_pname_com(body)))
    | ~ sP65(U_908,U_909) ),
    inference(clausify,[status(thm)],[f_341_5]) ).

cnf(f_341_9,plain,
    ( ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(U_908),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,hAPP_pname_com(body_1,sK23(U_909,U_908))),bot_bo620288102e_bool)))
    | ~ sP65(U_908,U_909) ),
    inference(clausify,[status(thm)],[f_341_5]) ).

fof(f_342_1,plain,
    ! [Pn,B_2] :
      ( hBOOL(wt(B_2))
      | hAPP_p799580910on_com(body,Pn) != some_com(B_2)
      | ~ hBOOL(wT_bodies) ),
    inference(fof_nnf,[status(thm)],[fact_288_WT__bodiesD]) ).

fof(f_342_2,plain,
    ! [U_911,U_910] :
      ( hBOOL(wt(U_910))
      | hAPP_p799580910on_com(body,U_911) != some_com(U_910)
      | ~ hBOOL(wT_bodies) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

fof(f_342_3,plain,
    ( ! [U_911,U_910] :
        ( hBOOL(wt(U_910))
        | hAPP_p799580910on_com(body,U_911) != some_com(U_910) )
    | ~ hBOOL(wT_bodies) ),
    inference(miniscope,[status(thm)],[f_342_2]) ).

fof(f_342_4,plain,
    ! [U_911,U_910] :
      ( hBOOL(wt(U_910))
      | hAPP_p799580910on_com(body,U_911) != some_com(U_910)
      | ~ hBOOL(wT_bodies) ),
    inference(definitional_conversion,[status(esa)],[f_342_3]) ).

cnf(f_342_5,plain,
    ( hBOOL(wt(U_910))
    | hAPP_p799580910on_com(body,U_911) != some_com(U_910)
    | ~ hBOOL(wT_bodies) ),
    inference(clausify,[status(thm)],[f_342_4]) ).

fof(f_343_1,plain,
    ! [B_1,F,A] :
      ( ? [X_1] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
          & B_1 = hAPP_p1422361149_state(F,X_1)
          & is_pname(X_1) )
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,B_1),image_2003357581_state(F,A))) ),
    inference(fof_nnf,[status(thm)],[fact_289_imageE]) ).

fof(f_343_2,plain,
    ! [U_915,U_914,U_913] :
      ( ? [U_912] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_912),U_913))
          & U_915 = hAPP_p1422361149_state(U_914,U_912)
          & is_pname(U_912) )
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_915),image_2003357581_state(U_914,U_913))) ),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

fof(f_343_3,plain,
    ! [U_915,U_914,U_913] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK24(U_915,U_914,U_913)),U_913))
        & U_915 = hAPP_p1422361149_state(U_914,sK24(U_915,U_914,U_913))
        & is_pname(sK24(U_915,U_914,U_913)) )
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_915),image_2003357581_state(U_914,U_913))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_912,sK24(U_915,U_914,U_913))],[f_343_2]) ).

fof(f_343_4,plain,
    ( ! [U_913,U_914,U_915] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK24(U_915,U_914,U_913)),U_913))
        | ~ sP66(U_913,U_914,U_915) )
    & ! [U_913,U_914,U_915] :
        ( U_915 = hAPP_p1422361149_state(U_914,sK24(U_915,U_914,U_913))
        | ~ sP66(U_913,U_914,U_915) )
    & ! [U_913,U_914,U_915] :
        ( is_pname(sK24(U_915,U_914,U_913))
        | ~ sP66(U_913,U_914,U_915) )
    & ! [U_913,U_914,U_915] :
        ( sP66(U_913,U_914,U_915)
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_915),image_2003357581_state(U_914,U_913))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66])],[f_343_3]) ).

cnf(f_343_5,plain,
    ( sP66(U_913,U_914,U_915)
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_915),image_2003357581_state(U_914,U_913))) ),
    inference(clausify,[status(thm)],[f_343_4]) ).

cnf(f_343_6,plain,
    ( is_pname(sK24(U_915,U_914,U_913))
    | ~ sP66(U_913,U_914,U_915) ),
    inference(clausify,[status(thm)],[f_343_4]) ).

cnf(f_343_7,plain,
    ( U_915 = hAPP_p1422361149_state(U_914,sK24(U_915,U_914,U_913))
    | ~ sP66(U_913,U_914,U_915) ),
    inference(clausify,[status(thm)],[f_343_4]) ).

cnf(f_343_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK24(U_915,U_914,U_913)),U_913))
    | ~ sP66(U_913,U_914,U_915) ),
    inference(clausify,[status(thm)],[f_343_4]) ).

fof(f_344_1,plain,
    ! [P_1,A,Fa] :
      ( hBOOL(hAPP_f1664156314l_bool(P_1,Fa))
      | ? [A_1,F_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(P_1,insert_pname(A_1,F_1)))
          & hBOOL(hAPP_f1664156314l_bool(P_1,F_1))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),F_1))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
          & is_fun_pname_bool(F_1)
          & is_pname(A_1) )
      | ~ hBOOL(hAPP_f1664156314l_bool(P_1,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,Fa),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_290_finite__subset__induct]) ).

fof(f_344_2,plain,
    ! [U_920,U_919,U_918] :
      ( hBOOL(hAPP_f1664156314l_bool(U_920,U_918))
      | ? [U_917,U_916] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_920,insert_pname(U_917,U_916)))
          & hBOOL(hAPP_f1664156314l_bool(U_920,U_916))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_917),U_916))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_917),U_919))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_916))
          & is_fun_pname_bool(U_916)
          & is_pname(U_917) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_920,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_918),U_919))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_918)) ),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

fof(f_344_3,plain,
    ! [U_920,U_919,U_918] :
      ( hBOOL(hAPP_f1664156314l_bool(U_920,U_918))
      | ? [U_916] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_920,insert_pname(sK25(U_920,U_919,U_918),U_916)))
          & hBOOL(hAPP_f1664156314l_bool(U_920,U_916))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK25(U_920,U_919,U_918)),U_916))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK25(U_920,U_919,U_918)),U_919))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_916))
          & is_fun_pname_bool(U_916)
          & is_pname(sK25(U_920,U_919,U_918)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_920,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_918),U_919))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_918)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_917,sK25(U_920,U_919,U_918))],[f_344_2]) ).

fof(f_344_4,plain,
    ! [U_920,U_919,U_918] :
      ( hBOOL(hAPP_f1664156314l_bool(U_920,U_918))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(U_920,insert_pname(sK25(U_920,U_919,U_918),sK26(U_920,U_919,U_918))))
        & hBOOL(hAPP_f1664156314l_bool(U_920,sK26(U_920,U_919,U_918)))
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK25(U_920,U_919,U_918)),sK26(U_920,U_919,U_918)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK25(U_920,U_919,U_918)),U_919))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK26(U_920,U_919,U_918)))
        & is_fun_pname_bool(sK26(U_920,U_919,U_918))
        & is_pname(sK25(U_920,U_919,U_918)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_920,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_918),U_919))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_918)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_916,sK26(U_920,U_919,U_918))],[f_344_3]) ).

fof(f_344_5,plain,
    ( ! [U_918,U_919,U_920] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(U_920,insert_pname(sK25(U_920,U_919,U_918),sK26(U_920,U_919,U_918))))
        | ~ sP67(U_918,U_919,U_920) )
    & ! [U_918,U_919,U_920] :
        ( hBOOL(hAPP_f1664156314l_bool(U_920,sK26(U_920,U_919,U_918)))
        | ~ sP67(U_918,U_919,U_920) )
    & ! [U_918,U_919,U_920] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK25(U_920,U_919,U_918)),sK26(U_920,U_919,U_918)))
        | ~ sP67(U_918,U_919,U_920) )
    & ! [U_918,U_919,U_920] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK25(U_920,U_919,U_918)),U_919))
        | ~ sP67(U_918,U_919,U_920) )
    & ! [U_918,U_919,U_920] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK26(U_920,U_919,U_918)))
        | ~ sP67(U_918,U_919,U_920) )
    & ! [U_918,U_919,U_920] :
        ( is_fun_pname_bool(sK26(U_920,U_919,U_918))
        | ~ sP67(U_918,U_919,U_920) )
    & ! [U_918,U_919,U_920] :
        ( is_pname(sK25(U_920,U_919,U_918))
        | ~ sP67(U_918,U_919,U_920) )
    & ! [U_918,U_919,U_920] :
        ( hBOOL(hAPP_f1664156314l_bool(U_920,U_918))
        | sP67(U_918,U_919,U_920)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_920,bot_bo844097828e_bool))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_918),U_919))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_918)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67])],[f_344_4]) ).

cnf(f_344_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_920,U_918))
    | sP67(U_918,U_919,U_920)
    | ~ hBOOL(hAPP_f1664156314l_bool(U_920,bot_bo844097828e_bool))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_918),U_919))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_918)) ),
    inference(clausify,[status(thm)],[f_344_5]) ).

cnf(f_344_7,plain,
    ( is_pname(sK25(U_920,U_919,U_918))
    | ~ sP67(U_918,U_919,U_920) ),
    inference(clausify,[status(thm)],[f_344_5]) ).

cnf(f_344_8,plain,
    ( is_fun_pname_bool(sK26(U_920,U_919,U_918))
    | ~ sP67(U_918,U_919,U_920) ),
    inference(clausify,[status(thm)],[f_344_5]) ).

cnf(f_344_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK26(U_920,U_919,U_918)))
    | ~ sP67(U_918,U_919,U_920) ),
    inference(clausify,[status(thm)],[f_344_5]) ).

cnf(f_344_10,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK25(U_920,U_919,U_918)),U_919))
    | ~ sP67(U_918,U_919,U_920) ),
    inference(clausify,[status(thm)],[f_344_5]) ).

cnf(f_344_11,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK25(U_920,U_919,U_918)),sK26(U_920,U_919,U_918)))
    | ~ sP67(U_918,U_919,U_920) ),
    inference(clausify,[status(thm)],[f_344_5]) ).

cnf(f_344_12,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_920,sK26(U_920,U_919,U_918)))
    | ~ sP67(U_918,U_919,U_920) ),
    inference(clausify,[status(thm)],[f_344_5]) ).

cnf(f_344_13,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(U_920,insert_pname(sK25(U_920,U_919,U_918),sK26(U_920,U_919,U_918))))
    | ~ sP67(U_918,U_919,U_920) ),
    inference(clausify,[status(thm)],[f_344_5]) ).

fof(f_345_1,plain,
    ! [P_1,A,Fa] :
      ( hBOOL(hAPP_f971112728l_bool(P_1,Fa))
      | ? [A_1,F_1] :
          ( ~ hBOOL(hAPP_f971112728l_bool(P_1,insert1415133716_state(A_1,F_1)))
          & hBOOL(hAPP_f971112728l_bool(P_1,F_1))
          & ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_1),F_1))
          & hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,A_1),A))
          & hBOOL(hAPP_f971112728l_bool(finite364844667_state,F_1)) )
      | ~ hBOOL(hAPP_f971112728l_bool(P_1,bot_bo620288102e_bool))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,Fa),A))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_291_finite__subset__induct]) ).

fof(f_345_2,plain,
    ! [U_925,U_924,U_923] :
      ( hBOOL(hAPP_f971112728l_bool(U_925,U_923))
      | ? [U_922,U_921] :
          ( ~ hBOOL(hAPP_f971112728l_bool(U_925,insert1415133716_state(U_922,U_921)))
          & hBOOL(hAPP_f971112728l_bool(U_925,U_921))
          & ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_922),U_921))
          & hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_922),U_924))
          & hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_921)) )
      | ~ hBOOL(hAPP_f971112728l_bool(U_925,bot_bo620288102e_bool))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_923),U_924))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_923)) ),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

fof(f_345_3,plain,
    ! [U_925,U_924,U_923] :
      ( hBOOL(hAPP_f971112728l_bool(U_925,U_923))
      | ? [U_921] :
          ( ~ hBOOL(hAPP_f971112728l_bool(U_925,insert1415133716_state(sK27(U_925,U_924,U_923),U_921)))
          & hBOOL(hAPP_f971112728l_bool(U_925,U_921))
          & ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK27(U_925,U_924,U_923)),U_921))
          & hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK27(U_925,U_924,U_923)),U_924))
          & hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_921)) )
      | ~ hBOOL(hAPP_f971112728l_bool(U_925,bot_bo620288102e_bool))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_923),U_924))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_923)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_922,sK27(U_925,U_924,U_923))],[f_345_2]) ).

fof(f_345_4,plain,
    ! [U_925,U_924,U_923] :
      ( hBOOL(hAPP_f971112728l_bool(U_925,U_923))
      | ( ~ hBOOL(hAPP_f971112728l_bool(U_925,insert1415133716_state(sK27(U_925,U_924,U_923),sK28(U_925,U_924,U_923))))
        & hBOOL(hAPP_f971112728l_bool(U_925,sK28(U_925,U_924,U_923)))
        & ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK27(U_925,U_924,U_923)),sK28(U_925,U_924,U_923)))
        & hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK27(U_925,U_924,U_923)),U_924))
        & hBOOL(hAPP_f971112728l_bool(finite364844667_state,sK28(U_925,U_924,U_923))) )
      | ~ hBOOL(hAPP_f971112728l_bool(U_925,bot_bo620288102e_bool))
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_923),U_924))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_923)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_921,sK28(U_925,U_924,U_923))],[f_345_3]) ).

fof(f_345_5,plain,
    ( ! [U_924,U_925,U_923] :
        ( ~ hBOOL(hAPP_f971112728l_bool(U_925,insert1415133716_state(sK27(U_925,U_924,U_923),sK28(U_925,U_924,U_923))))
        | ~ sP68(U_924,U_925,U_923) )
    & ! [U_924,U_925,U_923] :
        ( hBOOL(hAPP_f971112728l_bool(U_925,sK28(U_925,U_924,U_923)))
        | ~ sP68(U_924,U_925,U_923) )
    & ! [U_924,U_925,U_923] :
        ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK27(U_925,U_924,U_923)),sK28(U_925,U_924,U_923)))
        | ~ sP68(U_924,U_925,U_923) )
    & ! [U_924,U_925,U_923] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK27(U_925,U_924,U_923)),U_924))
        | ~ sP68(U_924,U_925,U_923) )
    & ! [U_924,U_925,U_923] :
        ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,sK28(U_925,U_924,U_923)))
        | ~ sP68(U_924,U_925,U_923) )
    & ! [U_924,U_925,U_923] :
        ( hBOOL(hAPP_f971112728l_bool(U_925,U_923))
        | sP68(U_924,U_925,U_923)
        | ~ hBOOL(hAPP_f971112728l_bool(U_925,bot_bo620288102e_bool))
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_923),U_924))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_923)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68])],[f_345_4]) ).

cnf(f_345_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(U_925,U_923))
    | sP68(U_924,U_925,U_923)
    | ~ hBOOL(hAPP_f971112728l_bool(U_925,bot_bo620288102e_bool))
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_923),U_924))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_923)) ),
    inference(clausify,[status(thm)],[f_345_5]) ).

cnf(f_345_7,plain,
    ( hBOOL(hAPP_f971112728l_bool(finite364844667_state,sK28(U_925,U_924,U_923)))
    | ~ sP68(U_924,U_925,U_923) ),
    inference(clausify,[status(thm)],[f_345_5]) ).

cnf(f_345_8,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK27(U_925,U_924,U_923)),U_924))
    | ~ sP68(U_924,U_925,U_923) ),
    inference(clausify,[status(thm)],[f_345_5]) ).

cnf(f_345_9,plain,
    ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK27(U_925,U_924,U_923)),sK28(U_925,U_924,U_923)))
    | ~ sP68(U_924,U_925,U_923) ),
    inference(clausify,[status(thm)],[f_345_5]) ).

cnf(f_345_10,plain,
    ( hBOOL(hAPP_f971112728l_bool(U_925,sK28(U_925,U_924,U_923)))
    | ~ sP68(U_924,U_925,U_923) ),
    inference(clausify,[status(thm)],[f_345_5]) ).

cnf(f_345_11,plain,
    ( ~ hBOOL(hAPP_f971112728l_bool(U_925,insert1415133716_state(sK27(U_925,U_924,U_923),sK28(U_925,U_924,U_923))))
    | ~ sP68(U_924,U_925,U_923) ),
    inference(clausify,[status(thm)],[f_345_5]) ).

fof(f_346_1,plain,
    ! [P_1,A,Fa] :
      ( hBOOL(hAPP_f1935102916l_bool(P_1,Fa))
      | ? [A_1,F_1] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(P_1,insert1325755072e_bool(A_1,F_1)))
          & hBOOL(hAPP_f1935102916l_bool(P_1,F_1))
          & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_1),F_1))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,A_1),A))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
          & is_fun1661590463l_bool(F_1)
          & is_fun_pname_bool(A_1) )
      | ~ hBOOL(hAPP_f1935102916l_bool(P_1,bot_bo1649642514l_bool))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,Fa),A))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_292_finite__subset__induct]) ).

fof(f_346_2,plain,
    ! [U_930,U_929,U_928] :
      ( hBOOL(hAPP_f1935102916l_bool(U_930,U_928))
      | ? [U_927,U_926] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(U_930,insert1325755072e_bool(U_927,U_926)))
          & hBOOL(hAPP_f1935102916l_bool(U_930,U_926))
          & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_927),U_926))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_927),U_929))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_926))
          & is_fun1661590463l_bool(U_926)
          & is_fun_pname_bool(U_927) )
      | ~ hBOOL(hAPP_f1935102916l_bool(U_930,bot_bo1649642514l_bool))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_928),U_929))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_928)) ),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

fof(f_346_3,plain,
    ! [U_930,U_929,U_928] :
      ( hBOOL(hAPP_f1935102916l_bool(U_930,U_928))
      | ? [U_926] :
          ( ~ hBOOL(hAPP_f1935102916l_bool(U_930,insert1325755072e_bool(sK29(U_930,U_929,U_928),U_926)))
          & hBOOL(hAPP_f1935102916l_bool(U_930,U_926))
          & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK29(U_930,U_929,U_928)),U_926))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK29(U_930,U_929,U_928)),U_929))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_926))
          & is_fun1661590463l_bool(U_926)
          & is_fun_pname_bool(sK29(U_930,U_929,U_928)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(U_930,bot_bo1649642514l_bool))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_928),U_929))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_928)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_927,sK29(U_930,U_929,U_928))],[f_346_2]) ).

fof(f_346_4,plain,
    ! [U_930,U_929,U_928] :
      ( hBOOL(hAPP_f1935102916l_bool(U_930,U_928))
      | ( ~ hBOOL(hAPP_f1935102916l_bool(U_930,insert1325755072e_bool(sK29(U_930,U_929,U_928),sK30(U_930,U_929,U_928))))
        & hBOOL(hAPP_f1935102916l_bool(U_930,sK30(U_930,U_929,U_928)))
        & ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK29(U_930,U_929,U_928)),sK30(U_930,U_929,U_928)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK29(U_930,U_929,U_928)),U_929))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK30(U_930,U_929,U_928)))
        & is_fun1661590463l_bool(sK30(U_930,U_929,U_928))
        & is_fun_pname_bool(sK29(U_930,U_929,U_928)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(U_930,bot_bo1649642514l_bool))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_928),U_929))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_928)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_926,sK30(U_930,U_929,U_928))],[f_346_3]) ).

fof(f_346_5,plain,
    ( ! [U_928,U_929,U_930] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(U_930,insert1325755072e_bool(sK29(U_930,U_929,U_928),sK30(U_930,U_929,U_928))))
        | ~ sP69(U_928,U_929,U_930) )
    & ! [U_928,U_929,U_930] :
        ( hBOOL(hAPP_f1935102916l_bool(U_930,sK30(U_930,U_929,U_928)))
        | ~ sP69(U_928,U_929,U_930) )
    & ! [U_928,U_929,U_930] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK29(U_930,U_929,U_928)),sK30(U_930,U_929,U_928)))
        | ~ sP69(U_928,U_929,U_930) )
    & ! [U_928,U_929,U_930] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK29(U_930,U_929,U_928)),U_929))
        | ~ sP69(U_928,U_929,U_930) )
    & ! [U_928,U_929,U_930] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK30(U_930,U_929,U_928)))
        | ~ sP69(U_928,U_929,U_930) )
    & ! [U_928,U_929,U_930] :
        ( is_fun1661590463l_bool(sK30(U_930,U_929,U_928))
        | ~ sP69(U_928,U_929,U_930) )
    & ! [U_928,U_929,U_930] :
        ( is_fun_pname_bool(sK29(U_930,U_929,U_928))
        | ~ sP69(U_928,U_929,U_930) )
    & ! [U_928,U_929,U_930] :
        ( hBOOL(hAPP_f1935102916l_bool(U_930,U_928))
        | sP69(U_928,U_929,U_930)
        | ~ hBOOL(hAPP_f1935102916l_bool(U_930,bot_bo1649642514l_bool))
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_928),U_929))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_928)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69])],[f_346_4]) ).

cnf(f_346_6,plain,
    ( hBOOL(hAPP_f1935102916l_bool(U_930,U_928))
    | sP69(U_928,U_929,U_930)
    | ~ hBOOL(hAPP_f1935102916l_bool(U_930,bot_bo1649642514l_bool))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_928),U_929))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_928)) ),
    inference(clausify,[status(thm)],[f_346_5]) ).

cnf(f_346_7,plain,
    ( is_fun_pname_bool(sK29(U_930,U_929,U_928))
    | ~ sP69(U_928,U_929,U_930) ),
    inference(clausify,[status(thm)],[f_346_5]) ).

cnf(f_346_8,plain,
    ( is_fun1661590463l_bool(sK30(U_930,U_929,U_928))
    | ~ sP69(U_928,U_929,U_930) ),
    inference(clausify,[status(thm)],[f_346_5]) ).

cnf(f_346_9,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK30(U_930,U_929,U_928)))
    | ~ sP69(U_928,U_929,U_930) ),
    inference(clausify,[status(thm)],[f_346_5]) ).

cnf(f_346_10,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK29(U_930,U_929,U_928)),U_929))
    | ~ sP69(U_928,U_929,U_930) ),
    inference(clausify,[status(thm)],[f_346_5]) ).

cnf(f_346_11,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,sK29(U_930,U_929,U_928)),sK30(U_930,U_929,U_928)))
    | ~ sP69(U_928,U_929,U_930) ),
    inference(clausify,[status(thm)],[f_346_5]) ).

cnf(f_346_12,plain,
    ( hBOOL(hAPP_f1935102916l_bool(U_930,sK30(U_930,U_929,U_928)))
    | ~ sP69(U_928,U_929,U_930) ),
    inference(clausify,[status(thm)],[f_346_5]) ).

cnf(f_346_13,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(U_930,insert1325755072e_bool(sK29(U_930,U_929,U_928),sK30(U_930,U_929,U_928))))
    | ~ sP69(U_928,U_929,U_930) ),
    inference(clausify,[status(thm)],[f_346_5]) ).

fof(f_347_1,plain,
    ! [P_1,A,Fa] :
      ( hBOOL(hAPP_f166538662l_bool(P_1,Fa))
      | ? [A_1,F_1] :
          ( ~ hBOOL(hAPP_f166538662l_bool(P_1,insert1556680138e_bool(A_1,F_1)))
          & hBOOL(hAPP_f166538662l_bool(P_1,F_1))
          & ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_1),F_1))
          & hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,A_1),A))
          & hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,F_1)) )
      | ~ hBOOL(hAPP_f166538662l_bool(P_1,bot_bo535777328l_bool))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,Fa),A))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,Fa)) ),
    inference(fof_nnf,[status(thm)],[fact_293_finite__subset__induct]) ).

fof(f_347_2,plain,
    ! [U_935,U_934,U_933] :
      ( hBOOL(hAPP_f166538662l_bool(U_935,U_933))
      | ? [U_932,U_931] :
          ( ~ hBOOL(hAPP_f166538662l_bool(U_935,insert1556680138e_bool(U_932,U_931)))
          & hBOOL(hAPP_f166538662l_bool(U_935,U_931))
          & ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_932),U_931))
          & hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,U_932),U_934))
          & hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_931)) )
      | ~ hBOOL(hAPP_f166538662l_bool(U_935,bot_bo535777328l_bool))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_933),U_934))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_933)) ),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

fof(f_347_3,plain,
    ! [U_935,U_934,U_933] :
      ( hBOOL(hAPP_f166538662l_bool(U_935,U_933))
      | ? [U_931] :
          ( ~ hBOOL(hAPP_f166538662l_bool(U_935,insert1556680138e_bool(sK31(U_935,U_934,U_933),U_931)))
          & hBOOL(hAPP_f166538662l_bool(U_935,U_931))
          & ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK31(U_935,U_934,U_933)),U_931))
          & hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK31(U_935,U_934,U_933)),U_934))
          & hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_931)) )
      | ~ hBOOL(hAPP_f166538662l_bool(U_935,bot_bo535777328l_bool))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_933),U_934))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_933)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_932,sK31(U_935,U_934,U_933))],[f_347_2]) ).

fof(f_347_4,plain,
    ! [U_935,U_934,U_933] :
      ( hBOOL(hAPP_f166538662l_bool(U_935,U_933))
      | ( ~ hBOOL(hAPP_f166538662l_bool(U_935,insert1556680138e_bool(sK31(U_935,U_934,U_933),sK32(U_935,U_934,U_933))))
        & hBOOL(hAPP_f166538662l_bool(U_935,sK32(U_935,U_934,U_933)))
        & ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK31(U_935,U_934,U_933)),sK32(U_935,U_934,U_933)))
        & hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK31(U_935,U_934,U_933)),U_934))
        & hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,sK32(U_935,U_934,U_933))) )
      | ~ hBOOL(hAPP_f166538662l_bool(U_935,bot_bo535777328l_bool))
      | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_933),U_934))
      | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_933)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_931,sK32(U_935,U_934,U_933))],[f_347_3]) ).

fof(f_347_5,plain,
    ( ! [U_934,U_933,U_935] :
        ( ~ hBOOL(hAPP_f166538662l_bool(U_935,insert1556680138e_bool(sK31(U_935,U_934,U_933),sK32(U_935,U_934,U_933))))
        | ~ sP70(U_934,U_933,U_935) )
    & ! [U_934,U_933,U_935] :
        ( hBOOL(hAPP_f166538662l_bool(U_935,sK32(U_935,U_934,U_933)))
        | ~ sP70(U_934,U_933,U_935) )
    & ! [U_934,U_933,U_935] :
        ( ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK31(U_935,U_934,U_933)),sK32(U_935,U_934,U_933)))
        | ~ sP70(U_934,U_933,U_935) )
    & ! [U_934,U_933,U_935] :
        ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK31(U_935,U_934,U_933)),U_934))
        | ~ sP70(U_934,U_933,U_935) )
    & ! [U_934,U_933,U_935] :
        ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,sK32(U_935,U_934,U_933)))
        | ~ sP70(U_934,U_933,U_935) )
    & ! [U_934,U_933,U_935] :
        ( hBOOL(hAPP_f166538662l_bool(U_935,U_933))
        | sP70(U_934,U_933,U_935)
        | ~ hBOOL(hAPP_f166538662l_bool(U_935,bot_bo535777328l_bool))
        | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_933),U_934))
        | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_933)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP70])],[f_347_4]) ).

cnf(f_347_6,plain,
    ( hBOOL(hAPP_f166538662l_bool(U_935,U_933))
    | sP70(U_934,U_933,U_935)
    | ~ hBOOL(hAPP_f166538662l_bool(U_935,bot_bo535777328l_bool))
    | ~ hBOOL(hAPP_f166538662l_bool(hAPP_f585161855l_bool(ord_le287025148l_bool,U_933),U_934))
    | ~ hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,U_933)) ),
    inference(clausify,[status(thm)],[f_347_5]) ).

cnf(f_347_7,plain,
    ( hBOOL(hAPP_f166538662l_bool(finite464017571e_bool,sK32(U_935,U_934,U_933)))
    | ~ sP70(U_934,U_933,U_935) ),
    inference(clausify,[status(thm)],[f_347_5]) ).

cnf(f_347_8,plain,
    ( hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK31(U_935,U_934,U_933)),U_934))
    | ~ sP70(U_934,U_933,U_935) ),
    inference(clausify,[status(thm)],[f_347_5]) ).

cnf(f_347_9,plain,
    ( ~ hBOOL(hAPP_f166538662l_bool(hAPP_f210337421l_bool(member2114907555e_bool,sK31(U_935,U_934,U_933)),sK32(U_935,U_934,U_933)))
    | ~ sP70(U_934,U_933,U_935) ),
    inference(clausify,[status(thm)],[f_347_5]) ).

cnf(f_347_10,plain,
    ( hBOOL(hAPP_f166538662l_bool(U_935,sK32(U_935,U_934,U_933)))
    | ~ sP70(U_934,U_933,U_935) ),
    inference(clausify,[status(thm)],[f_347_5]) ).

cnf(f_347_11,plain,
    ( ~ hBOOL(hAPP_f166538662l_bool(U_935,insert1556680138e_bool(sK31(U_935,U_934,U_933),sK32(U_935,U_934,U_933))))
    | ~ sP70(U_934,U_933,U_935) ),
    inference(clausify,[status(thm)],[f_347_5]) ).

fof(f_348_1,plain,
    ! [P] :
      ( ? [Y_1] : hAPP_p799580910on_com(body,P) = some_com(Y_1)
      | ~ hBOOL(wt(hAPP_pname_com(body_1,P))) ),
    inference(fof_nnf,[status(thm)],[fact_294_WTs__elim__cases_I7_J]) ).

fof(f_348_2,plain,
    ! [U_937] :
      ( ? [U_936] : hAPP_p799580910on_com(body,U_937) = some_com(U_936)
      | ~ hBOOL(wt(hAPP_pname_com(body_1,U_937))) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ! [U_937] :
      ( hAPP_p799580910on_com(body,U_937) = some_com(sK33(U_937))
      | ~ hBOOL(wt(hAPP_pname_com(body_1,U_937))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_936,sK33(U_937))],[f_348_2]) ).

fof(f_348_4,plain,
    ! [U_937] :
      ( hAPP_p799580910on_com(body,U_937) = some_com(sK33(U_937))
      | ~ hBOOL(wt(hAPP_pname_com(body_1,U_937))) ),
    inference(definitional_conversion,[status(esa)],[f_348_3]) ).

cnf(f_348_5,plain,
    ( hAPP_p799580910on_com(body,U_937) = some_com(sK33(U_937))
    | ~ hBOOL(wt(hAPP_pname_com(body_1,U_937))) ),
    inference(clausify,[status(thm)],[f_348_4]) ).

fof(f_349_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
          & is_pname(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_295_subsetI]) ).

fof(f_349_2,plain,
    ! [U_940,U_939] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_939),U_940))
      | ? [U_938] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_938),U_940))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_938),U_939))
          & is_pname(U_938) ) ),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

fof(f_349_3,plain,
    ! [U_940,U_939] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_939),U_940))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK34(U_940,U_939)),U_940))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK34(U_940,U_939)),U_939))
        & is_pname(sK34(U_940,U_939)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_938,sK34(U_940,U_939))],[f_349_2]) ).

fof(f_349_4,plain,
    ( ! [U_940,U_939] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK34(U_940,U_939)),U_940))
        | ~ sP71(U_940,U_939) )
    & ! [U_940,U_939] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK34(U_940,U_939)),U_939))
        | ~ sP71(U_940,U_939) )
    & ! [U_940,U_939] :
        ( is_pname(sK34(U_940,U_939))
        | ~ sP71(U_940,U_939) )
    & ! [U_940,U_939] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_939),U_940))
        | sP71(U_940,U_939) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71])],[f_349_3]) ).

cnf(f_349_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_939),U_940))
    | sP71(U_940,U_939) ),
    inference(clausify,[status(thm)],[f_349_4]) ).

cnf(f_349_6,plain,
    ( is_pname(sK34(U_940,U_939))
    | ~ sP71(U_940,U_939) ),
    inference(clausify,[status(thm)],[f_349_4]) ).

cnf(f_349_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK34(U_940,U_939)),U_939))
    | ~ sP71(U_940,U_939) ),
    inference(clausify,[status(thm)],[f_349_4]) ).

cnf(f_349_8,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK34(U_940,U_939)),U_940))
    | ~ sP71(U_940,U_939) ),
    inference(clausify,[status(thm)],[f_349_4]) ).

fof(f_350_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),B))
          & hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_296_subsetI]) ).

fof(f_350_2,plain,
    ! [U_943,U_942] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_942),U_943))
      | ? [U_941] :
          ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_941),U_943))
          & hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,U_941),U_942)) ) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

fof(f_350_3,plain,
    ! [U_943,U_942] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_942),U_943))
      | ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK35(U_943,U_942)),U_943))
        & hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK35(U_943,U_942)),U_942)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_941,sK35(U_943,U_942))],[f_350_2]) ).

fof(f_350_4,plain,
    ( ! [U_943,U_942] :
        ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK35(U_943,U_942)),U_943))
        | ~ sP72(U_943,U_942) )
    & ! [U_943,U_942] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK35(U_943,U_942)),U_942))
        | ~ sP72(U_943,U_942) )
    & ! [U_943,U_942] :
        ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_942),U_943))
        | sP72(U_943,U_942) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_350_3]) ).

cnf(f_350_5,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_942),U_943))
    | sP72(U_943,U_942) ),
    inference(clausify,[status(thm)],[f_350_4]) ).

cnf(f_350_6,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK35(U_943,U_942)),U_942))
    | ~ sP72(U_943,U_942) ),
    inference(clausify,[status(thm)],[f_350_4]) ).

cnf(f_350_7,plain,
    ( ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,sK35(U_943,U_942)),U_943))
    | ~ sP72(U_943,U_942) ),
    inference(clausify,[status(thm)],[f_350_4]) ).

fof(f_351_1,plain,
    ! [F,A,B] :
      ( ? [C] :
          ( B = image_2003357581_state(F,C)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),A))
          & is_fun_pname_bool(C) )
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,B),image_2003357581_state(F,A)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,B)) ),
    inference(fof_nnf,[status(thm)],[fact_297_finite__subset__image]) ).

fof(f_351_2,plain,
    ! [U_947,U_946,U_945] :
      ( ? [U_944] :
          ( U_945 = image_2003357581_state(U_947,U_944)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_944))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_944),U_946))
          & is_fun_pname_bool(U_944) )
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_945),image_2003357581_state(U_947,U_946)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_945)) ),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

fof(f_351_3,plain,
    ! [U_947,U_946,U_945] :
      ( ( U_945 = image_2003357581_state(U_947,sK36(U_947,U_946,U_945))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK36(U_947,U_946,U_945)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK36(U_947,U_946,U_945)),U_946))
        & is_fun_pname_bool(sK36(U_947,U_946,U_945)) )
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_945),image_2003357581_state(U_947,U_946)))
      | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_945)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_944,sK36(U_947,U_946,U_945))],[f_351_2]) ).

fof(f_351_4,plain,
    ( ! [U_945,U_946,U_947] :
        ( U_945 = image_2003357581_state(U_947,sK36(U_947,U_946,U_945))
        | ~ sP73(U_945,U_946,U_947) )
    & ! [U_945,U_946,U_947] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK36(U_947,U_946,U_945)))
        | ~ sP73(U_945,U_946,U_947) )
    & ! [U_945,U_946,U_947] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK36(U_947,U_946,U_945)),U_946))
        | ~ sP73(U_945,U_946,U_947) )
    & ! [U_945,U_946,U_947] :
        ( is_fun_pname_bool(sK36(U_947,U_946,U_945))
        | ~ sP73(U_945,U_946,U_947) )
    & ! [U_945,U_946,U_947] :
        ( sP73(U_945,U_946,U_947)
        | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_945),image_2003357581_state(U_947,U_946)))
        | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_945)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_351_3]) ).

cnf(f_351_5,plain,
    ( sP73(U_945,U_946,U_947)
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,U_945),image_2003357581_state(U_947,U_946)))
    | ~ hBOOL(hAPP_f971112728l_bool(finite364844667_state,U_945)) ),
    inference(clausify,[status(thm)],[f_351_4]) ).

cnf(f_351_6,plain,
    ( is_fun_pname_bool(sK36(U_947,U_946,U_945))
    | ~ sP73(U_945,U_946,U_947) ),
    inference(clausify,[status(thm)],[f_351_4]) ).

cnf(f_351_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK36(U_947,U_946,U_945)),U_946))
    | ~ sP73(U_945,U_946,U_947) ),
    inference(clausify,[status(thm)],[f_351_4]) ).

cnf(f_351_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK36(U_947,U_946,U_945)))
    | ~ sP73(U_945,U_946,U_947) ),
    inference(clausify,[status(thm)],[f_351_4]) ).

cnf(f_351_9,plain,
    ( U_945 = image_2003357581_state(U_947,sK36(U_947,U_946,U_945))
    | ~ sP73(U_945,U_946,U_947) ),
    inference(clausify,[status(thm)],[f_351_4]) ).

fof(f_352_1,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,dom_pname_com(body))),
    inference(fof_nnf,[status(thm)],[fact_298_finite__dom__body]) ).

fof(f_352_2,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,dom_pname_com(body))),
    inference(definitional_conversion,[status(esa)],[f_352_1]) ).

cnf(f_352_3,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,dom_pname_com(body))),
    inference(clausify,[status(thm)],[f_352_2]) ).

fof(f_353_1,plain,
    ! [Pname_1,Pname] :
      ( ( ( hAPP_pname_com(body_1,Pname_1) = hAPP_pname_com(body_1,Pname)
          | Pname_1 != Pname )
        & ( Pname_1 = Pname
          | hAPP_pname_com(body_1,Pname_1) != hAPP_pname_com(body_1,Pname) ) )
      | ~ is_pname(Pname)
      | ~ is_pname(Pname_1) ),
    inference(fof_nnf,[status(thm)],[fact_299_com_Osimps_I6_J]) ).

fof(f_353_2,plain,
    ! [U_949,U_948] :
      ( ( ( hAPP_pname_com(body_1,U_949) = hAPP_pname_com(body_1,U_948)
          | U_949 != U_948 )
        & ( U_949 = U_948
          | hAPP_pname_com(body_1,U_949) != hAPP_pname_com(body_1,U_948) ) )
      | ~ is_pname(U_948)
      | ~ is_pname(U_949) ),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

fof(f_353_3,plain,
    ( ! [U_948,U_949] :
        ( hAPP_pname_com(body_1,U_949) = hAPP_pname_com(body_1,U_948)
        | U_949 != U_948
        | ~ sP74(U_948,U_949) )
    & ! [U_948,U_949] :
        ( U_949 = U_948
        | hAPP_pname_com(body_1,U_949) != hAPP_pname_com(body_1,U_948)
        | ~ sP74(U_948,U_949) )
    & ! [U_948,U_949] :
        ( sP74(U_948,U_949)
        | ~ is_pname(U_948)
        | ~ is_pname(U_949) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74])],[f_353_2]) ).

cnf(f_353_4,plain,
    ( sP74(U_948,U_949)
    | ~ is_pname(U_948)
    | ~ is_pname(U_949) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

cnf(f_353_5,plain,
    ( U_949 = U_948
    | hAPP_pname_com(body_1,U_949) != hAPP_pname_com(body_1,U_948)
    | ~ sP74(U_948,U_949) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

cnf(f_353_6,plain,
    ( hAPP_pname_com(body_1,U_949) = hAPP_pname_com(body_1,U_948)
    | U_949 != U_948
    | ~ sP74(U_948,U_949) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

fof(f_354_1,plain,
    ! [P] :
      ( ~ hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(fNot,P)) ),
    inference(fof_nnf,[status(thm)],[help_fNot_1_1_U]) ).

fof(f_354_2,plain,
    ! [U_950] :
      ( ~ hBOOL(U_950)
      | ~ hBOOL(hAPP_bool_bool(fNot,U_950)) ),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

fof(f_354_3,plain,
    ! [U_950] :
      ( ~ hBOOL(U_950)
      | ~ hBOOL(hAPP_bool_bool(fNot,U_950)) ),
    inference(definitional_conversion,[status(esa)],[f_354_2]) ).

cnf(f_354_4,plain,
    ( ~ hBOOL(U_950)
    | ~ hBOOL(hAPP_bool_bool(fNot,U_950)) ),
    inference(clausify,[status(thm)],[f_354_3]) ).

fof(f_355_1,plain,
    ! [P] :
      ( hBOOL(hAPP_bool_bool(fNot,P))
      | hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fNot_2_1_U]) ).

fof(f_355_2,plain,
    ! [U_951] :
      ( hBOOL(hAPP_bool_bool(fNot,U_951))
      | hBOOL(U_951) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

fof(f_355_3,plain,
    ! [U_951] :
      ( hBOOL(hAPP_bool_bool(fNot,U_951))
      | hBOOL(U_951) ),
    inference(definitional_conversion,[status(esa)],[f_355_2]) ).

cnf(f_355_4,plain,
    ( hBOOL(hAPP_bool_bool(fNot,U_951))
    | hBOOL(U_951) ),
    inference(clausify,[status(thm)],[f_355_3]) ).

fof(f_356_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_356_2,plain,
    ! [U_953,U_952] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_952),U_953))
      | ~ hBOOL(U_953)
      | ~ hBOOL(U_952) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ! [U_953] :
      ( ! [U_952] :
          ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_952),U_953))
          | ~ hBOOL(U_952) )
      | ~ hBOOL(U_953) ),
    inference(miniscope,[status(thm)],[f_356_2]) ).

fof(f_356_4,plain,
    ! [U_952,U_953] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_952),U_953))
      | ~ hBOOL(U_952)
      | ~ hBOOL(U_953) ),
    inference(definitional_conversion,[status(esa)],[f_356_3]) ).

cnf(f_356_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_952),U_953))
    | ~ hBOOL(U_952)
    | ~ hBOOL(U_953) ),
    inference(clausify,[status(thm)],[f_356_4]) ).

fof(f_357_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_357_2,plain,
    ! [U_955,U_954] :
      ( hBOOL(U_955)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_955),U_954)) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

fof(f_357_3,plain,
    ! [U_955] :
      ( ! [U_954] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_955),U_954))
      | hBOOL(U_955) ),
    inference(miniscope,[status(thm)],[f_357_2]) ).

fof(f_357_4,plain,
    ! [U_954,U_955] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_955),U_954))
      | hBOOL(U_955) ),
    inference(definitional_conversion,[status(esa)],[f_357_3]) ).

cnf(f_357_5,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_955),U_954))
    | hBOOL(U_955) ),
    inference(clausify,[status(thm)],[f_357_4]) ).

fof(f_358_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_358_2,plain,
    ! [U_957,U_956] :
      ( hBOOL(U_956)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_957),U_956)) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

fof(f_358_3,plain,
    ! [U_956,U_957] :
      ( hBOOL(U_956)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_957),U_956)) ),
    inference(definitional_conversion,[status(esa)],[f_358_2]) ).

cnf(f_358_4,plain,
    ( hBOOL(U_956)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_957),U_956)) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

fof(f_359_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_359_2,plain,
    ! [U_959,U_958] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_958),U_959))
      | ~ hBOOL(U_958) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ! [U_958,U_959] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_958),U_959))
      | ~ hBOOL(U_958) ),
    inference(definitional_conversion,[status(esa)],[f_359_2]) ).

cnf(f_359_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_958),U_959))
    | ~ hBOOL(U_958) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

fof(f_360_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_360_2,plain,
    ! [U_961,U_960] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_961),U_960))
      | ~ hBOOL(U_960) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

fof(f_360_3,plain,
    ! [U_960,U_961] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_961),U_960))
      | ~ hBOOL(U_960) ),
    inference(definitional_conversion,[status(esa)],[f_360_2]) ).

cnf(f_360_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_961),U_960))
    | ~ hBOOL(U_960) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

fof(f_361_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_361_2,plain,
    ! [U_963,U_962] :
      ( hBOOL(U_962)
      | hBOOL(U_963)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_963),U_962)) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

fof(f_361_3,plain,
    ! [U_963] :
      ( ! [U_962] :
          ( hBOOL(U_962)
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_963),U_962)) )
      | hBOOL(U_963) ),
    inference(miniscope,[status(thm)],[f_361_2]) ).

fof(f_361_4,plain,
    ! [U_962,U_963] :
      ( hBOOL(U_962)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_963),U_962))
      | hBOOL(U_963) ),
    inference(definitional_conversion,[status(esa)],[f_361_3]) ).

cnf(f_361_5,plain,
    ( hBOOL(U_962)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_963),U_962))
    | hBOOL(U_963) ),
    inference(clausify,[status(thm)],[f_361_4]) ).

fof(f_362_1,plain,
    ~ hBOOL(fFalse),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_U]) ).

fof(f_362_2,plain,
    ~ hBOOL(fFalse),
    inference(definitional_conversion,[status(esa)],[f_362_1]) ).

cnf(f_362_3,plain,
    ~ hBOOL(fFalse),
    inference(clausify,[status(thm)],[f_362_2]) ).

fof(f_363_1,plain,
    ! [P] :
      ( P = fFalse
      | P = fTrue
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T]) ).

fof(f_363_2,plain,
    ! [U_964] :
      ( U_964 = fFalse
      | U_964 = fTrue
      | ~ is_bool(U_964) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

fof(f_363_3,plain,
    ! [U_964] :
      ( U_964 = fFalse
      | U_964 = fTrue
      | ~ is_bool(U_964) ),
    inference(definitional_conversion,[status(esa)],[f_363_2]) ).

cnf(f_363_4,plain,
    ( U_964 = fFalse
    | U_964 = fTrue
    | ~ is_bool(U_964) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

fof(f_364_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_364_2,plain,
    ! [U_966,U_965] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_965),U_966))
      | hBOOL(U_965) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

fof(f_364_3,plain,
    ! [U_965,U_966] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_965),U_966))
      | hBOOL(U_965) ),
    inference(definitional_conversion,[status(esa)],[f_364_2]) ).

cnf(f_364_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_965),U_966))
    | hBOOL(U_965) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

fof(f_365_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_365_2,plain,
    ! [U_968,U_967] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_968),U_967))
      | ~ hBOOL(U_967) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

fof(f_365_3,plain,
    ! [U_967,U_968] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_968),U_967))
      | ~ hBOOL(U_967) ),
    inference(definitional_conversion,[status(esa)],[f_365_2]) ).

cnf(f_365_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_968),U_967))
    | ~ hBOOL(U_967) ),
    inference(clausify,[status(thm)],[f_365_3]) ).

fof(f_366_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_366_2,plain,
    ! [U_970,U_969] :
      ( hBOOL(U_969)
      | ~ hBOOL(U_970)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_970),U_969)) ),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

fof(f_366_3,plain,
    ! [U_970] :
      ( ! [U_969] :
          ( hBOOL(U_969)
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_970),U_969)) )
      | ~ hBOOL(U_970) ),
    inference(miniscope,[status(thm)],[f_366_2]) ).

fof(f_366_4,plain,
    ! [U_969,U_970] :
      ( hBOOL(U_969)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_970),U_969))
      | ~ hBOOL(U_970) ),
    inference(definitional_conversion,[status(esa)],[f_366_3]) ).

cnf(f_366_5,plain,
    ( hBOOL(U_969)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_970),U_969))
    | ~ hBOOL(U_970) ),
    inference(clausify,[status(thm)],[f_366_4]) ).

fof(f_367_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_367_2,plain,
    ! [U_972,U_971] :
      ( U_972 = U_971
      | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_972),U_971))
      | ~ is_pname(U_971)
      | ~ is_pname(U_972) ),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

fof(f_367_3,plain,
    ! [U_972,U_971] :
      ( U_972 = U_971
      | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_972),U_971))
      | ~ is_pname(U_971)
      | ~ is_pname(U_972) ),
    inference(definitional_conversion,[status(esa)],[f_367_2]) ).

cnf(f_367_4,plain,
    ( U_972 = U_971
    | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_972),U_971))
    | ~ is_pname(U_971)
    | ~ is_pname(U_972) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

fof(f_368_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_368_2,plain,
    ! [U_974,U_973] :
      ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_974),U_973))
      | U_974 != U_973 ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

fof(f_368_3,plain,
    ! [U_974,U_973] :
      ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_974),U_973))
      | U_974 != U_973 ),
    inference(definitional_conversion,[status(esa)],[f_368_2]) ).

cnf(f_368_4,plain,
    ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_974),U_973))
    | U_974 != U_973 ),
    inference(clausify,[status(thm)],[f_368_3]) ).

fof(f_369_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_369_2,plain,
    ! [U_976,U_975] :
      ( hAPP_pname_bool(cOMBK_bool_pname(U_976),U_975) = U_976
      | ~ is_bool(U_976) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

fof(f_369_3,plain,
    ! [U_976] :
      ( ! [U_975] : hAPP_pname_bool(cOMBK_bool_pname(U_976),U_975) = U_976
      | ~ is_bool(U_976) ),
    inference(miniscope,[status(thm)],[f_369_2]) ).

fof(f_369_4,plain,
    ! [U_975,U_976] :
      ( hAPP_pname_bool(cOMBK_bool_pname(U_976),U_975) = U_976
      | ~ is_bool(U_976) ),
    inference(definitional_conversion,[status(esa)],[f_369_3]) ).

cnf(f_369_5,plain,
    ( hAPP_pname_bool(cOMBK_bool_pname(U_976),U_975) = U_976
    | ~ is_bool(U_976) ),
    inference(clausify,[status(thm)],[f_369_4]) ).

fof(f_370_1,plain,
    ! [P,Q] :
      ( hAPP_pname_pname(cOMBK_pname_pname(P),Q) = P
      | ~ is_pname(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U]) ).

fof(f_370_2,plain,
    ! [U_978,U_977] :
      ( hAPP_pname_pname(cOMBK_pname_pname(U_978),U_977) = U_978
      | ~ is_pname(U_978) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

fof(f_370_3,plain,
    ! [U_978] :
      ( ! [U_977] : hAPP_pname_pname(cOMBK_pname_pname(U_978),U_977) = U_978
      | ~ is_pname(U_978) ),
    inference(miniscope,[status(thm)],[f_370_2]) ).

fof(f_370_4,plain,
    ! [U_977,U_978] :
      ( hAPP_pname_pname(cOMBK_pname_pname(U_978),U_977) = U_978
      | ~ is_pname(U_978) ),
    inference(definitional_conversion,[status(esa)],[f_370_3]) ).

cnf(f_370_5,plain,
    ( hAPP_pname_pname(cOMBK_pname_pname(U_978),U_977) = U_978
    | ~ is_pname(U_978) ),
    inference(clausify,[status(thm)],[f_370_4]) ).

fof(f_371_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_371_2,plain,
    ! [U_980,U_979] :
      ( U_980 = U_979
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_980),U_979))
      | ~ is_fun_pname_bool(U_979)
      | ~ is_fun_pname_bool(U_980) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

fof(f_371_3,plain,
    ! [U_979,U_980] :
      ( U_980 = U_979
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_980),U_979))
      | ~ is_fun_pname_bool(U_979)
      | ~ is_fun_pname_bool(U_980) ),
    inference(definitional_conversion,[status(esa)],[f_371_2]) ).

cnf(f_371_4,plain,
    ( U_980 = U_979
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_980),U_979))
    | ~ is_fun_pname_bool(U_979)
    | ~ is_fun_pname_bool(U_980) ),
    inference(clausify,[status(thm)],[f_371_3]) ).

fof(f_372_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_372_2,plain,
    ! [U_982,U_981] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_982),U_981))
      | U_982 != U_981 ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

fof(f_372_3,plain,
    ! [U_982,U_981] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_982),U_981))
      | U_982 != U_981 ),
    inference(definitional_conversion,[status(esa)],[f_372_2]) ).

cnf(f_372_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_982),U_981))
    | U_982 != U_981 ),
    inference(clausify,[status(thm)],[f_372_3]) ).

fof(f_373_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_373_2,plain,
    ! [U_985,U_984,U_983] : hAPP_pname_bool(cOMBB_647938656_pname(U_985,U_984),U_983) = hAPP_bool_bool(U_985,hAPP_pname_bool(U_984,U_983)),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

fof(f_373_3,plain,
    ! [U_984,U_985,U_983] : hAPP_pname_bool(cOMBB_647938656_pname(U_985,U_984),U_983) = hAPP_bool_bool(U_985,hAPP_pname_bool(U_984,U_983)),
    inference(definitional_conversion,[status(esa)],[f_373_2]) ).

cnf(f_373_4,plain,
    hAPP_pname_bool(cOMBB_647938656_pname(U_985,U_984),U_983) = hAPP_bool_bool(U_985,hAPP_pname_bool(U_984,U_983)),
    inference(clausify,[status(thm)],[f_373_3]) ).

fof(f_374_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_374_2,plain,
    ! [U_988,U_987,U_986] : hAPP_pname_bool(cOMBS_568398431l_bool(U_988,U_987),U_986) = hAPP_bool_bool(hAPP_p393069232l_bool(U_988,U_986),hAPP_pname_bool(U_987,U_986)),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

fof(f_374_3,plain,
    ! [U_986,U_987,U_988] : hAPP_pname_bool(cOMBS_568398431l_bool(U_988,U_987),U_986) = hAPP_bool_bool(hAPP_p393069232l_bool(U_988,U_986),hAPP_pname_bool(U_987,U_986)),
    inference(definitional_conversion,[status(esa)],[f_374_2]) ).

cnf(f_374_4,plain,
    hAPP_pname_bool(cOMBS_568398431l_bool(U_988,U_987),U_986) = hAPP_bool_bool(hAPP_p393069232l_bool(U_988,U_986),hAPP_pname_bool(U_987,U_986)),
    inference(clausify,[status(thm)],[f_374_3]) ).

fof(f_375_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_375_2,plain,
    ! [U_991,U_990,U_989] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(U_991),U_990),U_989) = hAPP_pname_bool(hAPP_p61793385e_bool(U_991,U_989),U_990),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

fof(f_375_3,plain,
    ! [U_989,U_990,U_991] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(U_991),U_990),U_989) = hAPP_pname_bool(hAPP_p61793385e_bool(U_991,U_989),U_990),
    inference(definitional_conversion,[status(esa)],[f_375_2]) ).

cnf(f_375_4,plain,
    hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(U_991),U_990),U_989) = hAPP_pname_bool(hAPP_p61793385e_bool(U_991,U_989),U_990),
    inference(clausify,[status(thm)],[f_375_3]) ).

fof(f_376_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_376_2,plain,
    ! [U_993,U_992] :
      ( hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(U_993),U_992) = U_993
      | ~ is_bool(U_993) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

fof(f_376_3,plain,
    ! [U_993] :
      ( ! [U_992] : hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(U_993),U_992) = U_993
      | ~ is_bool(U_993) ),
    inference(miniscope,[status(thm)],[f_376_2]) ).

fof(f_376_4,plain,
    ! [U_992,U_993] :
      ( hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(U_993),U_992) = U_993
      | ~ is_bool(U_993) ),
    inference(definitional_conversion,[status(esa)],[f_376_3]) ).

cnf(f_376_5,plain,
    ( hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(U_993),U_992) = U_993
    | ~ is_bool(U_993) ),
    inference(clausify,[status(thm)],[f_376_4]) ).

fof(f_377_1,plain,
    ! [P,Q] :
      ( hAPP_f1297739591_pname(cOMBK_948730864e_bool(P),Q) = P
      | ~ is_pname(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob]) ).

fof(f_377_2,plain,
    ! [U_995,U_994] :
      ( hAPP_f1297739591_pname(cOMBK_948730864e_bool(U_995),U_994) = U_995
      | ~ is_pname(U_995) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

fof(f_377_3,plain,
    ! [U_995] :
      ( ! [U_994] : hAPP_f1297739591_pname(cOMBK_948730864e_bool(U_995),U_994) = U_995
      | ~ is_pname(U_995) ),
    inference(miniscope,[status(thm)],[f_377_2]) ).

fof(f_377_4,plain,
    ! [U_994,U_995] :
      ( hAPP_f1297739591_pname(cOMBK_948730864e_bool(U_995),U_994) = U_995
      | ~ is_pname(U_995) ),
    inference(definitional_conversion,[status(esa)],[f_377_3]) ).

cnf(f_377_5,plain,
    ( hAPP_f1297739591_pname(cOMBK_948730864e_bool(U_995),U_994) = U_995
    | ~ is_pname(U_995) ),
    inference(clausify,[status(thm)],[f_377_4]) ).

fof(f_378_1,plain,
    ! [P,Q] :
      ( hAPP_p61793385e_bool(cOMBK_37193422_pname(P),Q) = P
      | ~ is_fun_pname_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O]) ).

fof(f_378_2,plain,
    ! [U_997,U_996] :
      ( hAPP_p61793385e_bool(cOMBK_37193422_pname(U_997),U_996) = U_997
      | ~ is_fun_pname_bool(U_997) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

fof(f_378_3,plain,
    ! [U_997] :
      ( ! [U_996] : hAPP_p61793385e_bool(cOMBK_37193422_pname(U_997),U_996) = U_997
      | ~ is_fun_pname_bool(U_997) ),
    inference(miniscope,[status(thm)],[f_378_2]) ).

fof(f_378_4,plain,
    ! [U_996,U_997] :
      ( hAPP_p61793385e_bool(cOMBK_37193422_pname(U_997),U_996) = U_997
      | ~ is_fun_pname_bool(U_997) ),
    inference(definitional_conversion,[status(esa)],[f_378_3]) ).

cnf(f_378_5,plain,
    ( hAPP_p61793385e_bool(cOMBK_37193422_pname(U_997),U_996) = U_997
    | ~ is_fun_pname_bool(U_997) ),
    inference(clausify,[status(thm)],[f_378_4]) ).

fof(f_379_1,plain,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_H78829294e_bool(hAPP_H1049623551e_bool(fequal1111551311_state,X),Y)) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com]) ).

fof(f_379_2,plain,
    ! [U_999,U_998] :
      ( U_999 = U_998
      | ~ hBOOL(hAPP_H78829294e_bool(hAPP_H1049623551e_bool(fequal1111551311_state,U_999),U_998)) ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

fof(f_379_3,plain,
    ! [U_998,U_999] :
      ( U_999 = U_998
      | ~ hBOOL(hAPP_H78829294e_bool(hAPP_H1049623551e_bool(fequal1111551311_state,U_999),U_998)) ),
    inference(definitional_conversion,[status(esa)],[f_379_2]) ).

cnf(f_379_4,plain,
    ( U_999 = U_998
    | ~ hBOOL(hAPP_H78829294e_bool(hAPP_H1049623551e_bool(fequal1111551311_state,U_999),U_998)) ),
    inference(clausify,[status(thm)],[f_379_3]) ).

fof(f_380_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_H78829294e_bool(hAPP_H1049623551e_bool(fequal1111551311_state,X),Y))
      | X != Y ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com]) ).

fof(f_380_2,plain,
    ! [U_1001,U_1000] :
      ( hBOOL(hAPP_H78829294e_bool(hAPP_H1049623551e_bool(fequal1111551311_state,U_1001),U_1000))
      | U_1001 != U_1000 ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

fof(f_380_3,plain,
    ! [U_1000,U_1001] :
      ( hBOOL(hAPP_H78829294e_bool(hAPP_H1049623551e_bool(fequal1111551311_state,U_1001),U_1000))
      | U_1001 != U_1000 ),
    inference(definitional_conversion,[status(esa)],[f_380_2]) ).

cnf(f_380_4,plain,
    ( hBOOL(hAPP_H78829294e_bool(hAPP_H1049623551e_bool(fequal1111551311_state,U_1001),U_1000))
    | U_1001 != U_1000 ),
    inference(clausify,[status(thm)],[f_380_3]) ).

fof(f_381_1,plain,
    ! [P,Q,R] : hAPP_pname_com(cOMBB_923936821_pname(P,Q),R) = hAPP_option_com_com(P,hAPP_p799580910on_com(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00]) ).

fof(f_381_2,plain,
    ! [U_1004,U_1003,U_1002] : hAPP_pname_com(cOMBB_923936821_pname(U_1004,U_1003),U_1002) = hAPP_option_com_com(U_1004,hAPP_p799580910on_com(U_1003,U_1002)),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

fof(f_381_3,plain,
    ! [U_1002,U_1003,U_1004] : hAPP_pname_com(cOMBB_923936821_pname(U_1004,U_1003),U_1002) = hAPP_option_com_com(U_1004,hAPP_p799580910on_com(U_1003,U_1002)),
    inference(definitional_conversion,[status(esa)],[f_381_2]) ).

cnf(f_381_4,plain,
    hAPP_pname_com(cOMBB_923936821_pname(U_1004,U_1003),U_1002) = hAPP_option_com_com(U_1004,hAPP_p799580910on_com(U_1003,U_1002)),
    inference(clausify,[status(thm)],[f_381_3]) ).

fof(f_382_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_382_2,plain,
    ! [U_1007,U_1006,U_1005] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(U_1007,U_1006),U_1005) = hAPP_bool_bool(U_1007,hAPP_f1664156314l_bool(U_1006,U_1005)),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

fof(f_382_3,plain,
    ! [U_1005,U_1006,U_1007] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(U_1007,U_1006),U_1005) = hAPP_bool_bool(U_1007,hAPP_f1664156314l_bool(U_1006,U_1005)),
    inference(definitional_conversion,[status(esa)],[f_382_2]) ).

cnf(f_382_4,plain,
    hAPP_f1664156314l_bool(cOMBB_307249310e_bool(U_1007,U_1006),U_1005) = hAPP_bool_bool(U_1007,hAPP_f1664156314l_bool(U_1006,U_1005)),
    inference(clausify,[status(thm)],[f_382_3]) ).

fof(f_383_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]) ).

fof(f_383_2,plain,
    ! [U_1010,U_1009,U_1008] : hAPP_p393069232l_bool(cOMBB_675860798_pname(U_1010,U_1009),U_1008) = hAPP_b589554111l_bool(U_1010,hAPP_pname_bool(U_1009,U_1008)),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

fof(f_383_3,plain,
    ! [U_1008,U_1009,U_1010] : hAPP_p393069232l_bool(cOMBB_675860798_pname(U_1010,U_1009),U_1008) = hAPP_b589554111l_bool(U_1010,hAPP_pname_bool(U_1009,U_1008)),
    inference(definitional_conversion,[status(esa)],[f_383_2]) ).

cnf(f_383_4,plain,
    hAPP_p393069232l_bool(cOMBB_675860798_pname(U_1010,U_1009),U_1008) = hAPP_b589554111l_bool(U_1010,hAPP_pname_bool(U_1009,U_1008)),
    inference(clausify,[status(thm)],[f_383_3]) ).

fof(f_384_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_384_2,plain,
    ! [U_1013,U_1012,U_1011] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(U_1013,U_1012),U_1011) = hAPP_bool_bool(hAPP_f1476298914l_bool(U_1013,U_1011),hAPP_f1664156314l_bool(U_1012,U_1011)),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ! [U_1011,U_1012,U_1013] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(U_1013,U_1012),U_1011) = hAPP_bool_bool(hAPP_f1476298914l_bool(U_1013,U_1011),hAPP_f1664156314l_bool(U_1012,U_1011)),
    inference(definitional_conversion,[status(esa)],[f_384_2]) ).

cnf(f_384_4,plain,
    hAPP_f1664156314l_bool(cOMBS_350070575l_bool(U_1013,U_1012),U_1011) = hAPP_bool_bool(hAPP_f1476298914l_bool(U_1013,U_1011),hAPP_f1664156314l_bool(U_1012,U_1011)),
    inference(clausify,[status(thm)],[f_384_3]) ).

fof(f_385_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_385_2,plain,
    ! [U_1016,U_1015,U_1014] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(U_1016),U_1015),U_1014) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(U_1016,U_1014),U_1015),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

fof(f_385_3,plain,
    ! [U_1014,U_1015,U_1016] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(U_1016),U_1015),U_1014) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(U_1016,U_1014),U_1015),
    inference(definitional_conversion,[status(esa)],[f_385_2]) ).

cnf(f_385_4,plain,
    hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(U_1016),U_1015),U_1014) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(U_1016,U_1014),U_1015),
    inference(clausify,[status(thm)],[f_385_3]) ).

fof(f_386_1,plain,
    ! [P,Q] :
      ( hAPP_H78829294e_bool(cOMBK_659609255_state(P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__]) ).

fof(f_386_2,plain,
    ! [U_1018,U_1017] :
      ( hAPP_H78829294e_bool(cOMBK_659609255_state(U_1018),U_1017) = U_1018
      | ~ is_bool(U_1018) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

fof(f_386_3,plain,
    ! [U_1018] :
      ( ! [U_1017] : hAPP_H78829294e_bool(cOMBK_659609255_state(U_1018),U_1017) = U_1018
      | ~ is_bool(U_1018) ),
    inference(miniscope,[status(thm)],[f_386_2]) ).

fof(f_386_4,plain,
    ! [U_1017,U_1018] :
      ( hAPP_H78829294e_bool(cOMBK_659609255_state(U_1018),U_1017) = U_1018
      | ~ is_bool(U_1018) ),
    inference(definitional_conversion,[status(esa)],[f_386_3]) ).

cnf(f_386_5,plain,
    ( hAPP_H78829294e_bool(cOMBK_659609255_state(U_1018),U_1017) = U_1018
    | ~ is_bool(U_1018) ),
    inference(clausify,[status(thm)],[f_386_4]) ).

fof(f_387_1,plain,
    ! [P,Q] :
      ( hAPP_H1621176307_pname(cOMBK_168215364_state(P),Q) = P
      | ~ is_pname(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____jfehddehev_]) ).

fof(f_387_2,plain,
    ! [U_1020,U_1019] :
      ( hAPP_H1621176307_pname(cOMBK_168215364_state(U_1020),U_1019) = U_1020
      | ~ is_pname(U_1020) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

fof(f_387_3,plain,
    ! [U_1020] :
      ( ! [U_1019] : hAPP_H1621176307_pname(cOMBK_168215364_state(U_1020),U_1019) = U_1020
      | ~ is_pname(U_1020) ),
    inference(miniscope,[status(thm)],[f_387_2]) ).

fof(f_387_4,plain,
    ! [U_1019,U_1020] :
      ( hAPP_H1621176307_pname(cOMBK_168215364_state(U_1020),U_1019) = U_1020
      | ~ is_pname(U_1020) ),
    inference(definitional_conversion,[status(esa)],[f_387_3]) ).

cnf(f_387_5,plain,
    ( hAPP_H1621176307_pname(cOMBK_168215364_state(U_1020),U_1019) = U_1020
    | ~ is_pname(U_1020) ),
    inference(clausify,[status(thm)],[f_387_4]) ).

fof(f_388_1,plain,
    ! [P,Q] : hAPP_p1422361149_state(cOMBK_367030522_pname(P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__]) ).

fof(f_388_2,plain,
    ! [U_1022,U_1021] : hAPP_p1422361149_state(cOMBK_367030522_pname(U_1022),U_1021) = U_1022,
    inference(variable_rename,[status(thm)],[f_388_1]) ).

fof(f_388_3,plain,
    ! [U_1021,U_1022] : hAPP_p1422361149_state(cOMBK_367030522_pname(U_1022),U_1021) = U_1022,
    inference(definitional_conversion,[status(esa)],[f_388_2]) ).

cnf(f_388_4,plain,
    hAPP_p1422361149_state(cOMBK_367030522_pname(U_1022),U_1021) = U_1022,
    inference(clausify,[status(thm)],[f_388_3]) ).

fof(f_389_1,plain,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,X),Y)) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple]) ).

fof(f_389_2,plain,
    ! [U_1024,U_1023] :
      ( U_1024 = U_1023
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,U_1024),U_1023)) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

fof(f_389_3,plain,
    ! [U_1023,U_1024] :
      ( U_1024 = U_1023
      | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,U_1024),U_1023)) ),
    inference(definitional_conversion,[status(esa)],[f_389_2]) ).

cnf(f_389_4,plain,
    ( U_1024 = U_1023
    | ~ hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,U_1024),U_1023)) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

fof(f_390_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,X),Y))
      | X != Y ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple]) ).

fof(f_390_2,plain,
    ! [U_1026,U_1025] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,U_1026),U_1025))
      | U_1026 != U_1025 ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

fof(f_390_3,plain,
    ! [U_1025,U_1026] :
      ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,U_1026),U_1025))
      | U_1026 != U_1025 ),
    inference(definitional_conversion,[status(esa)],[f_390_2]) ).

cnf(f_390_4,plain,
    ( hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(fequal1311889615e_bool,U_1026),U_1025))
    | U_1026 != U_1025 ),
    inference(clausify,[status(thm)],[f_390_3]) ).

fof(f_391_1,plain,
    ! [P,Q,R] : hAPP_p1422361149_state(cOMBB_699532858_pname(P,Q),R) = hAPP_c1126217667_state(P,hAPP_pname_com(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____jfehddehev__O]) ).

fof(f_391_2,plain,
    ! [U_1029,U_1028,U_1027] : hAPP_p1422361149_state(cOMBB_699532858_pname(U_1029,U_1028),U_1027) = hAPP_c1126217667_state(U_1029,hAPP_pname_com(U_1028,U_1027)),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

fof(f_391_3,plain,
    ! [U_1027,U_1028,U_1029] : hAPP_p1422361149_state(cOMBB_699532858_pname(U_1029,U_1028),U_1027) = hAPP_c1126217667_state(U_1029,hAPP_pname_com(U_1028,U_1027)),
    inference(definitional_conversion,[status(esa)],[f_391_2]) ).

cnf(f_391_4,plain,
    hAPP_p1422361149_state(cOMBB_699532858_pname(U_1029,U_1028),U_1027) = hAPP_c1126217667_state(U_1029,hAPP_pname_com(U_1028,U_1027)),
    inference(clausify,[status(thm)],[f_391_3]) ).

fof(f_392_1,plain,
    ! [P,Q,R] : hAPP_H78829294e_bool(cOMBB_2144135922_state(P,Q),R) = hAPP_bool_bool(P,hAPP_H78829294e_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel]) ).

fof(f_392_2,plain,
    ! [U_1032,U_1031,U_1030] : hAPP_H78829294e_bool(cOMBB_2144135922_state(U_1032,U_1031),U_1030) = hAPP_bool_bool(U_1032,hAPP_H78829294e_bool(U_1031,U_1030)),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ! [U_1030,U_1031,U_1032] : hAPP_H78829294e_bool(cOMBB_2144135922_state(U_1032,U_1031),U_1030) = hAPP_bool_bool(U_1032,hAPP_H78829294e_bool(U_1031,U_1030)),
    inference(definitional_conversion,[status(esa)],[f_392_2]) ).

cnf(f_392_4,plain,
    hAPP_H78829294e_bool(cOMBB_2144135922_state(U_1032,U_1031),U_1030) = hAPP_bool_bool(U_1032,hAPP_H78829294e_bool(U_1031,U_1030)),
    inference(clausify,[status(thm)],[f_392_3]) ).

fof(f_393_1,plain,
    ! [P,Q,R] : hAPP_H78829294e_bool(cOMBS_458705923l_bool(P,Q),R) = hAPP_bool_bool(hAPP_H1187982158l_bool(P,R),hAPP_H78829294e_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__]) ).

fof(f_393_2,plain,
    ! [U_1035,U_1034,U_1033] : hAPP_H78829294e_bool(cOMBS_458705923l_bool(U_1035,U_1034),U_1033) = hAPP_bool_bool(hAPP_H1187982158l_bool(U_1035,U_1033),hAPP_H78829294e_bool(U_1034,U_1033)),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

fof(f_393_3,plain,
    ! [U_1033,U_1034,U_1035] : hAPP_H78829294e_bool(cOMBS_458705923l_bool(U_1035,U_1034),U_1033) = hAPP_bool_bool(hAPP_H1187982158l_bool(U_1035,U_1033),hAPP_H78829294e_bool(U_1034,U_1033)),
    inference(definitional_conversion,[status(esa)],[f_393_2]) ).

cnf(f_393_4,plain,
    hAPP_H78829294e_bool(cOMBS_458705923l_bool(U_1035,U_1034),U_1033) = hAPP_bool_bool(hAPP_H1187982158l_bool(U_1035,U_1033),hAPP_H78829294e_bool(U_1034,U_1033)),
    inference(clausify,[status(thm)],[f_393_3]) ).

fof(f_394_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_006]) ).

fof(f_394_2,plain,
    ! [U_1038,U_1037,U_1036] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(U_1038,U_1037),U_1036) = hAPP_b589554111l_bool(U_1038,hAPP_f1664156314l_bool(U_1037,U_1036)),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

fof(f_394_3,plain,
    ! [U_1036,U_1037,U_1038] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(U_1038,U_1037),U_1036) = hAPP_b589554111l_bool(U_1038,hAPP_f1664156314l_bool(U_1037,U_1036)),
    inference(definitional_conversion,[status(esa)],[f_394_2]) ).

cnf(f_394_4,plain,
    hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(U_1038,U_1037),U_1036) = hAPP_b589554111l_bool(U_1038,hAPP_f1664156314l_bool(U_1037,U_1036)),
    inference(clausify,[status(thm)],[f_394_3]) ).

fof(f_395_1,plain,
    ! [P,Q,R] : hAPP_f1935102916l_bool(cOMBS_811933079l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f32027384l_bool(P,R),hAPP_f1935102916l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_]) ).

fof(f_395_2,plain,
    ! [U_1041,U_1040,U_1039] : hAPP_f1935102916l_bool(cOMBS_811933079l_bool(U_1041,U_1040),U_1039) = hAPP_bool_bool(hAPP_f32027384l_bool(U_1041,U_1039),hAPP_f1935102916l_bool(U_1040,U_1039)),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

fof(f_395_3,plain,
    ! [U_1039,U_1040,U_1041] : hAPP_f1935102916l_bool(cOMBS_811933079l_bool(U_1041,U_1040),U_1039) = hAPP_bool_bool(hAPP_f32027384l_bool(U_1041,U_1039),hAPP_f1935102916l_bool(U_1040,U_1039)),
    inference(definitional_conversion,[status(esa)],[f_395_2]) ).

cnf(f_395_4,plain,
    hAPP_f1935102916l_bool(cOMBS_811933079l_bool(U_1041,U_1040),U_1039) = hAPP_bool_bool(hAPP_f32027384l_bool(U_1041,U_1039),hAPP_f1935102916l_bool(U_1040,U_1039)),
    inference(clausify,[status(thm)],[f_395_3]) ).

fof(f_396_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_396_2,plain,
    ! [U_1044,U_1043,U_1042] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(U_1044),U_1043),U_1042) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(U_1044,U_1042),U_1043),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

fof(f_396_3,plain,
    ! [U_1042,U_1043,U_1044] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(U_1044),U_1043),U_1042) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(U_1044,U_1042),U_1043),
    inference(definitional_conversion,[status(esa)],[f_396_2]) ).

cnf(f_396_4,plain,
    hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(U_1044),U_1043),U_1042) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(U_1044,U_1042),U_1043),
    inference(clausify,[status(thm)],[f_396_3]) ).

fof(f_397_1,plain,
    ! [P,Q] :
      ( hAPP_f971112728l_bool(cOMBK_129401207e_bool(P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____jfe]) ).

fof(f_397_2,plain,
    ! [U_1046,U_1045] :
      ( hAPP_f971112728l_bool(cOMBK_129401207e_bool(U_1046),U_1045) = U_1046
      | ~ is_bool(U_1046) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

fof(f_397_3,plain,
    ! [U_1046] :
      ( ! [U_1045] : hAPP_f971112728l_bool(cOMBK_129401207e_bool(U_1046),U_1045) = U_1046
      | ~ is_bool(U_1046) ),
    inference(miniscope,[status(thm)],[f_397_2]) ).

fof(f_397_4,plain,
    ! [U_1045,U_1046] :
      ( hAPP_f971112728l_bool(cOMBK_129401207e_bool(U_1046),U_1045) = U_1046
      | ~ is_bool(U_1046) ),
    inference(definitional_conversion,[status(esa)],[f_397_3]) ).

cnf(f_397_5,plain,
    ( hAPP_f971112728l_bool(cOMBK_129401207e_bool(U_1046),U_1045) = U_1046
    | ~ is_bool(U_1046) ),
    inference(clausify,[status(thm)],[f_397_4]) ).

fof(f_398_1,plain,
    ! [P,Q] :
      ( hAPP_f560369737_pname(cOMBK_1589414042e_bool(P),Q) = P
      | ~ is_pname(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____jf]) ).

fof(f_398_2,plain,
    ! [U_1048,U_1047] :
      ( hAPP_f560369737_pname(cOMBK_1589414042e_bool(U_1048),U_1047) = U_1048
      | ~ is_pname(U_1048) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

fof(f_398_3,plain,
    ! [U_1048] :
      ( ! [U_1047] : hAPP_f560369737_pname(cOMBK_1589414042e_bool(U_1048),U_1047) = U_1048
      | ~ is_pname(U_1048) ),
    inference(miniscope,[status(thm)],[f_398_2]) ).

fof(f_398_4,plain,
    ! [U_1047,U_1048] :
      ( hAPP_f560369737_pname(cOMBK_1589414042e_bool(U_1048),U_1047) = U_1048
      | ~ is_pname(U_1048) ),
    inference(definitional_conversion,[status(esa)],[f_398_3]) ).

cnf(f_398_5,plain,
    ( hAPP_f560369737_pname(cOMBK_1589414042e_bool(U_1048),U_1047) = U_1048
    | ~ is_pname(U_1048) ),
    inference(clausify,[status(thm)],[f_398_4]) ).

fof(f_399_1,plain,
    ! [P,Q] : hAPP_f888949707_state(cOMBK_1503445380e_bool(P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___007]) ).

fof(f_399_2,plain,
    ! [U_1050,U_1049] : hAPP_f888949707_state(cOMBK_1503445380e_bool(U_1050),U_1049) = U_1050,
    inference(variable_rename,[status(thm)],[f_399_1]) ).

fof(f_399_3,plain,
    ! [U_1049,U_1050] : hAPP_f888949707_state(cOMBK_1503445380e_bool(U_1050),U_1049) = U_1050,
    inference(definitional_conversion,[status(esa)],[f_399_2]) ).

cnf(f_399_4,plain,
    hAPP_f888949707_state(cOMBK_1503445380e_bool(U_1050),U_1049) = U_1050,
    inference(clausify,[status(thm)],[f_399_3]) ).

fof(f_400_1,plain,
    ! [P,Q] :
      ( hAPP_H356885323e_bool(cOMBK_2035509764_state(P),Q) = P
      | ~ is_fun_pname_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_]) ).

fof(f_400_2,plain,
    ! [U_1052,U_1051] :
      ( hAPP_H356885323e_bool(cOMBK_2035509764_state(U_1052),U_1051) = U_1052
      | ~ is_fun_pname_bool(U_1052) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

fof(f_400_3,plain,
    ! [U_1052] :
      ( ! [U_1051] : hAPP_H356885323e_bool(cOMBK_2035509764_state(U_1052),U_1051) = U_1052
      | ~ is_fun_pname_bool(U_1052) ),
    inference(miniscope,[status(thm)],[f_400_2]) ).

fof(f_400_4,plain,
    ! [U_1051,U_1052] :
      ( hAPP_H356885323e_bool(cOMBK_2035509764_state(U_1052),U_1051) = U_1052
      | ~ is_fun_pname_bool(U_1052) ),
    inference(definitional_conversion,[status(esa)],[f_400_3]) ).

cnf(f_400_5,plain,
    ( hAPP_H356885323e_bool(cOMBK_2035509764_state(U_1052),U_1051) = U_1052
    | ~ is_fun_pname_bool(U_1052) ),
    inference(clausify,[status(thm)],[f_400_4]) ).

fof(f_401_1,plain,
    ! [P,Q] : hAPP_p442853985e_bool(cOMBK_1706929794_pname(P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I]) ).

fof(f_401_2,plain,
    ! [U_1054,U_1053] : hAPP_p442853985e_bool(cOMBK_1706929794_pname(U_1054),U_1053) = U_1054,
    inference(variable_rename,[status(thm)],[f_401_1]) ).

fof(f_401_3,plain,
    ! [U_1053,U_1054] : hAPP_p442853985e_bool(cOMBK_1706929794_pname(U_1054),U_1053) = U_1054,
    inference(definitional_conversion,[status(esa)],[f_401_2]) ).

cnf(f_401_4,plain,
    hAPP_p442853985e_bool(cOMBK_1706929794_pname(U_1054),U_1053) = U_1054,
    inference(clausify,[status(thm)],[f_401_3]) ).

fof(f_402_1,plain,
    ! [P,Q,R] : hAPP_f971112728l_bool(cOMBB_1522210668e_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f971112728l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__]) ).

fof(f_402_2,plain,
    ! [U_1057,U_1056,U_1055] : hAPP_f971112728l_bool(cOMBB_1522210668e_bool(U_1057,U_1056),U_1055) = hAPP_bool_bool(U_1057,hAPP_f971112728l_bool(U_1056,U_1055)),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

fof(f_402_3,plain,
    ! [U_1055,U_1056,U_1057] : hAPP_f971112728l_bool(cOMBB_1522210668e_bool(U_1057,U_1056),U_1055) = hAPP_bool_bool(U_1057,hAPP_f971112728l_bool(U_1056,U_1055)),
    inference(definitional_conversion,[status(esa)],[f_402_2]) ).

cnf(f_402_4,plain,
    hAPP_f971112728l_bool(cOMBB_1522210668e_bool(U_1057,U_1056),U_1055) = hAPP_bool_bool(U_1057,hAPP_f971112728l_bool(U_1056,U_1055)),
    inference(clausify,[status(thm)],[f_402_3]) ).

fof(f_403_1,plain,
    ! [P,Q,R] : hAPP_H1187982158l_bool(cOMBB_962198420_state(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_H78829294e_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008]) ).

fof(f_403_2,plain,
    ! [U_1060,U_1059,U_1058] : hAPP_H1187982158l_bool(cOMBB_962198420_state(U_1060,U_1059),U_1058) = hAPP_b589554111l_bool(U_1060,hAPP_H78829294e_bool(U_1059,U_1058)),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

fof(f_403_3,plain,
    ! [U_1058,U_1059,U_1060] : hAPP_H1187982158l_bool(cOMBB_962198420_state(U_1060,U_1059),U_1058) = hAPP_b589554111l_bool(U_1060,hAPP_H78829294e_bool(U_1059,U_1058)),
    inference(definitional_conversion,[status(esa)],[f_403_2]) ).

cnf(f_403_4,plain,
    hAPP_H1187982158l_bool(cOMBB_962198420_state(U_1060,U_1059),U_1058) = hAPP_b589554111l_bool(U_1060,hAPP_H78829294e_bool(U_1059,U_1058)),
    inference(clausify,[status(thm)],[f_403_3]) ).

fof(f_404_1,plain,
    ! [P,Q,R] : hAPP_f971112728l_bool(cOMBS_2066081387l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f637090980l_bool(P,R),hAPP_f971112728l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I]) ).

fof(f_404_2,plain,
    ! [U_1063,U_1062,U_1061] : hAPP_f971112728l_bool(cOMBS_2066081387l_bool(U_1063,U_1062),U_1061) = hAPP_bool_bool(hAPP_f637090980l_bool(U_1063,U_1061),hAPP_f971112728l_bool(U_1062,U_1061)),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

fof(f_404_3,plain,
    ! [U_1061,U_1062,U_1063] : hAPP_f971112728l_bool(cOMBS_2066081387l_bool(U_1063,U_1062),U_1061) = hAPP_bool_bool(hAPP_f637090980l_bool(U_1063,U_1061),hAPP_f971112728l_bool(U_1062,U_1061)),
    inference(definitional_conversion,[status(esa)],[f_404_2]) ).

cnf(f_404_4,plain,
    hAPP_f971112728l_bool(cOMBS_2066081387l_bool(U_1063,U_1062),U_1061) = hAPP_bool_bool(hAPP_f637090980l_bool(U_1063,U_1061),hAPP_f971112728l_bool(U_1062,U_1061)),
    inference(clausify,[status(thm)],[f_404_3]) ).

fof(f_405_1,plain,
    ! [P,Q,R] : hAPP_f32027384l_bool(cOMBB_689948150l_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f1935102916l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009]) ).

fof(f_405_2,plain,
    ! [U_1066,U_1065,U_1064] : hAPP_f32027384l_bool(cOMBB_689948150l_bool(U_1066,U_1065),U_1064) = hAPP_b589554111l_bool(U_1066,hAPP_f1935102916l_bool(U_1065,U_1064)),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

fof(f_405_3,plain,
    ! [U_1064,U_1065,U_1066] : hAPP_f32027384l_bool(cOMBB_689948150l_bool(U_1066,U_1065),U_1064) = hAPP_b589554111l_bool(U_1066,hAPP_f1935102916l_bool(U_1065,U_1064)),
    inference(definitional_conversion,[status(esa)],[f_405_2]) ).

cnf(f_405_4,plain,
    hAPP_f32027384l_bool(cOMBB_689948150l_bool(U_1066,U_1065),U_1064) = hAPP_b589554111l_bool(U_1066,hAPP_f1935102916l_bool(U_1065,U_1064)),
    inference(clausify,[status(thm)],[f_405_3]) ).

fof(f_406_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_010]) ).

fof(f_406_2,plain,
    ! [U_1069,U_1068,U_1067] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(U_1069),U_1068),U_1067) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(U_1069,U_1067),U_1068),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ! [U_1067,U_1068,U_1069] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(U_1069),U_1068),U_1067) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(U_1069,U_1067),U_1068),
    inference(definitional_conversion,[status(esa)],[f_406_2]) ).

cnf(f_406_4,plain,
    hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(U_1069),U_1068),U_1067) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(U_1069,U_1067),U_1068),
    inference(clausify,[status(thm)],[f_406_3]) ).

fof(f_407_1,plain,
    ! [P,Q] :
      ( hAPP_f166538662l_bool(cOMBK_482404831l_bool(P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Hoare____Mirabel]) ).

fof(f_407_2,plain,
    ! [U_1071,U_1070] :
      ( hAPP_f166538662l_bool(cOMBK_482404831l_bool(U_1071),U_1070) = U_1071
      | ~ is_bool(U_1071) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ! [U_1071] :
      ( ! [U_1070] : hAPP_f166538662l_bool(cOMBK_482404831l_bool(U_1071),U_1070) = U_1071
      | ~ is_bool(U_1071) ),
    inference(miniscope,[status(thm)],[f_407_2]) ).

fof(f_407_4,plain,
    ! [U_1070,U_1071] :
      ( hAPP_f166538662l_bool(cOMBK_482404831l_bool(U_1071),U_1070) = U_1071
      | ~ is_bool(U_1071) ),
    inference(definitional_conversion,[status(esa)],[f_407_3]) ).

cnf(f_407_5,plain,
    ( hAPP_f166538662l_bool(cOMBK_482404831l_bool(U_1071),U_1070) = U_1071
    | ~ is_bool(U_1071) ),
    inference(clausify,[status(thm)],[f_407_4]) ).

fof(f_408_1,plain,
    ! [P,Q,R] : hAPP_H78829294e_bool(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(P),Q),R) = hAPP_H78829294e_bool(hAPP_H1049623551e_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__]) ).

fof(f_408_2,plain,
    ! [U_1074,U_1073,U_1072] : hAPP_H78829294e_bool(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(U_1074),U_1073),U_1072) = hAPP_H78829294e_bool(hAPP_H1049623551e_bool(U_1074,U_1072),U_1073),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

fof(f_408_3,plain,
    ! [U_1072,U_1073,U_1074] : hAPP_H78829294e_bool(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(U_1074),U_1073),U_1072) = hAPP_H78829294e_bool(hAPP_H1049623551e_bool(U_1074,U_1072),U_1073),
    inference(definitional_conversion,[status(esa)],[f_408_2]) ).

cnf(f_408_4,plain,
    hAPP_H78829294e_bool(hAPP_H1049623551e_bool(cOMBC_654211620e_bool(U_1074),U_1073),U_1072) = hAPP_H78829294e_bool(hAPP_H1049623551e_bool(U_1074,U_1072),U_1073),
    inference(clausify,[status(thm)],[f_408_3]) ).

fof(f_409_1,plain,
    ! [P,Q,R] : hAPP_f637090980l_bool(cOMBB_1585081418e_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f971112728l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011]) ).

fof(f_409_2,plain,
    ! [U_1077,U_1076,U_1075] : hAPP_f637090980l_bool(cOMBB_1585081418e_bool(U_1077,U_1076),U_1075) = hAPP_b589554111l_bool(U_1077,hAPP_f971112728l_bool(U_1076,U_1075)),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

fof(f_409_3,plain,
    ! [U_1075,U_1076,U_1077] : hAPP_f637090980l_bool(cOMBB_1585081418e_bool(U_1077,U_1076),U_1075) = hAPP_b589554111l_bool(U_1077,hAPP_f971112728l_bool(U_1076,U_1075)),
    inference(definitional_conversion,[status(esa)],[f_409_2]) ).

cnf(f_409_4,plain,
    hAPP_f637090980l_bool(cOMBB_1585081418e_bool(U_1077,U_1076),U_1075) = hAPP_b589554111l_bool(U_1077,hAPP_f971112728l_bool(U_1076,U_1075)),
    inference(clausify,[status(thm)],[f_409_3]) ).

fof(f_410_1,plain,
    ! [P,Q,R] : hAPP_f166538662l_bool(cOMBS_1358309691l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f2143399574l_bool(P,R),hAPP_f166538662l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__]) ).

fof(f_410_2,plain,
    ! [U_1080,U_1079,U_1078] : hAPP_f166538662l_bool(cOMBS_1358309691l_bool(U_1080,U_1079),U_1078) = hAPP_bool_bool(hAPP_f2143399574l_bool(U_1080,U_1078),hAPP_f166538662l_bool(U_1079,U_1078)),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

fof(f_410_3,plain,
    ! [U_1078,U_1079,U_1080] : hAPP_f166538662l_bool(cOMBS_1358309691l_bool(U_1080,U_1079),U_1078) = hAPP_bool_bool(hAPP_f2143399574l_bool(U_1080,U_1078),hAPP_f166538662l_bool(U_1079,U_1078)),
    inference(definitional_conversion,[status(esa)],[f_410_2]) ).

cnf(f_410_4,plain,
    hAPP_f166538662l_bool(cOMBS_1358309691l_bool(U_1080,U_1079),U_1078) = hAPP_bool_bool(hAPP_f2143399574l_bool(U_1080,U_1078),hAPP_f166538662l_bool(U_1079,U_1078)),
    inference(clausify,[status(thm)],[f_410_3]) ).

fof(f_411_1,plain,
    ! [P,Q] : hAPP_f1387463497_state(cOMBK_701929478e_bool(P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___012]) ).

fof(f_411_2,plain,
    ! [U_1082,U_1081] : hAPP_f1387463497_state(cOMBK_701929478e_bool(U_1082),U_1081) = U_1082,
    inference(variable_rename,[status(thm)],[f_411_1]) ).

fof(f_411_3,plain,
    ! [U_1081,U_1082] : hAPP_f1387463497_state(cOMBK_701929478e_bool(U_1082),U_1081) = U_1082,
    inference(definitional_conversion,[status(esa)],[f_411_2]) ).

cnf(f_411_4,plain,
    hAPP_f1387463497_state(cOMBK_701929478e_bool(U_1082),U_1081) = U_1082,
    inference(clausify,[status(thm)],[f_411_3]) ).

fof(f_412_1,plain,
    ! [P,Q] : hAPP_H1049623551e_bool(cOMBK_1039769424_state(P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_013]) ).

fof(f_412_2,plain,
    ! [U_1084,U_1083] : hAPP_H1049623551e_bool(cOMBK_1039769424_state(U_1084),U_1083) = U_1084,
    inference(variable_rename,[status(thm)],[f_412_1]) ).

fof(f_412_3,plain,
    ! [U_1083,U_1084] : hAPP_H1049623551e_bool(cOMBK_1039769424_state(U_1084),U_1083) = U_1084,
    inference(definitional_conversion,[status(esa)],[f_412_2]) ).

cnf(f_412_4,plain,
    hAPP_H1049623551e_bool(cOMBK_1039769424_state(U_1084),U_1083) = U_1084,
    inference(clausify,[status(thm)],[f_412_3]) ).

fof(f_413_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_413_2,plain,
    ! [U_1087,U_1086,U_1085] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(U_1087),U_1086),U_1085) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(U_1087,U_1085),U_1086),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ! [U_1085,U_1086,U_1087] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(U_1087),U_1086),U_1085) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(U_1087,U_1085),U_1086),
    inference(definitional_conversion,[status(esa)],[f_413_2]) ).

cnf(f_413_4,plain,
    hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(U_1087),U_1086),U_1085) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(U_1087,U_1085),U_1086),
    inference(clausify,[status(thm)],[f_413_3]) ).

fof(f_414_1,plain,
    ! [P,Q,R] : hAPP_H78829294e_bool(hAPP_f98417237e_bool(cOMBC_1734175330l_bool(P),Q),R) = hAPP_f971112728l_bool(hAPP_H30606679l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___014]) ).

fof(f_414_2,plain,
    ! [U_1090,U_1089,U_1088] : hAPP_H78829294e_bool(hAPP_f98417237e_bool(cOMBC_1734175330l_bool(U_1090),U_1089),U_1088) = hAPP_f971112728l_bool(hAPP_H30606679l_bool(U_1090,U_1088),U_1089),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

fof(f_414_3,plain,
    ! [U_1090,U_1088,U_1089] : hAPP_H78829294e_bool(hAPP_f98417237e_bool(cOMBC_1734175330l_bool(U_1090),U_1089),U_1088) = hAPP_f971112728l_bool(hAPP_H30606679l_bool(U_1090,U_1088),U_1089),
    inference(definitional_conversion,[status(esa)],[f_414_2]) ).

cnf(f_414_4,plain,
    hAPP_H78829294e_bool(hAPP_f98417237e_bool(cOMBC_1734175330l_bool(U_1090),U_1089),U_1088) = hAPP_f971112728l_bool(hAPP_H30606679l_bool(U_1090,U_1088),U_1089),
    inference(clausify,[status(thm)],[f_414_3]) ).

fof(f_415_1,plain,
    ! [P,Q,R] : hAPP_f2143399574l_bool(cOMBB_404111180l_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f166538662l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_015]) ).

fof(f_415_2,plain,
    ! [U_1093,U_1092,U_1091] : hAPP_f2143399574l_bool(cOMBB_404111180l_bool(U_1093,U_1092),U_1091) = hAPP_b589554111l_bool(U_1093,hAPP_f166538662l_bool(U_1092,U_1091)),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

fof(f_415_3,plain,
    ! [U_1091,U_1092,U_1093] : hAPP_f2143399574l_bool(cOMBB_404111180l_bool(U_1093,U_1092),U_1091) = hAPP_b589554111l_bool(U_1093,hAPP_f166538662l_bool(U_1092,U_1091)),
    inference(definitional_conversion,[status(esa)],[f_415_2]) ).

cnf(f_415_4,plain,
    hAPP_f2143399574l_bool(cOMBB_404111180l_bool(U_1093,U_1092),U_1091) = hAPP_b589554111l_bool(U_1093,hAPP_f166538662l_bool(U_1092,U_1091)),
    inference(clausify,[status(thm)],[f_415_3]) ).

fof(f_416_1,plain,
    ! [P,Q,R] : hAPP_f971112728l_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(P),Q),R) = hAPP_f971112728l_bool(hAPP_f72706945l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I]) ).

fof(f_416_2,plain,
    ! [U_1096,U_1095,U_1094] : hAPP_f971112728l_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(U_1096),U_1095),U_1094) = hAPP_f971112728l_bool(hAPP_f72706945l_bool(U_1096,U_1094),U_1095),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

fof(f_416_3,plain,
    ! [U_1094,U_1095,U_1096] : hAPP_f971112728l_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(U_1096),U_1095),U_1094) = hAPP_f971112728l_bool(hAPP_f72706945l_bool(U_1096,U_1094),U_1095),
    inference(definitional_conversion,[status(esa)],[f_416_2]) ).

cnf(f_416_4,plain,
    hAPP_f971112728l_bool(hAPP_f72706945l_bool(cOMBC_449066458l_bool(U_1096),U_1095),U_1094) = hAPP_f971112728l_bool(hAPP_f72706945l_bool(U_1096,U_1094),U_1095),
    inference(clausify,[status(thm)],[f_416_3]) ).

fof(f_417_1,plain,
    ! [P,Q,R] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(P),Q),R) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo]) ).

fof(f_417_2,plain,
    ! [U_1099,U_1098,U_1097] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(U_1099),U_1098),U_1097) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(U_1099,U_1097),U_1098),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

fof(f_417_3,plain,
    ! [U_1097,U_1098,U_1099] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(U_1099),U_1098),U_1097) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(U_1099,U_1097),U_1098),
    inference(definitional_conversion,[status(esa)],[f_417_2]) ).

cnf(f_417_4,plain,
    hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(U_1099),U_1098),U_1097) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(U_1099,U_1097),U_1098),
    inference(clausify,[status(thm)],[f_417_3]) ).

fof(f_418_1,plain,
    ! [P,Q,R] : hAPP_f971112728l_bool(hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(P),Q),R) = hAPP_f166538662l_bool(hAPP_f210337421l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_016]) ).

fof(f_418_2,plain,
    ! [U_1102,U_1101,U_1100] : hAPP_f971112728l_bool(hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(U_1102),U_1101),U_1100) = hAPP_f166538662l_bool(hAPP_f210337421l_bool(U_1102,U_1100),U_1101),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

fof(f_418_3,plain,
    ! [U_1100,U_1101,U_1102] : hAPP_f971112728l_bool(hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(U_1102),U_1101),U_1100) = hAPP_f166538662l_bool(hAPP_f210337421l_bool(U_1102,U_1100),U_1101),
    inference(definitional_conversion,[status(esa)],[f_418_2]) ).

cnf(f_418_4,plain,
    hAPP_f971112728l_bool(hAPP_f1201187855l_bool(cOMBC_1114453604l_bool(U_1102),U_1101),U_1100) = hAPP_f166538662l_bool(hAPP_f210337421l_bool(U_1102,U_1100),U_1101),
    inference(clausify,[status(thm)],[f_418_3]) ).

fof(f_419_1,plain,
    ! [P,Q,R] : hAPP_f166538662l_bool(hAPP_f585161855l_bool(cOMBC_1691491604l_bool(P),Q),R) = hAPP_f166538662l_bool(hAPP_f585161855l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__]) ).

fof(f_419_2,plain,
    ! [U_1105,U_1104,U_1103] : hAPP_f166538662l_bool(hAPP_f585161855l_bool(cOMBC_1691491604l_bool(U_1105),U_1104),U_1103) = hAPP_f166538662l_bool(hAPP_f585161855l_bool(U_1105,U_1103),U_1104),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

fof(f_419_3,plain,
    ! [U_1103,U_1104,U_1105] : hAPP_f166538662l_bool(hAPP_f585161855l_bool(cOMBC_1691491604l_bool(U_1105),U_1104),U_1103) = hAPP_f166538662l_bool(hAPP_f585161855l_bool(U_1105,U_1103),U_1104),
    inference(definitional_conversion,[status(esa)],[f_419_2]) ).

cnf(f_419_4,plain,
    hAPP_f166538662l_bool(hAPP_f585161855l_bool(cOMBC_1691491604l_bool(U_1105),U_1104),U_1103) = hAPP_f166538662l_bool(hAPP_f585161855l_bool(U_1105,U_1103),U_1104),
    inference(clausify,[status(thm)],[f_419_3]) ).

fof(f_420_1,plain,
    ! [P,Q,R] : hAPP_f468958928l_bool(hAPP_f667366769l_bool(cOMBC_747715418l_bool(P),Q),R) = hAPP_f468958928l_bool(hAPP_f667366769l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfe]) ).

fof(f_420_2,plain,
    ! [U_1108,U_1107,U_1106] : hAPP_f468958928l_bool(hAPP_f667366769l_bool(cOMBC_747715418l_bool(U_1108),U_1107),U_1106) = hAPP_f468958928l_bool(hAPP_f667366769l_bool(U_1108,U_1106),U_1107),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

fof(f_420_3,plain,
    ! [U_1106,U_1107,U_1108] : hAPP_f468958928l_bool(hAPP_f667366769l_bool(cOMBC_747715418l_bool(U_1108),U_1107),U_1106) = hAPP_f468958928l_bool(hAPP_f667366769l_bool(U_1108,U_1106),U_1107),
    inference(definitional_conversion,[status(esa)],[f_420_2]) ).

cnf(f_420_4,plain,
    hAPP_f468958928l_bool(hAPP_f667366769l_bool(cOMBC_747715418l_bool(U_1108),U_1107),U_1106) = hAPP_f468958928l_bool(hAPP_f667366769l_bool(U_1108,U_1106),U_1107),
    inference(clausify,[status(thm)],[f_420_3]) ).

fof(f_421_1,plain,
    hBOOL(hoare_165779456gleton),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

fof(f_421_2,plain,
    hBOOL(hoare_165779456gleton),
    inference(definitional_conversion,[status(esa)],[f_421_1]) ).

cnf(f_421_3,plain,
    hBOOL(hoare_165779456gleton),
    inference(clausify,[status(thm)],[f_421_2]) ).

fof(f_422_1,plain,
    hBOOL(wT_bodies),
    inference(fof_nnf,[status(thm)],[conj_1]) ).

fof(f_422_2,plain,
    hBOOL(wT_bodies),
    inference(definitional_conversion,[status(esa)],[f_422_1]) ).

cnf(f_422_3,plain,
    hBOOL(wT_bodies),
    inference(clausify,[status(thm)],[f_422_2]) ).

fof(f_423_1,plain,
    hBOOL(hAPP_f971112728l_bool(finite364844667_state,fa)),
    inference(fof_nnf,[status(thm)],[conj_2]) ).

fof(f_423_2,plain,
    hBOOL(hAPP_f971112728l_bool(finite364844667_state,fa)),
    inference(definitional_conversion,[status(esa)],[f_423_1]) ).

cnf(f_423_3,plain,
    hBOOL(hAPP_f971112728l_bool(finite364844667_state,fa)),
    inference(clausify,[status(thm)],[f_423_2]) ).

fof(f_424_1,plain,
    ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y)),fa)),
    inference(fof_nnf,[status(thm)],[conj_3]) ).

fof(f_424_2,plain,
    ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y)),fa)),
    inference(definitional_conversion,[status(esa)],[f_424_1]) ).

cnf(f_424_3,plain,
    ~ hBOOL(hAPP_f971112728l_bool(hAPP_H30606679l_bool(member1338687867_state,hAPP_c1126217667_state(hoare_Mirabelle_MGT,y)),fa)),
    inference(clausify,[status(thm)],[f_424_2]) ).

fof(f_425_1,plain,
    hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,fa),image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,cOMBB_923936821_pname(the_com,body)),dom_pname_com(body)))),
    inference(fof_nnf,[status(thm)],[conj_4]) ).

fof(f_425_2,plain,
    hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,fa),image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,cOMBB_923936821_pname(the_com,body)),dom_pname_com(body)))),
    inference(definitional_conversion,[status(esa)],[f_425_1]) ).

cnf(f_425_3,plain,
    hBOOL(hAPP_f971112728l_bool(hAPP_f72706945l_bool(ord_le1285840794e_bool,fa),image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,cOMBB_923936821_pname(the_com,body)),dom_pname_com(body)))),
    inference(clausify,[status(thm)],[f_425_2]) ).

fof(f_426_1,plain,
    hAPP_p799580910on_com(body,pn) = some_com(y),
    inference(fof_nnf,[status(thm)],[conj_5]) ).

fof(f_426_2,plain,
    hAPP_p799580910on_com(body,pn) = some_com(y),
    inference(definitional_conversion,[status(esa)],[f_426_1]) ).

cnf(f_426_3,plain,
    hAPP_p799580910on_com(body,pn) = some_com(y),
    inference(clausify,[status(thm)],[f_426_2]) ).

fof(f_427_1,plain,
    hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),fa)),
    inference(fof_nnf,[status(thm)],[conj_6]) ).

fof(f_427_2,plain,
    hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),fa)),
    inference(definitional_conversion,[status(esa)],[f_427_1]) ).

cnf(f_427_3,plain,
    hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),fa)),
    inference(clausify,[status(thm)],[f_427_2]) ).

fof(f_428_1,negated_conjecture,
    ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,y),bot_bo620288102e_bool))),
    inference(negate,[status(cth)],[conj_7]) ).

fof(f_428_2,negated_conjecture,
    ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,y),bot_bo620288102e_bool))),
    inference(definitional_conversion,[status(esa)],[f_428_1]) ).

cnf(f_428_3,negated_conjecture,
    ~ hBOOL(hAPP_f971112728l_bool(hoare_1598289066_state(image_2003357581_state(cOMBB_699532858_pname(hoare_Mirabelle_MGT,body_1),dom_pname_com(body))),insert1415133716_state(hAPP_c1126217667_state(hoare_Mirabelle_MGT,y),bot_bo620288102e_bool))),
    inference(clausify,[status(thm)],[f_428_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_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_5,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_6,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_7,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_8,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_9,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_10,axiom,
    ( wt(Eq_x_0) = wt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_11,axiom,
    ( undefined_pname(Eq_x_0) = undefined_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_12,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_13,axiom,
    ( undefi17486888e_bool(Eq_x_0) = undefi17486888e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,axiom,
    ( undefi64961550l_bool(Eq_x_0) = undefi64961550l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_15,axiom,
    ( dom_pname_com(Eq_x_0) = dom_pname_com(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_16,axiom,
    ( dom_fu2081503504ol_com(Eq_x_0) = dom_fu2081503504ol_com(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_17,axiom,
    ( collect_pname(Eq_x_0) = collect_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,axiom,
    ( collec1974731493e_bool(Eq_x_0) = collec1974731493e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,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_20,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_21,axiom,
    ( image_54689091_pname(Eq_x_0,Eq_x_1) = image_54689091_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_22,axiom,
    ( image_2131964411e_bool(Eq_x_0,Eq_x_1) = image_2131964411e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_23,axiom,
    ( 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_24,axiom,
    ( image_187965177_pname(Eq_x_0,Eq_x_1) = image_187965177_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,axiom,
    ( image_1705983821_pname(Eq_x_0,Eq_x_1) = image_1705983821_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_26,axiom,
    ( image_1619336331_pname(Eq_x_0,Eq_x_1) = image_1619336331_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,axiom,
    ( 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_28,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_29,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_30,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_31,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_32,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_33,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_34,axiom,
    ( hAPP_H1621176307_pname(Eq_x_0,Eq_x_1) = hAPP_H1621176307_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_35,axiom,
    ( hAPP_H78829294e_bool(Eq_x_0,Eq_x_1) = hAPP_H78829294e_bool(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,
    ( hAPP_H356885323e_bool(Eq_x_0,Eq_x_1) = hAPP_H356885323e_bool(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,
    ( 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_38,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_39,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_40,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_41,axiom,
    ( hAPP_f560369737_pname(Eq_x_0,Eq_x_1) = hAPP_f560369737_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_42,axiom,
    ( hAPP_f971112728l_bool(Eq_x_0,Eq_x_1) = hAPP_f971112728l_bool(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,
    ( 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_44,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_45,axiom,
    ( hAPP_f166538662l_bool(Eq_x_0,Eq_x_1) = hAPP_f166538662l_bool(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,
    ( 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_47,axiom,
    ( hAPP_f468958928l_bool(Eq_x_0,Eq_x_1) = hAPP_f468958928l_bool(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,
    ( hAPP_f595608956l_bool(Eq_x_0,Eq_x_1) = hAPP_f595608956l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_49,axiom,
    ( hAPP_f1022807134l_bool(Eq_x_0,Eq_x_1) = hAPP_f1022807134l_bool(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,
    ( hoare_1598289066_state(Eq_x_0) = hoare_1598289066_state(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_51,axiom,
    ( hAPP_f72706945l_bool(Eq_x_0,Eq_x_1) = hAPP_f72706945l_bool(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,
    ( insert1415133716_state(Eq_x_0,Eq_x_1) = insert1415133716_state(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_53,axiom,
    ( hAPP_pname_com(Eq_x_0,Eq_x_1) = hAPP_pname_com(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_c1126217667_state(Eq_x_0,Eq_x_1) = hAPP_c1126217667_state(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_p799580910on_com(Eq_x_0,Eq_x_1) = hAPP_p799580910on_com(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_option_com_com(Eq_x_0,Eq_x_1) = hAPP_option_com_com(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,
    ( cOMBC_1284144636l_bool(Eq_x_0) = cOMBC_1284144636l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_58,axiom,
    ( cOMBC_449066458l_bool(Eq_x_0) = cOMBC_449066458l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_59,axiom,
    ( collec1823980261e_bool(Eq_x_0) = collec1823980261e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_60,axiom,
    ( cOMBC_336095980l_bool(Eq_x_0) = cOMBC_336095980l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_61,axiom,
    ( hAPP_f1759205631l_bool(Eq_x_0,Eq_x_1) = hAPP_f1759205631l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_62,axiom,
    ( collec792590109l_bool(Eq_x_0) = collec792590109l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_63,axiom,
    ( cOMBC_747715418l_bool(Eq_x_0) = cOMBC_747715418l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_64,axiom,
    ( hAPP_f667366769l_bool(Eq_x_0,Eq_x_1) = hAPP_f667366769l_bool(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,
    ( collec256567069l_bool(Eq_x_0) = collec256567069l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_66,axiom,
    ( cOMBC_1691491604l_bool(Eq_x_0) = cOMBC_1691491604l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_67,axiom,
    ( hAPP_f585161855l_bool(Eq_x_0,Eq_x_1) = hAPP_f585161855l_bool(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,
    ( collec488126193l_bool(Eq_x_0) = collec488126193l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_69,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_70,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_71,axiom,
    ( collec1613912337l_bool(Eq_x_0) = collec1613912337l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_72,axiom,
    ( image_2003357581_state(Eq_x_0,Eq_x_1) = image_2003357581_state(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,
    ( image_677922117_state(Eq_x_0,Eq_x_1) = image_677922117_state(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,
    ( image_892968839_state(Eq_x_0,Eq_x_1) = image_892968839_state(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,
    ( image_18964633_state(Eq_x_0,Eq_x_1) = image_18964633_state(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,
    ( image_516545147_state(Eq_x_0,Eq_x_1) = image_516545147_state(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,
    ( image_1642285373l_bool(Eq_x_0,Eq_x_1) = image_1642285373l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_78,axiom,
    ( image_288317893l_bool(Eq_x_0,Eq_x_1) = image_288317893l_bool(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,
    ( image_70449425e_bool(Eq_x_0,Eq_x_1) = image_70449425e_bool(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,
    ( image_1210605179l_bool(Eq_x_0,Eq_x_1) = image_1210605179l_bool(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,
    ( image_1761575943l_bool(Eq_x_0,Eq_x_1) = image_1761575943l_bool(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,
    ( image_1828608335e_bool(Eq_x_0,Eq_x_1) = image_1828608335e_bool(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,
    ( insert1117693814l_bool(Eq_x_0,Eq_x_1) = insert1117693814l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_84,axiom,
    ( insert203537868l_bool(Eq_x_0,Eq_x_1) = insert203537868l_bool(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,
    ( insert1556680138e_bool(Eq_x_0,Eq_x_1) = insert1556680138e_bool(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,
    ( 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_87,axiom,
    ( collec307967673_state(Eq_x_0) = collec307967673_state(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_88,axiom,
    ( cOMBB_962198420_state(Eq_x_0,Eq_x_1) = cOMBB_962198420_state(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,
    ( cOMBS_458705923l_bool(Eq_x_0,Eq_x_1) = cOMBS_458705923l_bool(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,
    ( cOMBB_689948150l_bool(Eq_x_0,Eq_x_1) = cOMBB_689948150l_bool(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,
    ( cOMBS_811933079l_bool(Eq_x_0,Eq_x_1) = cOMBS_811933079l_bool(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,
    ( cOMBB_404111180l_bool(Eq_x_0,Eq_x_1) = cOMBB_404111180l_bool(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,
    ( cOMBS_1358309691l_bool(Eq_x_0,Eq_x_1) = cOMBS_1358309691l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_94,axiom,
    ( cOMBB_1585081418e_bool(Eq_x_0,Eq_x_1) = cOMBB_1585081418e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_95,axiom,
    ( cOMBS_2066081387l_bool(Eq_x_0,Eq_x_1) = cOMBS_2066081387l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_96,axiom,
    ( 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_97,axiom,
    ( cOMBK_367030522_pname(Eq_x_0) = cOMBK_367030522_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_98,axiom,
    ( cOMBK_168215364_state(Eq_x_0) = cOMBK_168215364_state(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_99,axiom,
    ( cOMBK_2035509764_state(Eq_x_0) = cOMBK_2035509764_state(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_100,axiom,
    ( cOMBK_1039769424_state(Eq_x_0) = cOMBK_1039769424_state(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_101,axiom,
    ( cOMBK_37193422_pname(Eq_x_0) = cOMBK_37193422_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_102,axiom,
    ( cOMBK_1706929794_pname(Eq_x_0) = cOMBK_1706929794_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_103,axiom,
    ( cOMBK_pname_pname(Eq_x_0) = cOMBK_pname_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_104,axiom,
    ( cOMBK_1503445380e_bool(Eq_x_0) = cOMBK_1503445380e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_105,axiom,
    ( cOMBK_701929478e_bool(Eq_x_0) = cOMBK_701929478e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_106,axiom,
    ( cOMBK_948730864e_bool(Eq_x_0) = cOMBK_948730864e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_107,axiom,
    ( cOMBK_1589414042e_bool(Eq_x_0) = cOMBK_1589414042e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_108,axiom,
    ( hAPP_H30606679l_bool(Eq_x_0,Eq_x_1) = hAPP_H30606679l_bool(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,
    ( 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_110,axiom,
    ( hAPP_f210337421l_bool(Eq_x_0,Eq_x_1) = hAPP_f210337421l_bool(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,
    ( some_com(Eq_x_0) = some_com(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_112,axiom,
    ( hAPP_f2138803836on_com(Eq_x_0,Eq_x_1) = hAPP_f2138803836on_com(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,
    ( hAPP_f2134636538on_com(Eq_x_0,Eq_x_1) = hAPP_f2134636538on_com(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,
    ( dom_fu1342267980ol_com(Eq_x_0) = dom_fu1342267980ol_com(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_115,axiom,
    ( hAPP_H1049623551e_bool(Eq_x_0,Eq_x_1) = hAPP_H1049623551e_bool(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,
    ( hAPP_p442853985e_bool(Eq_x_0,Eq_x_1) = hAPP_p442853985e_bool(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,
    ( hAPP_f888949707_state(Eq_x_0,Eq_x_1) = hAPP_f888949707_state(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_f1387463497_state(Eq_x_0,Eq_x_1) = hAPP_f1387463497_state(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_p1422361149_state(Eq_x_0,Eq_x_1) = hAPP_p1422361149_state(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,
    ( cOMBK_482404831l_bool(Eq_x_0) = cOMBK_482404831l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_121,axiom,
    ( cOMBK_129401207e_bool(Eq_x_0) = cOMBK_129401207e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_122,axiom,
    ( cOMBK_659609255_state(Eq_x_0) = cOMBK_659609255_state(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_123,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_124,axiom,
    ( cOMBC_654211620e_bool(Eq_x_0) = cOMBC_654211620e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_125,axiom,
    ( cOMBB_2144135922_state(Eq_x_0,Eq_x_1) = cOMBB_2144135922_state(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,
    ( cOMBB_1522210668e_bool(Eq_x_0,Eq_x_1) = cOMBB_1522210668e_bool(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,
    ( cOMBC_1058051404l_bool(Eq_x_0) = cOMBC_1058051404l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_128,axiom,
    ( cOMBC_1734175330l_bool(Eq_x_0) = cOMBC_1734175330l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_129,axiom,
    ( hAPP_f98417237e_bool(Eq_x_0,Eq_x_1) = hAPP_f98417237e_bool(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,
    ( cOMBC_1988546018l_bool(Eq_x_0) = cOMBC_1988546018l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_131,axiom,
    ( cOMBC_1114453604l_bool(Eq_x_0) = cOMBC_1114453604l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_132,axiom,
    ( hAPP_f1201187855l_bool(Eq_x_0,Eq_x_1) = hAPP_f1201187855l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_133,axiom,
    ( hAPP_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_134,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_135,axiom,
    ( cOMBB_923936821_pname(Eq_x_0,Eq_x_1) = cOMBB_923936821_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_136,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_137,axiom,
    ( cOMBB_699532858_pname(Eq_x_0,Eq_x_1) = cOMBB_699532858_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_138,axiom,
    ( hAPP_H1187982158l_bool(Eq_x_0,Eq_x_1) = hAPP_H1187982158l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_139,axiom,
    ( hAPP_f32027384l_bool(Eq_x_0,Eq_x_1) = hAPP_f32027384l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_140,axiom,
    ( hAPP_f637090980l_bool(Eq_x_0,Eq_x_1) = hAPP_f637090980l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_141,axiom,
    ( hAPP_f2143399574l_bool(Eq_x_0,Eq_x_1) = hAPP_f2143399574l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_142,axiom,
    ( sK1(Eq_x_0) = sK1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_143,axiom,
    ( sK2(Eq_x_0) = sK2(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_144,axiom,
    ( sK3(Eq_x_0) = sK3(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_145,axiom,
    ( sK4(Eq_x_0) = sK4(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_146,axiom,
    ( sK5(Eq_x_0) = sK5(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_147,axiom,
    ( sK6(Eq_x_0) = sK6(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_148,axiom,
    ( sK7(Eq_x_0) = sK7(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_149,axiom,
    ( sK8(Eq_x_0) = sK8(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_150,axiom,
    ( sK9(Eq_x_0) = sK9(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_151,axiom,
    ( sK10(Eq_x_0) = sK10(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_152,axiom,
    ( sK11(Eq_x_0) = sK11(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_153,axiom,
    ( sK12(Eq_x_0) = sK12(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_154,axiom,
    ( sK13(Eq_x_0) = sK13(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_155,axiom,
    ( sK14(Eq_x_0) = sK14(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_156,axiom,
    ( sK15(Eq_x_0) = sK15(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_157,axiom,
    ( sK16(Eq_x_0) = sK16(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_158,axiom,
    ( sK17(Eq_x_0) = sK17(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_159,axiom,
    ( sK18(Eq_x_0) = sK18(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_160,axiom,
    ( sK19(Eq_x_0) = sK19(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_161,axiom,
    ( sK20(Eq_x_0) = sK20(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_162,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_163,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_164,axiom,
    ( sK23(Eq_x_0,Eq_x_1) = sK23(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_165,axiom,
    ( 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_166,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_167,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_168,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_169,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_170,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_171,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_172,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_173,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_174,axiom,
    ( sK33(Eq_x_0) = sK33(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_175,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_176,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_177,axiom,
    ( sK36(Eq_x_0,Eq_x_1,Eq_x_2) = sK36(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_178,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_179,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_180,axiom,
    ( is_bool(Eq_y_0)
    | ~ is_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_181,axiom,
    ( is_pname(Eq_y_0)
    | ~ is_pname(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_182,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_183,axiom,
    ( sP0(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP0(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_184,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_185,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_186,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_187,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_188,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_189,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_190,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_191,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_192,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_193,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_194,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_195,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_196,axiom,
    ( sP13(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP13(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_197,axiom,
    ( sP14(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP14(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_198,axiom,
    ( sP15(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP15(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_199,axiom,
    ( sP16(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP16(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_200,axiom,
    ( sP17(Eq_y_0)
    | ~ sP17(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_201,axiom,
    ( sP18(Eq_y_0)
    | ~ sP18(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_202,axiom,
    ( sP19(Eq_y_0)
    | ~ sP19(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_203,axiom,
    ( sP20(Eq_y_0)
    | ~ sP20(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_204,axiom,
    ( sP21(Eq_y_0)
    | ~ sP21(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_205,axiom,
    ( sP22(Eq_y_0)
    | ~ sP22(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_206,axiom,
    ( sP23(Eq_y_0)
    | ~ sP23(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_207,axiom,
    ( sP24(Eq_y_0,Eq_y_1)
    | ~ sP24(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_208,axiom,
    ( sP25(Eq_y_0)
    | ~ sP25(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_209,axiom,
    ( sP26(Eq_y_0,Eq_y_1)
    | ~ sP26(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_210,axiom,
    ( sP27(Eq_y_0)
    | ~ sP27(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_211,axiom,
    ( sP28(Eq_y_0,Eq_y_1)
    | ~ sP28(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_212,axiom,
    ( sP29(Eq_y_0)
    | ~ sP29(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_213,axiom,
    ( sP30(Eq_y_0,Eq_y_1)
    | ~ sP30(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_214,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_215,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_216,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_217,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_218,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_219,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_220,axiom,
    ( sP37(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP37(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_221,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_222,axiom,
    ( sP39(Eq_y_0,Eq_y_1)
    | ~ sP39(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_223,axiom,
    ( sP40(Eq_y_0,Eq_y_1)
    | ~ sP40(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_224,axiom,
    ( sP41(Eq_y_0,Eq_y_1)
    | ~ sP41(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_225,axiom,
    ( sP42(Eq_y_0,Eq_y_1)
    | ~ sP42(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_226,axiom,
    ( sP43(Eq_y_0,Eq_y_1)
    | ~ sP43(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_227,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_228,axiom,
    ( sP45(Eq_y_0,Eq_y_1)
    | ~ sP45(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_229,axiom,
    ( sP46(Eq_y_0,Eq_y_1)
    | ~ sP46(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_230,axiom,
    ( sP47(Eq_y_0,Eq_y_1)
    | ~ sP47(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_231,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_232,axiom,
    ( sP49(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP49(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_233,axiom,
    ( sP50(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP50(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_234,axiom,
    ( sP51(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP51(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_235,axiom,
    ( sP52(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP52(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_236,axiom,
    ( sP53(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP53(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_237,axiom,
    ( sP54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP54(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_238,axiom,
    ( sP55(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP55(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_239,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_240,axiom,
    ( sP57(Eq_y_0)
    | ~ sP57(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_241,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_242,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_243,axiom,
    ( sP60(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP60(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_244,axiom,
    ( sP61(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP61(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_245,axiom,
    ( sP62(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP62(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_246,axiom,
    ( sP63(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP63(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_247,axiom,
    ( sP64(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP64(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_248,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_249,axiom,
    ( sP66(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP66(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_250,axiom,
    ( sP67(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP67(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_251,axiom,
    ( sP68(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP68(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_252,axiom,
    ( sP69(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP69(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_253,axiom,
    ( sP70(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_254,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_255,axiom,
    ( sP72(Eq_y_0,Eq_y_1)
    | ~ sP72(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_256,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_257,axiom,
    ( sP74(Eq_y_0,Eq_y_1)
    | ~ sP74(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW474+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03  This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04  % Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.37  % Computer : n015.cluster.edu
% 0.08/10.37  % Model    : x86_64 x86_64
% 0.08/10.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37  % Memory   : 8046.5625MB
% 0.08/10.37  % OS       : Linux 6.8.0-71-generic
% 0.08/10.37  % CPULimit : 300
% 0.08/10.37  % WCLimit  : 300
% 0.08/10.37  % DateTime : Sun Sep 20 05:45:15 UTC 2026
% 0.08/10.38  % CPUTime  : 
% 150.12/160.49  % SZS status Theorem for theBenchmark
% 150.12/160.49  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------