ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW473+6 : 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 : n020.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 09:08:00 AM UTC 2026

% Result   : Theorem 57.50s 57.93s
% Output   : Proof 57.66s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(tsy_c_COMBB_res,axiom,
    ! [X_b,X_c,X_a] : ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a)) = combb(X_b,X_c,X_a),
    file('theBenchmark.p',tsy_c_COMBB_res) ).

fof(tsy_c_COMBC_res,axiom,
    ! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c),
    file('theBenchmark.p',tsy_c_COMBC_res) ).

fof(tsy_c_COMBI_res,axiom,
    ! [X_a] : ti(fun(X_a,X_a),combi(X_a)) = combi(X_a),
    file('theBenchmark.p',tsy_c_COMBI_res) ).

fof(tsy_c_COMBK_res,axiom,
    ! [X_a,X_b] : ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b),
    file('theBenchmark.p',tsy_c_COMBK_res) ).

fof(tsy_c_COMBS_res,axiom,
    ! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c)) = combs(X_a,X_b,X_c),
    file('theBenchmark.p',tsy_c_COMBS_res) ).

fof(tsy_c_Com_Obody_res,axiom,
    ti(fun(pname,option(com)),body) = body,
    file('theBenchmark.p',tsy_c_Com_Obody_res) ).

fof(tsy_c_Finite__Set_Ocard_res,axiom,
    ! [X_c] : ti(fun(fun(X_c,bool),nat),finite_card(X_c)) = finite_card(X_c),
    file('theBenchmark.p',tsy_c_Finite__Set_Ocard_res) ).

fof(tsy_c_Finite__Set_Ocomp__fun__idem_res,axiom,
    ! [X_b,X_c] : ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite_comp_fun_idem(X_b,X_c)) = finite_comp_fun_idem(X_b,X_c),
    file('theBenchmark.p',tsy_c_Finite__Set_Ocomp__fun__idem_res) ).

fof(tsy_c_Finite__Set_Ofinite_res,axiom,
    ! [X_b] : ti(fun(fun(X_b,bool),bool),finite_finite(X_b)) = finite_finite(X_b),
    file('theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).

fof(tsy_c_Finite__Set_Ofolding__image__simple_res,axiom,
    ! [X_b,X_c] : ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite1357897459simple(X_b,X_c)) = finite1357897459simple(X_b,X_c),
    file('theBenchmark.p',tsy_c_Finite__Set_Ofolding__image__simple_res) ).

fof(tsy_c_Finite__Set_Ofolding__one_res,axiom,
    ! [X_b] : ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite_folding_one(X_b)) = finite_folding_one(X_b),
    file('theBenchmark.p',tsy_c_Finite__Set_Ofolding__one_res) ).

fof(tsy_c_Finite__Set_Ofolding__one__idem_res,axiom,
    ! [X_b] : ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite2073411215e_idem(X_b)) = finite2073411215e_idem(X_b),
    file('theBenchmark.p',tsy_c_Finite__Set_Ofolding__one__idem_res) ).

fof(tsy_c_Groups_Ominus__class_Ominus_res,axiom,
    ! [X_c] :
      ( minus(X_c)
     => ti(fun(X_c,fun(X_c,X_c)),minus_minus(X_c)) = minus_minus(X_c) ),
    file('theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_res) ).

fof(tsy_c_Groups_Oone__class_Oone_res,axiom,
    ! [X_b] :
      ( one(X_b)
     => ti(X_b,one_one(X_b)) = one_one(X_b) ),
    file('theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_0_res,axiom,
    ! [X_a] :
      ( monoid_add(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_1_res,axiom,
    ! [X_a] :
      ( ab_semigroup_add(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).

fof(tsy_c_Groups_Oplus__class_Oplus_2_res,axiom,
    ! [X_a] :
      ( cancel_semigroup_add(X_a)
     => ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a) ),
    file('theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_2_res) ).

fof(tsy_c_Groups_Ozero__class_Ozero_res,axiom,
    ! [X_b] :
      ( zero(X_b)
     => ti(X_b,zero_zero(X_b)) = zero_zero(X_b) ),
    file('theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_res) ).

fof(tsy_c_HOL_OThe_res,axiom,
    ! [X_b] : ti(fun(fun(X_b,bool),X_b),the(X_b)) = the(X_b),
    file('theBenchmark.p',tsy_c_HOL_OThe_res) ).

fof(tsy_c_HOL_Oundefined_res,axiom,
    ! [X_a] : ti(X_a,undefined(X_a)) = undefined(X_a),
    file('theBenchmark.p',tsy_c_HOL_Oundefined_res) ).

fof(tsy_c_Nat_OSuc_res,hypothesis,
    ti(fun(nat,nat),suc) = suc,
    file('theBenchmark.p',tsy_c_Nat_OSuc_res) ).

fof(tsy_c_Nat_Onat_Onat__case_res,axiom,
    ! [X_b] : ti(fun(X_b,fun(fun(nat,X_b),fun(nat,X_b))),nat_case(X_b)) = nat_case(X_b),
    file('theBenchmark.p',tsy_c_Nat_Onat_Onat__case_res) ).

fof(tsy_c_Option_Othe_res,axiom,
    ti(fun(option(com),com),the_1(com)) = the_1(com),
    file('theBenchmark.p',tsy_c_Option_Othe_res) ).

fof(tsy_c_Orderings_Obot__class_Obot_res,axiom,
    ! [X_c] :
      ( bot(X_c)
     => ti(X_c,bot_bot(X_c)) = bot_bot(X_c) ),
    file('theBenchmark.p',tsy_c_Orderings_Obot__class_Obot_res) ).

fof(tsy_c_Orderings_Oord__class_Oless_res,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a) ),
    file('theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_res) ).

fof(tsy_c_Orderings_Oord__class_Oless__eq_res,axiom,
    ! [X_c] :
      ( ord(X_c)
     => ti(fun(X_c,fun(X_c,bool)),ord_less_eq(X_c)) = ord_less_eq(X_c) ),
    file('theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).

fof(tsy_c_Partial__Function_Oflat__lub_res,axiom,
    ! [X_b] : ti(fun(X_b,fun(fun(X_b,bool),X_b)),partial_flat_lub(X_b)) = partial_flat_lub(X_b),
    file('theBenchmark.p',tsy_c_Partial__Function_Oflat__lub_res) ).

fof(tsy_c_Set_OCollect_res,axiom,
    ! [X_b] : ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b)) = collect(X_b),
    file('theBenchmark.p',tsy_c_Set_OCollect_res) ).

fof(tsy_c_Set_Oimage_res,axiom,
    ! [X_b,X_c] : ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool))),image(X_b,X_c)) = image(X_b,X_c),
    file('theBenchmark.p',tsy_c_Set_Oimage_res) ).

fof(tsy_c_Set_Oinsert_res,axiom,
    ! [X_b] : ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b)) = insert(X_b),
    file('theBenchmark.p',tsy_c_Set_Oinsert_res) ).

fof(tsy_c_Set_Othe__elem_res,axiom,
    ! [X_b] : ti(fun(fun(X_b,bool),X_b),the_elem(X_b)) = the_elem(X_b),
    file('theBenchmark.p',tsy_c_Set_Othe__elem_res) ).

fof(tsy_c_Sum__Type_OPlus_res,axiom,
    ! [X_b,X_c] : ti(fun(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool))),sum_Plus(X_b,X_c)) = sum_Plus(X_b,X_c),
    file('theBenchmark.p',tsy_c_Sum__Type_OPlus_res) ).

fof(tsy_c_fFalse_res,axiom,
    ti(bool,fFalse) = fFalse,
    file('theBenchmark.p',tsy_c_fFalse_res) ).

fof(tsy_c_fNot_res,axiom,
    ti(fun(bool,bool),fNot) = fNot,
    file('theBenchmark.p',tsy_c_fNot_res) ).

fof(tsy_c_fTrue_res,axiom,
    ti(bool,fTrue) = fTrue,
    file('theBenchmark.p',tsy_c_fTrue_res) ).

fof(tsy_c_fconj_res,axiom,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    file('theBenchmark.p',tsy_c_fconj_res) ).

fof(tsy_c_fdisj_res,axiom,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    file('theBenchmark.p',tsy_c_fdisj_res) ).

fof(tsy_c_fequal_res,axiom,
    ! [X_a] : ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a),
    file('theBenchmark.p',tsy_c_fequal_res) ).

fof(tsy_c_fimplies_res,axiom,
    ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
    file('theBenchmark.p',tsy_c_fimplies_res) ).

fof(tsy_c_hAPP_arg1,axiom,
    ! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1),
    file('theBenchmark.p',tsy_c_hAPP_arg1) ).

fof(tsy_c_hAPP_arg2,axiom,
    ! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
    file('theBenchmark.p',tsy_c_hAPP_arg2) ).

fof(tsy_c_hAPP_res,axiom,
    ! [X_c,X_a,B_1_1,B_2_1] : ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
    file('theBenchmark.p',tsy_c_hAPP_res) ).

fof(tsy_c_hBOOL_arg1,hypothesis,
    ! [B_1_1] :
      ( hBOOL(ti(bool,B_1_1))
    <=> hBOOL(B_1_1) ),
    file('theBenchmark.p',tsy_c_hBOOL_arg1) ).

fof(tsy_c_member_res,axiom,
    ! [X_b] : ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b),
    file('theBenchmark.p',tsy_c_member_res) ).

fof(tsy_v_G_res,hypothesis,
    ti(fun(x_a,bool),g) = g,
    file('theBenchmark.p',tsy_v_G_res) ).

fof(tsy_v_P_res,axiom,
    ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
    file('theBenchmark.p',tsy_v_P_res) ).

fof(tsy_v_U_res,hypothesis,
    ti(fun(pname,bool),u) = u,
    file('theBenchmark.p',tsy_v_U_res) ).

fof(tsy_v_mgt_res,axiom,
    ti(fun(com,x_a),mgt) = mgt,
    file('theBenchmark.p',tsy_v_mgt_res) ).

fof(tsy_v_mgt__call_res,hypothesis,
    ti(fun(pname,x_a),mgt_call) = mgt_call,
    file('theBenchmark.p',tsy_v_mgt__call_res) ).

fof(tsy_v_na_res,hypothesis,
    ti(nat,na) = na,
    file('theBenchmark.p',tsy_v_na_res) ).

fof(tsy_v_pn_res,hypothesis,
    ti(pname,pn) = pn,
    file('theBenchmark.p',tsy_v_pn_res) ).

fof(tsy_v_wt_res,axiom,
    ti(fun(com,bool),wt) = wt,
    file('theBenchmark.p',tsy_v_wt_res) ).

fof(fact_0_assms_I1_J,axiom,
    ! [Ts,G_1] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),Ts),G_1))
     => hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),Ts)) ),
    file('theBenchmark.p',fact_0_assms_I1_J) ).

fof(fact_1_finite__Collect__subsets,axiom,
    ! [X_b,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite(fun(X_b,bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,bool),bool),collect(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),combc(fun(X_b,bool),fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool))),A_3)))) ),
    file('theBenchmark.p',fact_1_finite__Collect__subsets) ).

fof(fact_2_finite__imageI,axiom,
    ! [X_c,X_b,H,F_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_2))
     => hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),H),F_2))) ),
    file('theBenchmark.p',fact_2_finite__imageI) ).

fof(fact_3_finite_OinsertI,axiom,
    ! [X_b,A_2,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))) ),
    file('theBenchmark.p',fact_3_finite_OinsertI) ).

fof(fact_4_card__image__le,axiom,
    ! [X_c,X_b,F,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_c,bool),nat,finite_card(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) ),
    file('theBenchmark.p',fact_4_card__image__le) ).

fof(fact_5_card__mono,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))) ) ),
    file('theBenchmark.p',fact_5_card__mono) ).

fof(fact_6_card__seteq,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))
         => ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) ) ) ),
    file('theBenchmark.p',fact_6_card__seteq) ).

fof(fact_7_card__insert__le,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)))) ),
    file('theBenchmark.p',fact_7_card__insert__le) ).

fof(fact_8_card__insert__if,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
         => hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)) )
        & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
         => hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) ) ) ),
    file('theBenchmark.p',fact_8_card__insert__if) ).

fof(fact_9_card__insert__disjoint,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
       => hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)) ) ),
    file('theBenchmark.p',fact_9_card__insert__disjoint) ).

fof(fact_10_finite__Collect__conjI,axiom,
    ! [X_b,Q_1,Pa] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1)))
        | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) )
     => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Q_1)))) ),
    file('theBenchmark.p',fact_10_finite__Collect__conjI) ).

fof(fact_11_Suc__diff__le,axiom,
    ! [N,M] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) ),
    file('theBenchmark.p',fact_11_Suc__diff__le) ).

fof(fact_12_finite__Collect__le__nat,axiom,
    ! [K_2] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),K_2)))),
    file('theBenchmark.p',fact_12_finite__Collect__le__nat) ).

fof(fact_13_card__Collect__le__nat,axiom,
    ! [Na] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),Na))) = hAPP(nat,nat,suc,Na),
    file('theBenchmark.p',fact_13_card__Collect__le__nat) ).

fof(fact_14_finite__code,axiom,
    ! [X_b] :
      ( finite_finite_1(X_b)
     => ! [A_3] : hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    file('theBenchmark.p',fact_14_finite__code) ).

fof(fact_15_finite,axiom,
    ! [X_b] :
      ( finite_finite_1(X_b)
     => ! [A_3] : hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    file('theBenchmark.p',fact_15_finite) ).

fof(fact_16_Suc__inject,axiom,
    ! [X,Y] :
      ( hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y)
     => X = Y ),
    file('theBenchmark.p',fact_16_Suc__inject) ).

fof(fact_17_nat_Oinject,axiom,
    ! [Nat_2,Nat_3] :
      ( hAPP(nat,nat,suc,Nat_2) = hAPP(nat,nat,suc,Nat_3)
    <=> Nat_2 = Nat_3 ),
    file('theBenchmark.p',fact_17_nat_Oinject) ).

fof(fact_18_Suc__n__not__n,axiom,
    ! [N] : hAPP(nat,nat,suc,N) != N,
    file('theBenchmark.p',fact_18_Suc__n__not__n) ).

fof(fact_19_n__not__Suc__n,axiom,
    ! [N] : N != hAPP(nat,nat,suc,N),
    file('theBenchmark.p',fact_19_n__not__Suc__n) ).

fof(fact_20_le__antisym,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M))
       => M = N ) ),
    file('theBenchmark.p',fact_20_le__antisym) ).

fof(fact_21_le__trans,axiom,
    ! [K,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),K))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K)) ) ),
    file('theBenchmark.p',fact_21_le__trans) ).

fof(fact_22_eq__imp__le,axiom,
    ! [M,N] :
      ( M = N
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    file('theBenchmark.p',fact_22_eq__imp__le) ).

fof(fact_23_nat__le__linear,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    file('theBenchmark.p',fact_23_nat__le__linear) ).

fof(fact_24_le__refl,axiom,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N)),
    file('theBenchmark.p',fact_24_le__refl) ).

fof(fact_25_diff__commute,axiom,
    ! [I,J_2,K] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_2)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),K)),J_2),
    file('theBenchmark.p',fact_25_diff__commute) ).

fof(fact_26_finite__Collect__disjI,axiom,
    ! [X_b,Pa,Q_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_1))))
    <=> ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1)))
        & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) ) ),
    file('theBenchmark.p',fact_26_finite__Collect__disjI) ).

fof(fact_27_finite__insert,axiom,
    ! [X_b,A_2,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)))
    <=> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    file('theBenchmark.p',fact_27_finite__insert) ).

fof(fact_28_finite__subset,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2))
       => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ) ),
    file('theBenchmark.p',fact_28_finite__subset) ).

fof(fact_29_rev__finite__subset,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
       => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ) ),
    file('theBenchmark.p',fact_29_rev__finite__subset) ).

fof(fact_30_Suc__leD,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    file('theBenchmark.p',fact_30_Suc__leD) ).

fof(fact_31_le__SucE,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
       => M = hAPP(nat,nat,suc,N) ) ),
    file('theBenchmark.p',fact_31_le__SucE) ).

fof(fact_32_le__SucI,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))) ),
    file('theBenchmark.p',fact_32_le__SucI) ).

fof(fact_33_Suc__le__mono,axiom,
    ! [Na,M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_1)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_1)) ),
    file('theBenchmark.p',fact_33_Suc__le__mono) ).

fof(fact_34_le__Suc__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,Na)))
    <=> ( M_1 = hAPP(nat,nat,suc,Na)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ) ),
    file('theBenchmark.p',fact_34_le__Suc__eq) ).

fof(fact_35_not__less__eq__eq,axiom,
    ! [M_1,Na] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_1)) ),
    file('theBenchmark.p',fact_35_not__less__eq__eq) ).

fof(fact_36_Suc__n__not__le__n,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),N)),
    file('theBenchmark.p',fact_36_Suc__n__not__le__n) ).

fof(fact_37_Suc__diff__diff,axiom,
    ! [M,N,K] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,suc,K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),K),
    file('theBenchmark.p',fact_37_Suc__diff__diff) ).

fof(fact_38_diff__Suc__Suc,axiom,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N),
    file('theBenchmark.p',fact_38_diff__Suc__Suc) ).

fof(fact_39_le__diff__iff,axiom,
    ! [Na,K_2,M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),M_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K_2)))
        <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ) ) ),
    file('theBenchmark.p',fact_39_le__diff__iff) ).

fof(fact_40_Nat_Odiff__diff__eq,axiom,
    ! [N,K,M] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N))
       => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) ) ),
    file('theBenchmark.p',fact_40_Nat_Odiff__diff__eq) ).

fof(fact_41_eq__diff__iff,axiom,
    ! [Na,K_2,M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),M_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na))
       => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K_2)
        <=> M_1 = Na ) ) ),
    file('theBenchmark.p',fact_41_eq__diff__iff) ).

fof(fact_42_diff__diff__cancel,axiom,
    ! [I,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),N))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),I)) = I ),
    file('theBenchmark.p',fact_42_diff__diff__cancel) ).

fof(fact_43_diff__le__mono,axiom,
    ! [L,M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L))) ),
    file('theBenchmark.p',fact_43_diff__le__mono) ).

fof(fact_44_diff__le__mono2,axiom,
    ! [L,M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))) ),
    file('theBenchmark.p',fact_44_diff__le__mono2) ).

fof(fact_45_diff__le__self,axiom,
    ! [M,N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M)),
    file('theBenchmark.p',fact_45_diff__le__self) ).

fof(fact_46_finite__surj,axiom,
    ! [X_c,X_b,B_2,F,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),B_2),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
       => hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2)) ) ),
    file('theBenchmark.p',fact_46_finite__surj) ).

fof(fact_47_finite__subset__image,axiom,
    ! [X_c,X_b,F,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))
       => ? [C_3] :
            ( ti(fun(X_b,bool),B_2) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),C_3)
            & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),C_3))
            & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),C_3),A_3)) ) ) ),
    file('theBenchmark.p',fact_47_finite__subset__image) ).

fof(fact_48_lift__Suc__mono__le,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [Na,N_3,F] :
          ( ! [N_2] : hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,N_2)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_2))))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_3))
           => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3))) ) ) ),
    file('theBenchmark.p',fact_48_lift__Suc__mono__le) ).

fof(fact_49_pigeonhole__infinite,axiom,
    ! [X_c,X_b,F,A_3] :
      ( ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
       => ? [X_2] :
            ( ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_b),fequal(X_c)),F)),hAPP(X_b,X_c,F,X_2))))))
            & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) ) ) ),
    file('theBenchmark.p',fact_49_pigeonhole__infinite) ).

fof(fact_50_image__eqI,axiom,
    ! [X_b,X_c,A_3,B,F,X_1] :
      ( ti(X_b,B) = hAPP(X_c,X_b,F,X_1)
     => ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) ) ),
    file('theBenchmark.p',fact_50_image__eqI) ).

fof(fact_51_equalityI,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))
       => ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) ) ),
    file('theBenchmark.p',fact_51_equalityI) ).

fof(fact_52_subsetD,axiom,
    ! [X_b,C_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)) ) ),
    file('theBenchmark.p',fact_52_subsetD) ).

fof(fact_53_insertCI,axiom,
    ! [X_b,B,A_2,B_2] :
      ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2))
       => ti(X_b,A_2) = ti(X_b,B) )
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),B_2))) ),
    file('theBenchmark.p',fact_53_insertCI) ).

fof(fact_54_insertE,axiom,
    ! [X_b,A_2,B,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),A_3)))
     => ( ti(X_b,A_2) != ti(X_b,B)
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) ) ),
    file('theBenchmark.p',fact_54_insertE) ).

fof(fact_55_zero__induct__lemma,axiom,
    ! [I_1,Pa,K_2] :
      ( hBOOL(hAPP(nat,bool,Pa,K_2))
     => ( ! [N_2] :
            ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_2)))
           => hBOOL(hAPP(nat,bool,Pa,N_2)) )
       => hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_2),I_1))) ) ),
    file('theBenchmark.p',fact_55_zero__induct__lemma) ).

fof(fact_56_Suc__le__D,axiom,
    ! [N,M_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M_3))
     => ? [M_2] : M_3 = hAPP(nat,nat,suc,M_2) ),
    file('theBenchmark.p',fact_56_Suc__le__D) ).

fof(fact_57_insertI1,axiom,
    ! [X_b,A_2,B_2] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2))),
    file('theBenchmark.p',fact_57_insertI1) ).

fof(fact_58_insert__compr,axiom,
    ! [X_b,A_2,B_2] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2))),
    file('theBenchmark.p',fact_58_insert__compr) ).

fof(fact_59_insert__Collect,axiom,
    ! [X_b,A_2,Pa] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fimplies),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)))),Pa)),
    file('theBenchmark.p',fact_59_insert__Collect) ).

fof(fact_60_insert__absorb2,axiom,
    ! [X_b,X_1,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3),
    file('theBenchmark.p',fact_60_insert__absorb2) ).

fof(fact_61_insert__commute,axiom,
    ! [X_b,X_1,Y_1,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),
    file('theBenchmark.p',fact_61_insert__commute) ).

fof(fact_62_insert__iff,axiom,
    ! [X_b,A_2,B,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),A_3)))
    <=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))
        | ti(X_b,A_2) = ti(X_b,B) ) ),
    file('theBenchmark.p',fact_62_insert__iff) ).

fof(fact_63_insert__code,axiom,
    ! [X_b,Y_1,A_3,X_1] :
      ( hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),A_3),X_1))
    <=> ( hBOOL(hAPP(X_b,bool,A_3,X_1))
        | ti(X_b,Y_1) = ti(X_b,X_1) ) ),
    file('theBenchmark.p',fact_63_insert__code) ).

fof(fact_64_insert__ident,axiom,
    ! [X_b,B_2,X_1,A_3] :
      ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
     => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
       => ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2)
        <=> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) ) ) ),
    file('theBenchmark.p',fact_64_insert__ident) ).

fof(fact_65_insertI2,axiom,
    ! [X_b,B,A_2,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2))
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),B_2))) ),
    file('theBenchmark.p',fact_65_insertI2) ).

fof(fact_66_insert__absorb,axiom,
    ! [X_b,A_2,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))
     => hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) = ti(fun(X_b,bool),A_3) ),
    file('theBenchmark.p',fact_66_insert__absorb) ).

fof(fact_67_subset__refl,axiom,
    ! [X_b,A_3] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),A_3)),
    file('theBenchmark.p',fact_67_subset__refl) ).

fof(fact_68_set__eq__subset,axiom,
    ! [X_b,A_3,B_2] :
      ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)
    <=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))
        & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ),
    file('theBenchmark.p',fact_68_set__eq__subset) ).

fof(fact_69_equalityD1,axiom,
    ! [X_b,A_3,B_2] :
      ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    file('theBenchmark.p',fact_69_equalityD1) ).

fof(fact_70_equalityD2,axiom,
    ! [X_b,A_3,B_2] :
      ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) ),
    file('theBenchmark.p',fact_70_equalityD2) ).

fof(fact_71_in__mono,axiom,
    ! [X_b,X_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) ) ),
    file('theBenchmark.p',fact_71_in__mono) ).

fof(fact_72_set__rev__mp,axiom,
    ! [X_b,B_2,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) ) ),
    file('theBenchmark.p',fact_72_set__rev__mp) ).

fof(fact_73_set__mp,axiom,
    ! [X_b,X_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) ) ),
    file('theBenchmark.p',fact_73_set__mp) ).

fof(fact_74_ext,axiom,
    ! [X_b,X_c,F,G] :
      ( ! [X_2] : hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,X_2)
     => ti(fun(X_b,X_c),F) = ti(fun(X_b,X_c),G) ),
    file('theBenchmark.p',fact_74_ext) ).

fof(fact_75_mem__def,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
    <=> hBOOL(hAPP(X_b,bool,A_3,X_1)) ),
    file('theBenchmark.p',fact_75_mem__def) ).

fof(fact_76_Collect__def,axiom,
    ! [X_b,Pa] : hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa),
    file('theBenchmark.p',fact_76_Collect__def) ).

fof(fact_77_subset__trans,axiom,
    ! [X_b,C_2,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),C_2))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_2)) ) ),
    file('theBenchmark.p',fact_77_subset__trans) ).

fof(fact_78_equalityE,axiom,
    ! [X_b,A_3,B_2] :
      ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)
     => ~ ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
         => ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3)) ) ),
    file('theBenchmark.p',fact_78_equalityE) ).

fof(fact_79_image__iff,axiom,
    ! [X_b,X_c,Z_1,F,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))
    <=> ? [X_2] :
          ( ti(X_b,Z_1) = hAPP(X_c,X_b,F,X_2)
          & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) ) ),
    file('theBenchmark.p',fact_79_image__iff) ).

fof(fact_80_imageI,axiom,
    ! [X_c,X_b,F,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
     => hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) ),
    file('theBenchmark.p',fact_80_imageI) ).

fof(fact_81_rev__image__eqI,axiom,
    ! [X_c,X_b,B,F,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
     => ( ti(X_c,B) = hAPP(X_b,X_c,F,X_1)
       => hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) ) ),
    file('theBenchmark.p',fact_81_rev__image__eqI) ).

fof(fact_82_insert__compr__raw,axiom,
    ! [X_b,X_2,Xa] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),Xa) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Xa))),
    file('theBenchmark.p',fact_82_insert__compr__raw) ).

fof(fact_83_image__image,axiom,
    ! [X_c,X_b,X_d,F,G,A_3] : hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_d,bool),fun(X_c,bool),hAPP(fun(X_d,X_c),fun(fun(X_d,bool),fun(X_c,bool)),image(X_d,X_c),G),A_3)) = hAPP(fun(X_d,bool),fun(X_b,bool),hAPP(fun(X_d,X_b),fun(fun(X_d,bool),fun(X_b,bool)),image(X_d,X_b),hAPP(fun(X_d,X_c),fun(X_d,X_b),hAPP(fun(X_c,X_b),fun(fun(X_d,X_c),fun(X_d,X_b)),combb(X_c,X_b,X_d),F),G)),A_3),
    file('theBenchmark.p',fact_83_image__image) ).

fof(fact_84_image__ident,axiom,
    ! [X_b,Y_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),combi(X_b)),Y_3) = ti(fun(X_b,bool),Y_3),
    file('theBenchmark.p',fact_84_image__ident) ).

fof(fact_85_subset__insertI,axiom,
    ! [X_b,B_2,A_2] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2))),
    file('theBenchmark.p',fact_85_subset__insertI) ).

fof(fact_86_insert__subset,axiom,
    ! [X_b,X_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
    <=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
        & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) ) ),
    file('theBenchmark.p',fact_86_insert__subset) ).

fof(fact_87_subset__insert,axiom,
    ! [X_b,B_2,X_1,A_3] :
      ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2)))
      <=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ),
    file('theBenchmark.p',fact_87_subset__insert) ).

fof(fact_88_subset__insertI2,axiom,
    ! [X_b,B,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),B_2))) ),
    file('theBenchmark.p',fact_88_subset__insertI2) ).

fof(fact_89_insert__mono,axiom,
    ! [X_b,A_2,C_2,D_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_2),D_2))
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),C_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),D_2))) ),
    file('theBenchmark.p',fact_89_insert__mono) ).

fof(fact_90_image__insert,axiom,
    ! [X_c,X_b,F,A_2,B_2] : hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),hAPP(X_c,X_b,F,A_2)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_2)),
    file('theBenchmark.p',fact_90_image__insert) ).

fof(fact_91_insert__image,axiom,
    ! [X_c,X_b,F,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
     => hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3) ),
    file('theBenchmark.p',fact_91_insert__image) ).

fof(fact_92_subset__image__iff,axiom,
    ! [X_b,X_c,B_2,F,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))
    <=> ? [AA] :
          ( ti(fun(X_b,bool),B_2) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),AA)
          & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),AA),A_3)) ) ),
    file('theBenchmark.p',fact_92_subset__image__iff) ).

fof(fact_93_image__mono,axiom,
    ! [X_c,X_b,F,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
     => hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),B_2))) ),
    file('theBenchmark.p',fact_93_image__mono) ).

fof(fact_94_imageE,axiom,
    ! [X_b,X_c,B,F,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))
     => ~ ! [X_2] :
            ( ti(X_b,B) = hAPP(X_c,X_b,F,X_2)
           => ~ hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) ) ),
    file('theBenchmark.p',fact_94_imageE) ).

fof(fact_95_subsetI,axiom,
    ! [X_b,B_2,A_3] :
      ( ! [X_2] :
          ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) )
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    file('theBenchmark.p',fact_95_subsetI) ).

fof(fact_96_image__subsetI,axiom,
    ! [X_c,X_b,F,B_2,A_3] :
      ( ! [X_2] :
          ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))
         => hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_2)),B_2)) )
     => hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),B_2)) ),
    file('theBenchmark.p',fact_96_image__subsetI) ).

fof(fact_97_order__refl,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X)) ),
    file('theBenchmark.p',fact_97_order__refl) ).

fof(fact_98_finite__nat__set__iff__bounded__le,axiom,
    ! [N_1] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_1))
    <=> ? [M_2] :
        ! [X_2] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_1))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M_2)) ) ),
    file('theBenchmark.p',fact_98_finite__nat__set__iff__bounded__le) ).

fof(fact_99_assms_I3_J,axiom,
    ! [G_1,C_1] :
      ( hBOOL(hAPP(com,bool,wt,C_1))
     => ( ! [X_2] :
            ( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X_2),u))
           => hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X_2)),bot_bot(fun(x_a,bool))))) )
       => hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,C_1)),bot_bot(fun(x_a,bool))))) ) ),
    file('theBenchmark.p',fact_99_assms_I3_J) ).

fof(fact_100_le__fun__def,axiom,
    ! [X_b,X_c] :
      ( ord(X_c)
     => ! [F,G] :
          ( hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G))
        <=> ! [X_2] : hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))) ) ),
    file('theBenchmark.p',fact_100_le__fun__def) ).

fof(fact_101_le__funD,axiom,
    ! [X_b,X_c] :
      ( ord(X_c)
     => ! [X_1,F,G] :
          ( hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G))
         => hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))) ) ),
    file('theBenchmark.p',fact_101_le__funD) ).

fof(fact_102_le__funE,axiom,
    ! [X_b,X_c] :
      ( ord(X_c)
     => ! [X_1,F,G] :
          ( hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G))
         => hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))) ) ),
    file('theBenchmark.p',fact_102_le__funE) ).

fof(fact_103_emptyE,axiom,
    ! [X_b,A_2] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),bot_bot(fun(X_b,bool)))),
    file('theBenchmark.p',fact_103_emptyE) ).

fof(fact_104_finite_OemptyI,axiom,
    ! [X_b] : hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),bot_bot(fun(X_b,bool)))),
    file('theBenchmark.p',fact_104_finite_OemptyI) ).

fof(fact_105_empty__subsetI,axiom,
    ! [X_b,A_3] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3)),
    file('theBenchmark.p',fact_105_empty__subsetI) ).

fof(fact_106_equals0D,axiom,
    ! [X_b,A_2,A_3] :
      ( ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool))
     => ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) ),
    file('theBenchmark.p',fact_106_equals0D) ).

fof(fact_107_Collect__empty__eq,axiom,
    ! [X_b,Pa] :
      ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = bot_bot(fun(X_b,bool))
    <=> ! [X_2] : ~ hBOOL(hAPP(X_b,bool,Pa,X_2)) ),
    file('theBenchmark.p',fact_107_Collect__empty__eq) ).

fof(fact_108_empty__iff,axiom,
    ! [X_b,C_1] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),bot_bot(fun(X_b,bool)))),
    file('theBenchmark.p',fact_108_empty__iff) ).

fof(fact_109_empty__Collect__eq,axiom,
    ! [X_b,Pa] :
      ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)
    <=> ! [X_2] : ~ hBOOL(hAPP(X_b,bool,Pa,X_2)) ),
    file('theBenchmark.p',fact_109_empty__Collect__eq) ).

fof(fact_110_ex__in__conv,axiom,
    ! [X_b,A_3] :
      ( ? [X_2] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))
    <=> ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) ),
    file('theBenchmark.p',fact_110_ex__in__conv) ).

fof(fact_111_all__not__in__conv,axiom,
    ! [X_b,A_3] :
      ( ! [X_2] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))
    <=> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) ),
    file('theBenchmark.p',fact_111_all__not__in__conv) ).

fof(fact_112_empty__def,axiom,
    ! [X_b] : bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)),
    file('theBenchmark.p',fact_112_empty__def) ).

fof(fact_113_bot__fun__def,axiom,
    ! [X_b,X_c] :
      ( bot(X_c)
     => ! [X_2] : hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c) ),
    file('theBenchmark.p',fact_113_bot__fun__def) ).

fof(fact_114_bot__apply,axiom,
    ! [X_c,X_b] :
      ( bot(X_b)
     => ! [X_1] : hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_1) = bot_bot(X_b) ),
    file('theBenchmark.p',fact_114_bot__apply) ).

fof(fact_115_le__bot,axiom,
    ! [X_a] :
      ( bot(X_a)
     => ! [A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),bot_bot(X_a)))
         => ti(X_a,A_1) = bot_bot(X_a) ) ),
    file('theBenchmark.p',fact_115_le__bot) ).

fof(fact_116_bot__unique,axiom,
    ! [X_b] :
      ( bot(X_b)
     => ! [A_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),bot_bot(X_b)))
        <=> ti(X_b,A_2) = bot_bot(X_b) ) ),
    file('theBenchmark.p',fact_116_bot__unique) ).

fof(fact_117_bot__least,axiom,
    ! [X_a] :
      ( bot(X_a)
     => ! [A_1] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),bot_bot(X_a)),A_1)) ),
    file('theBenchmark.p',fact_117_bot__least) ).

fof(fact_118_singleton__inject,axiom,
    ! [X_b,A_2,B] :
      ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool)))
     => ti(X_b,A_2) = ti(X_b,B) ),
    file('theBenchmark.p',fact_118_singleton__inject) ).

fof(fact_119_singletonE,axiom,
    ! [X_b,B,A_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))
     => ti(X_b,B) = ti(X_b,A_2) ),
    file('theBenchmark.p',fact_119_singletonE) ).

fof(fact_120_doubleton__eq__iff,axiom,
    ! [X_b,A_2,B,C_1,D_1] :
      ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_1),bot_bot(fun(X_b,bool))))
    <=> ( ( ti(X_b,B) = ti(X_b,C_1)
          & ti(X_b,A_2) = ti(X_b,D_1) )
        | ( ti(X_b,B) = ti(X_b,D_1)
          & ti(X_b,A_2) = ti(X_b,C_1) ) ) ),
    file('theBenchmark.p',fact_120_doubleton__eq__iff) ).

fof(fact_121_singleton__iff,axiom,
    ! [X_b,B,A_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))
    <=> ti(X_b,B) = ti(X_b,A_2) ),
    file('theBenchmark.p',fact_121_singleton__iff) ).

fof(fact_122_insert__not__empty,axiom,
    ! [X_b,A_2,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) != bot_bot(fun(X_b,bool)),
    file('theBenchmark.p',fact_122_insert__not__empty) ).

fof(fact_123_empty__not__insert,axiom,
    ! [X_b,A_2,A_3] : bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3),
    file('theBenchmark.p',fact_123_empty__not__insert) ).

fof(fact_124_subset__empty,axiom,
    ! [X_b,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))))
    <=> ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) ),
    file('theBenchmark.p',fact_124_subset__empty) ).

fof(fact_125_image__is__empty,axiom,
    ! [X_c,X_b,F,A_3] :
      ( hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3) = bot_bot(fun(X_b,bool))
    <=> ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool)) ),
    file('theBenchmark.p',fact_125_image__is__empty) ).

fof(fact_126_image__empty,axiom,
    ! [X_c,X_b,F] : hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),bot_bot(fun(X_c,bool))) = bot_bot(fun(X_b,bool)),
    file('theBenchmark.p',fact_126_image__empty) ).

fof(fact_127_empty__is__image,axiom,
    ! [X_b,X_c,F,A_3] :
      ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)
    <=> ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool)) ),
    file('theBenchmark.p',fact_127_empty__is__image) ).

fof(fact_128_Collect__conv__if,axiom,
    ! [X_b,Pa,A_2] :
      ( ( ~ hBOOL(hAPP(X_b,bool,Pa,A_2))
       => hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = bot_bot(fun(X_b,bool)) )
      & ( hBOOL(hAPP(X_b,bool,Pa,A_2))
       => hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) ) ),
    file('theBenchmark.p',fact_128_Collect__conv__if) ).

fof(fact_129_Collect__conv__if2,axiom,
    ! [X_b,Pa,A_2] :
      ( ( ~ hBOOL(hAPP(X_b,bool,Pa,A_2))
       => hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa)) = bot_bot(fun(X_b,bool)) )
      & ( hBOOL(hAPP(X_b,bool,Pa,A_2))
       => hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) ) ),
    file('theBenchmark.p',fact_129_Collect__conv__if2) ).

fof(fact_130_singleton__conv,axiom,
    ! [X_b,A_2] : hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))),
    file('theBenchmark.p',fact_130_singleton__conv) ).

fof(fact_131_singleton__conv2,axiom,
    ! [X_b,A_2] : hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))),
    file('theBenchmark.p',fact_131_singleton__conv2) ).

fof(fact_132_subset__singletonD,axiom,
    ! [X_b,A_3,X_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))
     => ( ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))
        | ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) ) ),
    file('theBenchmark.p',fact_132_subset__singletonD) ).

fof(fact_133_image__constant,axiom,
    ! [X_c,X_b,C_1,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
     => hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C_1),bot_bot(fun(X_c,bool))) ),
    file('theBenchmark.p',fact_133_image__constant) ).

fof(fact_134_image__constant__conv,axiom,
    ! [X_c,X_b,C_1,A_3] :
      ( ( ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool))
       => hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C_1),bot_bot(fun(X_c,bool))) )
      & ( ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool))
       => hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = bot_bot(fun(X_c,bool)) ) ),
    file('theBenchmark.p',fact_134_image__constant__conv) ).

fof(fact_135_linorder__le__cases,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) ) ),
    file('theBenchmark.p',fact_135_linorder__le__cases) ).

fof(fact_136_xt1_I6_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X)) ) ) ),
    file('theBenchmark.p',fact_136_xt1_I6_J) ).

fof(fact_137_xt1_I5_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
           => ti(X_a,X) = ti(X_a,Y) ) ) ),
    file('theBenchmark.p',fact_137_xt1_I5_J) ).

fof(fact_138_order__trans,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z)) ) ) ),
    file('theBenchmark.p',fact_138_order__trans) ).

fof(fact_139_order__antisym,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
           => ti(X_a,X) = ti(X_a,Y) ) ) ),
    file('theBenchmark.p',fact_139_order__antisym) ).

fof(fact_140_xt1_I4_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [C,B_1,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_1))
         => ( ti(X_a,B_1) = ti(X_a,C)
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1)) ) ) ),
    file('theBenchmark.p',fact_140_xt1_I4_J) ).

fof(fact_141_ord__le__eq__trans,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1))
         => ( B_1 = C
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) ) ) ),
    file('theBenchmark.p',fact_141_ord__le__eq__trans) ).

fof(fact_142_xt1_I3_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [C,A_1,B_1] :
          ( ti(X_a,A_1) = ti(X_a,B_1)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1)) ) ) ),
    file('theBenchmark.p',fact_142_xt1_I3_J) ).

fof(fact_143_ord__eq__le__trans,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [C,A_1,B_1] :
          ( A_1 = B_1
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) ) ) ),
    file('theBenchmark.p',fact_143_ord__eq__le__trans) ).

fof(fact_144_order__antisym__conv,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [Y_1,X_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1))
          <=> ti(X_b,X_1) = ti(X_b,Y_1) ) ) ),
    file('theBenchmark.p',fact_144_order__antisym__conv) ).

fof(fact_145_order__eq__refl,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X,Y] :
          ( X = Y
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_145_order__eq__refl) ).

fof(fact_146_order__eq__iff,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [X_1,Y_1] :
          ( ti(X_b,X_1) = ti(X_b,Y_1)
        <=> ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1))
            & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) ) ) ),
    file('theBenchmark.p',fact_146_order__eq__iff) ).

fof(fact_147_linorder__linear,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_147_linorder__linear) ).

fof(fact_148_finite__subset__induct,axiom,
    ! [X_b,Pa,A_3,F_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),F_2),A_3))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))
         => ( ! [A_5,F_3] :
                ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_3))
               => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_3))
                 => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),F_3))
                   => ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3))
                     => hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),F_3))) ) ) ) )
           => hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)) ) ) ) ),
    file('theBenchmark.p',fact_148_finite__subset__induct) ).

fof(fact_149_assms_I2_J,axiom,
    ! [Pn,G_1] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,Pn)),G_1)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,Pn)))),bot_bot(fun(x_a,bool)))))
     => hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,Pn)),bot_bot(fun(x_a,bool))))) ),
    file('theBenchmark.p',fact_149_assms_I2_J) ).

fof(fact_150_finite__induct,axiom,
    ! [X_b,Pa,F_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))
       => ( ! [X_2,F_3] :
              ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_3))
             => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3))
               => ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3))
                 => hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_3))) ) ) )
         => hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)) ) ) ),
    file('theBenchmark.p',fact_150_finite__induct) ).

fof(fact_151_finite_Osimps,axiom,
    ! [X_b,A_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2))
    <=> ( ? [A_4,A_5] :
            ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_4))
            & ti(fun(X_b,bool),A_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),A_4) )
        | ti(fun(X_b,bool),A_2) = bot_bot(fun(X_b,bool)) ) ),
    file('theBenchmark.p',fact_151_finite_Osimps) ).

fof(fact_152_finite__less__ub,axiom,
    ! [U,F] :
      ( ! [N_2] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),hAPP(nat,nat,F,N_2)))
     => hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U)))) ),
    file('theBenchmark.p',fact_152_finite__less__ub) ).

fof(fact_153_the__elem__eq,axiom,
    ! [X_b,X_1] : hAPP(fun(X_b,bool),X_b,the_elem(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1),
    file('theBenchmark.p',fact_153_the__elem__eq) ).

fof(fact_154_nonempty__iff,axiom,
    ! [X_b,A_3] :
      ( ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool))
    <=> ? [X_2,B_4] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_4))
          & ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B_4) ) ),
    file('theBenchmark.p',fact_154_nonempty__iff) ).

fof(fact_155_le__funI,axiom,
    ! [X_b,X_c] :
      ( ord(X_c)
     => ! [F,G] :
          ( ! [X_2] : hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2)))
         => hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) ) ),
    file('theBenchmark.p',fact_155_le__funI) ).

fof(fact_156_assms_I4_J,axiom,
    ! [Pn] :
      ( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn),u))
     => hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,Pn)))) ),
    file('theBenchmark.p',fact_156_assms_I4_J) ).

fof(fact_157_diff__eq__diff__less__eq,axiom,
    ! [X_b] :
      ( ordered_ab_group_add(X_b)
     => ! [A_2,B,C_1,D_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1)
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B))
          <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),D_1)) ) ) ),
    file('theBenchmark.p',fact_157_diff__eq__diff__less__eq) ).

fof(fact_158_folding__one__idem_Osubset__idem,axiom,
    ! [X_b,B_2,A_3,F,F_2] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
       => ( ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool))
         => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))
           => hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_2,B_2)),hAPP(fun(X_b,bool),X_b,F_2,A_3)) = hAPP(fun(X_b,bool),X_b,F_2,A_3) ) ) ) ),
    file('theBenchmark.p',fact_158_folding__one__idem_Osubset__idem) ).

fof(fact_159_folding__one__idem_Oinsert__idem,axiom,
    ! [X_b,X_1,A_3,F,F_2] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
       => ( ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool))
         => hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3)) ) ) ),
    file('theBenchmark.p',fact_159_folding__one__idem_Oinsert__idem) ).

fof(fact_160_finite__ne__induct,axiom,
    ! [X_b,Pa,F_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_2))
     => ( ti(fun(X_b,bool),F_2) != bot_bot(fun(X_b,bool))
       => ( ! [X_2] : hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))
         => ( ! [X_2,F_3] :
                ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_3))
               => ( ti(fun(X_b,bool),F_3) != bot_bot(fun(X_b,bool))
                 => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3))
                   => ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3))
                     => hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_3))) ) ) ) )
           => hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)) ) ) ) ),
    file('theBenchmark.p',fact_160_finite__ne__induct) ).

fof(fact_161_the__elem__def,axiom,
    ! [X_b,X_3] : hAPP(fun(X_b,bool),X_b,the_elem(X_b),X_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),fequal(fun(X_b,bool)),X_3)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))),
    file('theBenchmark.p',fact_161_the__elem__def) ).

fof(fact_162_folding__one_Oinsert,axiom,
    ! [X_b,X_1,A_3,F,F_2] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
       => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
         => ( ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool))
           => hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3)) ) ) ) ),
    file('theBenchmark.p',fact_162_folding__one_Oinsert) ).

fof(fact_163_finite__Diff,axiom,
    ! [X_b,B_2,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) ),
    file('theBenchmark.p',fact_163_finite__Diff) ).

fof(fact_164_folding__one__idem_Oidem,axiom,
    ! [X_b,X_1,F,F_2] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2))
     => hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1) = ti(X_b,X_1) ),
    file('theBenchmark.p',fact_164_folding__one__idem_Oidem) ).

fof(fact_165_Diff__cancel,axiom,
    ! [X_b,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),A_3) = bot_bot(fun(X_b,bool)),
    file('theBenchmark.p',fact_165_Diff__cancel) ).

fof(fact_166_Diff__empty,axiom,
    ! [X_b,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_3),
    file('theBenchmark.p',fact_166_Diff__empty) ).

fof(fact_167_empty__Diff,axiom,
    ! [X_b,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3) = bot_bot(fun(X_b,bool)),
    file('theBenchmark.p',fact_167_empty__Diff) ).

fof(fact_168_finite__Diff2,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))
      <=> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ) ),
    file('theBenchmark.p',fact_168_finite__Diff2) ).

fof(fact_169_insert__Diff1,axiom,
    ! [X_b,A_3,X_1,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
     => hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2) ),
    file('theBenchmark.p',fact_169_insert__Diff1) ).

fof(fact_170_insert__Diff__if,axiom,
    ! [X_b,A_3,X_1,B_2] :
      ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
       => hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) )
      & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
       => hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2) ) ),
    file('theBenchmark.p',fact_170_insert__Diff__if) ).

fof(fact_171_double__diff,axiom,
    ! [X_b,C_2,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),C_2))
       => hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_2),A_3)) = ti(fun(X_b,bool),A_3) ) ),
    file('theBenchmark.p',fact_171_double__diff) ).

fof(fact_172_Diff__mono,axiom,
    ! [X_b,D_2,B_2,A_3,C_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),D_2),B_2))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_2),D_2))) ) ),
    file('theBenchmark.p',fact_172_Diff__mono) ).

fof(fact_173_Diff__subset,axiom,
    ! [X_b,A_3,B_2] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),A_3)),
    file('theBenchmark.p',fact_173_Diff__subset) ).

fof(fact_174_folding__one_Oremove,axiom,
    ! [X_b,X_1,A_3,F,F_2] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
         => ( ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool))
             => hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) )
            & ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool))
             => hAPP(fun(X_b,bool),X_b,F_2,A_3) = ti(X_b,X_1) ) ) ) ) ),
    file('theBenchmark.p',fact_174_folding__one_Oremove) ).

fof(fact_175_folding__one_Oinsert__remove,axiom,
    ! [X_b,X_1,A_3,F,F_2] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
       => ( ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool))
           => hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) )
          & ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool))
           => hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = ti(X_b,X_1) ) ) ) ),
    file('theBenchmark.p',fact_175_folding__one_Oinsert__remove) ).

fof(fact_176_Diff__insert,axiom,
    ! [X_b,A_3,A_2,B_2] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))),
    file('theBenchmark.p',fact_176_Diff__insert) ).

fof(fact_177_Diff__insert2,axiom,
    ! [X_b,A_3,A_2,B_2] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),B_2),
    file('theBenchmark.p',fact_177_Diff__insert2) ).

fof(fact_178_insert__Diff__single,axiom,
    ! [X_b,A_2,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3),
    file('theBenchmark.p',fact_178_insert__Diff__single) ).

fof(fact_179_Diff__insert__absorb,axiom,
    ! [X_b,X_1,A_3] :
      ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
     => hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(fun(X_b,bool),A_3) ),
    file('theBenchmark.p',fact_179_Diff__insert__absorb) ).

fof(fact_180_insert__Diff,axiom,
    ! [X_b,A_2,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))
     => hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = ti(fun(X_b,bool),A_3) ),
    file('theBenchmark.p',fact_180_insert__Diff) ).

fof(fact_181_finite__Diff__insert,axiom,
    ! [X_b,A_3,A_2,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2))))
    <=> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) ),
    file('theBenchmark.p',fact_181_finite__Diff__insert) ).

fof(fact_182_image__diff__subset,axiom,
    ! [X_b,X_c,F,A_3,B_2] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_2))),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),B_2)))),
    file('theBenchmark.p',fact_182_image__diff__subset) ).

fof(fact_183_folding__one__idem_Oin__idem,axiom,
    ! [X_b,X_1,A_3,F,F_2] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
         => hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3)) = hAPP(fun(X_b,bool),X_b,F_2,A_3) ) ) ),
    file('theBenchmark.p',fact_183_folding__one__idem_Oin__idem) ).

fof(fact_184_diff__single__insert,axiom,
    ! [X_b,A_3,X_1,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2))) ) ),
    file('theBenchmark.p',fact_184_diff__single__insert) ).

fof(fact_185_subset__insert__iff,axiom,
    ! [X_b,A_3,X_1,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2)))
    <=> ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) )
        & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_2)) ) ) ),
    file('theBenchmark.p',fact_185_subset__insert__iff) ).

fof(fact_186_diff__eq__diff__eq,axiom,
    ! [X_b] :
      ( ab_group_add(X_b)
     => ! [A_2,B,C_1,D_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1)
         => ( ti(X_b,A_2) = ti(X_b,B)
          <=> ti(X_b,C_1) = ti(X_b,D_1) ) ) ),
    file('theBenchmark.p',fact_186_diff__eq__diff__eq) ).

fof(fact_187_folding__one_Osingleton,axiom,
    ! [X_b,X_1,F,F_2] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2))
     => hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1) ),
    file('theBenchmark.p',fact_187_folding__one_Osingleton) ).

fof(fact_188_card__Diff__subset,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))
       => hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)) ) ),
    file('theBenchmark.p',fact_188_card__Diff__subset) ).

fof(fact_189_diff__card__le__card__Diff,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))) ),
    file('theBenchmark.p',fact_189_diff__card__le__card__Diff) ).

fof(fact_190_card__Suc__Diff1,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
       => hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) ) ),
    file('theBenchmark.p',fact_190_card__Suc__Diff1) ).

fof(fact_191_card__insert,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) ),
    file('theBenchmark.p',fact_191_card__insert) ).

fof(fact_192_card__Diff1__le,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) ),
    file('theBenchmark.p',fact_192_card__Diff1__le) ).

fof(fact_193_folding__one__idem_Ohom__commute,axiom,
    ! [X_b,N_1,H,F,F_2] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2))
     => ( ! [X_2,Y_2] : hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_2))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),N_1))
         => ( ti(fun(X_b,bool),N_1) != bot_bot(fun(X_b,bool))
           => hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_2,N_1)) = hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_1)) ) ) ) ),
    file('theBenchmark.p',fact_193_folding__one__idem_Ohom__commute) ).

fof(fact_194_folding__one_Oclosed,axiom,
    ! [X_b,A_3,F,F_2] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
       => ( ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool))
         => ( ! [X_2,Y_2] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool))))))
           => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,F_2,A_3)),A_3)) ) ) ) ),
    file('theBenchmark.p',fact_194_folding__one_Oclosed) ).

fof(fact_195_finite__empty__induct,axiom,
    ! [X_b,Pa,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3))
       => ( ! [A_5,A_4] :
              ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_4))
             => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_4))
               => ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_4))
                 => hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_4),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),bot_bot(fun(X_b,bool)))))) ) ) )
         => hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) ) ) ),
    file('theBenchmark.p',fact_195_finite__empty__induct) ).

fof(fact_196_folding__image__simple_Oremove,axiom,
    ! [X_c,X_b,X_1,A_3,F,Z_1,G,F_2] :
      ( hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_2))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))
       => ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))
         => hAPP(fun(X_c,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool)))))) ) ) ),
    file('theBenchmark.p',fact_196_folding__image__simple_Oremove) ).

fof(fact_197_folding__image__simple_Oinsert__remove,axiom,
    ! [X_c,X_b,X_1,A_3,F,Z_1,G,F_2] :
      ( hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_2))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))
       => hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool)))))) ) ),
    file('theBenchmark.p',fact_197_folding__image__simple_Oinsert__remove) ).

fof(fact_198_the__sym__eq__trivial,axiom,
    ! [X_b,X_1] : hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_1)) = ti(X_b,X_1),
    file('theBenchmark.p',fact_198_the__sym__eq__trivial) ).

fof(fact_199_DiffE,axiom,
    ! [X_b,C_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))
     => ~ ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)) ) ),
    file('theBenchmark.p',fact_199_DiffE) ).

fof(fact_200_DiffI,axiom,
    ! [X_b,B_2,C_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))
     => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) ) ),
    file('theBenchmark.p',fact_200_DiffI) ).

fof(fact_201_DiffD2,axiom,
    ! [X_b,C_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))
     => ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)) ),
    file('theBenchmark.p',fact_201_DiffD2) ).

fof(fact_202_DiffD1,axiom,
    ! [X_b,C_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) ),
    file('theBenchmark.p',fact_202_DiffD1) ).

fof(fact_203_Diff__idemp,axiom,
    ! [X_b,A_3,B_2] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2),
    file('theBenchmark.p',fact_203_Diff__idemp) ).

fof(fact_204_Diff__iff,axiom,
    ! [X_b,C_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))
    <=> ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))
        & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) ) ),
    file('theBenchmark.p',fact_204_Diff__iff) ).

fof(fact_205_set__diff__eq,axiom,
    ! [X_b,A_3,B_2] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))),
    file('theBenchmark.p',fact_205_set__diff__eq) ).

fof(fact_206_folding__image__simple_Oempty,axiom,
    ! [X_c,X_b,F,Z_1,G,F_2] :
      ( hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_2))
     => hAPP(fun(X_c,bool),X_b,F_2,bot_bot(fun(X_c,bool))) = ti(X_b,Z_1) ),
    file('theBenchmark.p',fact_206_folding__image__simple_Oempty) ).

fof(fact_207_folding__image__simple_Oinsert,axiom,
    ! [X_c,X_b,X_1,A_3,F,Z_1,G,F_2] :
      ( hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_2))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))
       => ( ~ hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))
         => hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,A_3)) ) ) ),
    file('theBenchmark.p',fact_207_folding__image__simple_Oinsert) ).

fof(fact_208_If__def,axiom,
    ! [X_b,X_1,Y_1,Pa] :
      ( ( ~ hBOOL(Pa)
       => ti(X_b,Y_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_1)))) )
      & ( hBOOL(Pa)
       => ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_1)))) ) ),
    file('theBenchmark.p',fact_208_If__def) ).

fof(fact_209_the__eq__trivial,axiom,
    ! [X_b,A_2] : hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = ti(X_b,A_2),
    file('theBenchmark.p',fact_209_the__eq__trivial) ).

fof(fact_210_the__equality,axiom,
    ! [X_b,Pa,A_2] :
      ( hBOOL(hAPP(X_b,bool,Pa,A_2))
     => ( ! [X_2] :
            ( hBOOL(hAPP(X_b,bool,Pa,X_2))
           => ti(X_b,X_2) = ti(X_b,A_2) )
       => hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_2) ) ),
    file('theBenchmark.p',fact_210_the__equality) ).

fof(fact_211_folding__image__simple_Oneutral,axiom,
    ! [X_c,X_b,A_3,F,Z_1,G,F_2] :
      ( hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_2))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))
       => ( ! [X_2] :
              ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3))
             => hAPP(X_c,X_b,G,X_2) = ti(X_b,Z_1) )
         => hAPP(fun(X_c,bool),X_b,F_2,A_3) = ti(X_b,Z_1) ) ) ),
    file('theBenchmark.p',fact_211_folding__image__simple_Oneutral) ).

fof(fact_212_fun__diff__def,axiom,
    ! [X_b,X_c] :
      ( minus(X_c)
     => ! [A_3,B_2,X_2] : hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),minus_minus(fun(X_b,X_c)),A_3),B_2),X_2) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,A_3,X_2)),hAPP(X_b,X_c,B_2,X_2)) ),
    file('theBenchmark.p',fact_212_fun__diff__def) ).

fof(fact_213_minus__apply,axiom,
    ! [X_c,X_b] :
      ( minus(X_b)
     => ! [A_3,B_2,X_1] : hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),minus_minus(fun(X_c,X_b)),A_3),B_2),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_c,X_b,A_3,X_1)),hAPP(X_c,X_b,B_2,X_1)) ),
    file('theBenchmark.p',fact_213_minus__apply) ).

fof(fact_214_theI,axiom,
    ! [X_b,Pa,A_2] :
      ( hBOOL(hAPP(X_b,bool,Pa,A_2))
     => ( ! [X_2] :
            ( hBOOL(hAPP(X_b,bool,Pa,X_2))
           => ti(X_b,X_2) = ti(X_b,A_2) )
       => hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))) ) ),
    file('theBenchmark.p',fact_214_theI) ).

fof(fact_215_theI_H,axiom,
    ! [X_b,Pa] :
      ( ? [X_2] :
          ( ! [Y_2] :
              ( hBOOL(hAPP(X_b,bool,Pa,Y_2))
             => ti(X_b,Y_2) = ti(X_b,X_2) )
          & hBOOL(hAPP(X_b,bool,Pa,X_2)) )
     => hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))) ),
    file('theBenchmark.p',fact_215_theI_H) ).

fof(fact_216_the1__equality,axiom,
    ! [X_b,A_2,Pa] :
      ( ? [X_2] :
          ( ! [Y_2] :
              ( hBOOL(hAPP(X_b,bool,Pa,Y_2))
             => ti(X_b,Y_2) = ti(X_b,X_2) )
          & hBOOL(hAPP(X_b,bool,Pa,X_2)) )
     => ( hBOOL(hAPP(X_b,bool,Pa,A_2))
       => hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_2) ) ),
    file('theBenchmark.p',fact_216_the1__equality) ).

fof(fact_217_flat__lub__def,axiom,
    ! [X_b,A_3,B] :
      ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool)))))
       => hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B),A_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool)))))) )
      & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool)))))
       => hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B),A_3) = ti(X_b,B) ) ),
    file('theBenchmark.p',fact_217_flat__lub__def) ).

fof(fact_218_card__Diff__singleton,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
       => hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat)) ) ),
    file('theBenchmark.p',fact_218_card__Diff__singleton) ).

fof(fact_219_card__Diff__singleton__if,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
         => hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) )
        & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
         => hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat)) ) ) ),
    file('theBenchmark.p',fact_219_card__Diff__singleton__if) ).

fof(fact_220_one__reorient,axiom,
    ! [X_b] :
      ( one(X_b)
     => ! [X_1] :
          ( one_one(X_b) = ti(X_b,X_1)
        <=> ti(X_b,X_1) = one_one(X_b) ) ),
    file('theBenchmark.p',fact_220_one__reorient) ).

fof(fact_221_diff__Suc__eq__diff__pred,axiom,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N),
    file('theBenchmark.p',fact_221_diff__Suc__eq__diff__pred) ).

fof(fact_222_diff__Suc__1,axiom,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat)) = N,
    file('theBenchmark.p',fact_222_diff__Suc__1) ).

fof(fact_223_card__Diff__insert,axiom,
    ! [X_b,B_2,A_2,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))
       => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2))
         => hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))),one_one(nat)) ) ) ),
    file('theBenchmark.p',fact_223_card__Diff__insert) ).

fof(fact_224_card_Oinsert__remove,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) ),
    file('theBenchmark.p',fact_224_card_Oinsert__remove) ).

fof(fact_225_card_Oremove,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
       => hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) ) ),
    file('theBenchmark.p',fact_225_card_Oremove) ).

fof(fact_226_comp__fun__idem__remove,axiom,
    ! [X_b] : hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool)))))),
    file('theBenchmark.p',fact_226_comp__fun__idem__remove) ).

fof(fact_227_less__eq__nat_Osimps_I2_J,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),Na))
    <=> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1)),Na)) ),
    file('theBenchmark.p',fact_227_less__eq__nat_Osimps_I2_J) ).

fof(fact_228_add__le__cancel__right,axiom,
    ! [X_b] :
      ( ordere236663937imp_le(X_b)
     => ! [A_2,C_1,B] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C_1)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B)) ) ),
    file('theBenchmark.p',fact_228_add__le__cancel__right) ).

fof(fact_229_add__le__cancel__left,axiom,
    ! [X_b] :
      ( ordere236663937imp_le(X_b)
     => ! [C_1,A_2,B] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B)) ) ),
    file('theBenchmark.p',fact_229_add__le__cancel__left) ).

fof(fact_230_add__right__mono,axiom,
    ! [X_a] :
      ( ordere779506340up_add(X_a)
     => ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C))) ) ),
    file('theBenchmark.p',fact_230_add__right__mono) ).

fof(fact_231_add__left__mono,axiom,
    ! [X_a] :
      ( ordere779506340up_add(X_a)
     => ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))) ) ),
    file('theBenchmark.p',fact_231_add__left__mono) ).

fof(fact_232_add__mono,axiom,
    ! [X_a] :
      ( ordere779506340up_add(X_a)
     => ! [C,D,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ),
    file('theBenchmark.p',fact_232_add__mono) ).

fof(fact_233_add__le__imp__le__right,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [A_1,C,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) ) ),
    file('theBenchmark.p',fact_233_add__le__imp__le__right) ).

fof(fact_234_add__le__imp__le__left,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1)))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) ) ),
    file('theBenchmark.p',fact_234_add__le__imp__le__left) ).

fof(fact_235_add__Suc__right,axiom,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),
    file('theBenchmark.p',fact_235_add__Suc__right) ).

fof(fact_236_add__Suc,axiom,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),
    file('theBenchmark.p',fact_236_add__Suc) ).

fof(fact_237_add__Suc__shift,axiom,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N)),
    file('theBenchmark.p',fact_237_add__Suc__shift) ).

fof(fact_238_comp__fun__idem_Ofun__left__idem,axiom,
    ! [X_b,X_c,X_1,Z_1,F] :
      ( hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F))
     => hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_1)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_1) ),
    file('theBenchmark.p',fact_238_comp__fun__idem_Ofun__left__idem) ).

fof(fact_239_nat__add__right__cancel,axiom,
    ! [M_1,K_2,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K_2)
    <=> M_1 = Na ),
    file('theBenchmark.p',fact_239_nat__add__right__cancel) ).

fof(fact_240_nat__add__left__cancel,axiom,
    ! [K_2,M_1,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),Na)
    <=> M_1 = Na ),
    file('theBenchmark.p',fact_240_nat__add__left__cancel) ).

fof(fact_241_nat__add__assoc,axiom,
    ! [M,N,K] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K)),
    file('theBenchmark.p',fact_241_nat__add__assoc) ).

fof(fact_242_nat__add__left__commute,axiom,
    ! [X,Y,Z] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z)),
    file('theBenchmark.p',fact_242_nat__add__left__commute) ).

fof(fact_243_nat__add__commute,axiom,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M),
    file('theBenchmark.p',fact_243_nat__add__commute) ).

fof(fact_244_add__right__imp__eq,axiom,
    ! [X_a] :
      ( cancel_semigroup_add(X_a)
     => ! [B_1,A_1,C] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)
         => ti(X_a,B_1) = ti(X_a,C) ) ),
    file('theBenchmark.p',fact_244_add__right__imp__eq) ).

fof(fact_245_add__imp__eq,axiom,
    ! [X_a] :
      ( cancel146912293up_add(X_a)
     => ! [A_1,B_1,C] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)
         => ti(X_a,B_1) = ti(X_a,C) ) ),
    file('theBenchmark.p',fact_245_add__imp__eq) ).

fof(fact_246_add__left__imp__eq,axiom,
    ! [X_a] :
      ( cancel_semigroup_add(X_a)
     => ! [A_1,B_1,C] :
          ( hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)
         => ti(X_a,B_1) = ti(X_a,C) ) ),
    file('theBenchmark.p',fact_246_add__left__imp__eq) ).

fof(fact_247_add__right__cancel,axiom,
    ! [X_b] :
      ( cancel_semigroup_add(X_b)
     => ! [B,A_2,C_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)
        <=> ti(X_b,B) = ti(X_b,C_1) ) ),
    file('theBenchmark.p',fact_247_add__right__cancel) ).

fof(fact_248_add__left__cancel,axiom,
    ! [X_b] :
      ( cancel_semigroup_add(X_b)
     => ! [A_2,B,C_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)
        <=> ti(X_b,B) = ti(X_b,C_1) ) ),
    file('theBenchmark.p',fact_248_add__left__cancel) ).

fof(fact_249_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X_a] :
      ( ab_semigroup_add(X_a)
     => ! [A_1,B_1,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)) ),
    file('theBenchmark.p',fact_249_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_250_diff__add__inverse2,axiom,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N) = M,
    file('theBenchmark.p',fact_250_diff__add__inverse2) ).

fof(fact_251_diff__add__inverse,axiom,
    ! [N,M] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),N) = M,
    file('theBenchmark.p',fact_251_diff__add__inverse) ).

fof(fact_252_diff__diff__left,axiom,
    ! [I,J_2,K] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_2)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K)),
    file('theBenchmark.p',fact_252_diff__diff__left) ).

fof(fact_253_diff__cancel,axiom,
    ! [K,M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N),
    file('theBenchmark.p',fact_253_diff__cancel) ).

fof(fact_254_diff__cancel2,axiom,
    ! [M,K,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N),
    file('theBenchmark.p',fact_254_diff__cancel2) ).

fof(fact_255_le__add2,axiom,
    ! [N,M] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))),
    file('theBenchmark.p',fact_255_le__add2) ).

fof(fact_256_le__add1,axiom,
    ! [N,M] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M))),
    file('theBenchmark.p',fact_256_le__add1) ).

fof(fact_257_le__iff__add,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
    <=> ? [K_1] : Na = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1) ),
    file('theBenchmark.p',fact_257_le__iff__add) ).

fof(fact_258_nat__add__left__cancel__le,axiom,
    ! [K_2,M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ),
    file('theBenchmark.p',fact_258_nat__add__left__cancel__le) ).

fof(fact_259_trans__le__add1,axiom,
    ! [M,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M))) ),
    file('theBenchmark.p',fact_259_trans__le__add1) ).

fof(fact_260_trans__le__add2,axiom,
    ! [M,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_2))) ),
    file('theBenchmark.p',fact_260_trans__le__add2) ).

fof(fact_261_add__le__mono1,axiom,
    ! [K,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K))) ),
    file('theBenchmark.p',fact_261_add__le__mono1) ).

fof(fact_262_add__le__mono,axiom,
    ! [K,L,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L))) ) ),
    file('theBenchmark.p',fact_262_add__le__mono) ).

fof(fact_263_add__leD2,axiom,
    ! [M,K,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N)) ),
    file('theBenchmark.p',fact_263_add__leD2) ).

fof(fact_264_add__leD1,axiom,
    ! [M,K,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    file('theBenchmark.p',fact_264_add__leD1) ).

fof(fact_265_add__leE,axiom,
    ! [M,K,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N))
     => ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
         => ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N)) ) ),
    file('theBenchmark.p',fact_265_add__leE) ).

fof(fact_266_diff__add__cancel,axiom,
    ! [X_a] :
      ( group_add(X_a)
     => ! [A_1,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B_1)),B_1) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_266_diff__add__cancel) ).

fof(fact_267_add__diff__cancel,axiom,
    ! [X_a] :
      ( group_add(X_a)
     => ! [A_1,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1)),B_1) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_267_add__diff__cancel) ).

fof(fact_268_comp__fun__idem__insert,axiom,
    ! [X_b] : hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),insert(X_b))),
    file('theBenchmark.p',fact_268_comp__fun__idem__insert) ).

fof(fact_269_diff__add__assoc2,axiom,
    ! [I,K,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)),I) ),
    file('theBenchmark.p',fact_269_diff__add__assoc2) ).

fof(fact_270_add__diff__assoc2,axiom,
    ! [I,K,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)),I) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I)),K) ),
    file('theBenchmark.p',fact_270_add__diff__assoc2) ).

fof(fact_271_diff__add__assoc,axiom,
    ! [I,K,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_2)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)) ),
    file('theBenchmark.p',fact_271_diff__add__assoc) ).

fof(fact_272_le__imp__diff__is__add,axiom,
    ! [K_2,I_1,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1))
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1) = K_2
      <=> J_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),I_1) ) ),
    file('theBenchmark.p',fact_272_le__imp__diff__is__add) ).

fof(fact_273_le__add__diff__inverse2,axiom,
    ! [N,M] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N) = M ),
    file('theBenchmark.p',fact_273_le__add__diff__inverse2) ).

fof(fact_274_le__diff__conv2,axiom,
    ! [I_1,K_2,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),J_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)))
      <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_2)),J_1)) ) ),
    file('theBenchmark.p',fact_274_le__diff__conv2) ).

fof(fact_275_add__diff__assoc,axiom,
    ! [I,K,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_2)),K) ),
    file('theBenchmark.p',fact_275_add__diff__assoc) ).

fof(fact_276_le__add__diff__inverse,axiom,
    ! [N,M] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M ),
    file('theBenchmark.p',fact_276_le__add__diff__inverse) ).

fof(fact_277_le__add__diff,axiom,
    ! [M,K,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),K))) ),
    file('theBenchmark.p',fact_277_le__add__diff) ).

fof(fact_278_le__diff__conv,axiom,
    ! [J_1,K_2,I_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)),I_1))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_2))) ),
    file('theBenchmark.p',fact_278_le__diff__conv) ).

fof(fact_279_diff__diff__right,axiom,
    ! [I,K,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J_2) ),
    file('theBenchmark.p',fact_279_diff__diff__right) ).

fof(fact_280_Suc__eq__plus1,axiom,
    ! [N] : hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat)),
    file('theBenchmark.p',fact_280_Suc__eq__plus1) ).

fof(fact_281_Suc__eq__plus1__left,axiom,
    ! [N] : hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N),
    file('theBenchmark.p',fact_281_Suc__eq__plus1__left) ).

fof(fact_282_nat__case__Suc,axiom,
    ! [X_b,F1,F2,Nat_2] : hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),hAPP(nat,nat,suc,Nat_2)) = hAPP(nat,X_b,F2,Nat_2),
    file('theBenchmark.p',fact_282_nat__case__Suc) ).

fof(fact_283_diff__Suc__diff__eq2,axiom,
    ! [M,K,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K))),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)) ),
    file('theBenchmark.p',fact_283_diff__Suc__diff__eq2) ).

fof(fact_284_diff__Suc__diff__eq1,axiom,
    ! [M,K,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,suc,J_2)) ),
    file('theBenchmark.p',fact_284_diff__Suc__diff__eq1) ).

fof(fact_285_card_Oinsert,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
       => hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)) ) ),
    file('theBenchmark.p',fact_285_card_Oinsert) ).

fof(fact_286_termination__basic__simps_I3_J,axiom,
    ! [Z,X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))) ),
    file('theBenchmark.p',fact_286_termination__basic__simps_I3_J) ).

fof(fact_287_termination__basic__simps_I4_J,axiom,
    ! [Y,X,Z] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))) ),
    file('theBenchmark.p',fact_287_termination__basic__simps_I4_J) ).

fof(fact_288_card__Diff2__less,axiom,
    ! [X_b,Y_1,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
       => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_3))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) ) ) ),
    file('theBenchmark.p',fact_288_card__Diff2__less) ).

fof(fact_289_card__Diff1__less,axiom,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) ) ),
    file('theBenchmark.p',fact_289_card__Diff1__less) ).

fof(fact_290_lessI,axiom,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N))),
    file('theBenchmark.p',fact_290_lessI) ).

fof(fact_291_Suc__mono,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) ),
    file('theBenchmark.p',fact_291_Suc__mono) ).

fof(fact_292_finite__Collect__less__nat,axiom,
    ! [K_2] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),K_2)))),
    file('theBenchmark.p',fact_292_finite__Collect__less__nat) ).

fof(fact_293_termination__basic__simps_I1_J,axiom,
    ! [Z,X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))) ),
    file('theBenchmark.p',fact_293_termination__basic__simps_I1_J) ).

fof(fact_294_termination__basic__simps_I2_J,axiom,
    ! [Y,X,Z] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))) ),
    file('theBenchmark.p',fact_294_termination__basic__simps_I2_J) ).

fof(fact_295_add__lessD1,axiom,
    ! [I,J_2,K] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_2)),K))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K)) ),
    file('theBenchmark.p',fact_295_add__lessD1) ).

fof(fact_296_less__add__eq__less,axiom,
    ! [M,N,K,L] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ) ),
    file('theBenchmark.p',fact_296_less__add__eq__less) ).

fof(fact_297_add__less__mono,axiom,
    ! [K,L,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L))) ) ),
    file('theBenchmark.p',fact_297_add__less__mono) ).

fof(fact_298_add__less__mono1,axiom,
    ! [K,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K))) ),
    file('theBenchmark.p',fact_298_add__less__mono1) ).

fof(fact_299_trans__less__add2,axiom,
    ! [M,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_2))) ),
    file('theBenchmark.p',fact_299_trans__less__add2) ).

fof(fact_300_trans__less__add1,axiom,
    ! [M,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M))) ),
    file('theBenchmark.p',fact_300_trans__less__add1) ).

fof(fact_301_nat__add__left__cancel__less,axiom,
    ! [K_2,M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ),
    file('theBenchmark.p',fact_301_nat__add__left__cancel__less) ).

fof(fact_302_not__add__less2,axiom,
    ! [J_2,I] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I)),I)),
    file('theBenchmark.p',fact_302_not__add__less2) ).

fof(fact_303_not__add__less1,axiom,
    ! [I,J_2] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_2)),I)),
    file('theBenchmark.p',fact_303_not__add__less1) ).

fof(fact_304_add__less__imp__less__left,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1)))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) ) ),
    file('theBenchmark.p',fact_304_add__less__imp__less__left) ).

fof(fact_305_add__less__imp__less__right,axiom,
    ! [X_a] :
      ( ordere236663937imp_le(X_a)
     => ! [A_1,C,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) ) ),
    file('theBenchmark.p',fact_305_add__less__imp__less__right) ).

fof(fact_306_add__strict__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C,D,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ),
    file('theBenchmark.p',fact_306_add__strict__mono) ).

fof(fact_307_add__strict__left__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))) ) ),
    file('theBenchmark.p',fact_307_add__strict__left__mono) ).

fof(fact_308_add__strict__right__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C))) ) ),
    file('theBenchmark.p',fact_308_add__strict__right__mono) ).

fof(fact_309_add__less__cancel__left,axiom,
    ! [X_b] :
      ( ordere236663937imp_le(X_b)
     => ! [C_1,A_2,B] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B)) ) ),
    file('theBenchmark.p',fact_309_add__less__cancel__left) ).

fof(fact_310_add__less__cancel__right,axiom,
    ! [X_b] :
      ( ordere236663937imp_le(X_b)
     => ! [A_2,C_1,B] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C_1)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B)) ) ),
    file('theBenchmark.p',fact_310_add__less__cancel__right) ).

fof(fact_311_diff__eq__diff__less,axiom,
    ! [X_b] :
      ( ordered_ab_group_add(X_b)
     => ! [A_2,B,C_1,D_1] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1)
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B))
          <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D_1)) ) ) ),
    file('theBenchmark.p',fact_311_diff__eq__diff__less) ).

fof(fact_312_Suc__less__SucD,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ),
    file('theBenchmark.p',fact_312_Suc__less__SucD) ).

fof(fact_313_Suc__lessD,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ),
    file('theBenchmark.p',fact_313_Suc__lessD) ).

fof(fact_314_less__SucE,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
       => M = N ) ),
    file('theBenchmark.p',fact_314_less__SucE) ).

fof(fact_315_less__trans__Suc,axiom,
    ! [K,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K)) ) ),
    file('theBenchmark.p',fact_315_less__trans__Suc) ).

fof(fact_316_Suc__lessI,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
     => ( hAPP(nat,nat,suc,M) != N
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N)) ) ),
    file('theBenchmark.p',fact_316_Suc__lessI) ).

fof(fact_317_less__SucI,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) ),
    file('theBenchmark.p',fact_317_less__SucI) ).

fof(fact_318_less__antisym,axiom,
    ! [N,M] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M)))
       => M = N ) ),
    file('theBenchmark.p',fact_318_less__antisym) ).

fof(fact_319_not__less__less__Suc__eq,axiom,
    ! [Na,M_1] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_1)))
      <=> Na = M_1 ) ),
    file('theBenchmark.p',fact_319_not__less__less__Suc__eq) ).

fof(fact_320_Suc__less__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ),
    file('theBenchmark.p',fact_320_Suc__less__eq) ).

fof(fact_321_less__Suc__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,Na)))
    <=> ( M_1 = Na
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) ),
    file('theBenchmark.p',fact_321_less__Suc__eq) ).

fof(fact_322_not__less__eq,axiom,
    ! [M_1,Na] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_1))) ),
    file('theBenchmark.p',fact_322_not__less__eq) ).

fof(fact_323_less__or__eq__imp__le,axiom,
    ! [M,N] :
      ( ( M = N
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) )
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    file('theBenchmark.p',fact_323_less__or__eq__imp__le) ).

fof(fact_324_le__neq__implies__less,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
     => ( M != N
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ) ),
    file('theBenchmark.p',fact_324_le__neq__implies__less) ).

fof(fact_325_less__imp__le__nat,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    file('theBenchmark.p',fact_325_less__imp__le__nat) ).

fof(fact_326_le__eq__less__or__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
    <=> ( M_1 = Na
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) ),
    file('theBenchmark.p',fact_326_le__eq__less__or__eq) ).

fof(fact_327_nat__less__le,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
    <=> ( M_1 != Na
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ) ),
    file('theBenchmark.p',fact_327_nat__less__le) ).

fof(fact_328_diff__less__mono2,axiom,
    ! [L,M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M))) ) ),
    file('theBenchmark.p',fact_328_diff__less__mono2) ).

fof(fact_329_less__imp__diff__less,axiom,
    ! [N,J_2,K] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),N)),K)) ),
    file('theBenchmark.p',fact_329_less__imp__diff__less) ).

fof(fact_330_order__less__irrefl,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X)) ),
    file('theBenchmark.p',fact_330_order__less__irrefl) ).

fof(fact_331_linorder__neq__iff,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [X_1,Y_1] :
          ( ti(X_b,X_1) != ti(X_b,Y_1)
        <=> ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) ) ) ),
    file('theBenchmark.p',fact_331_linorder__neq__iff) ).

fof(fact_332_not__less__iff__gr__or__eq,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [X_1,Y_1] :
          ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
        <=> ( ti(X_b,X_1) = ti(X_b,Y_1)
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) ) ) ),
    file('theBenchmark.p',fact_332_not__less__iff__gr__or__eq) ).

fof(fact_333_linorder__less__linear,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | ti(X_a,X) = ti(X_a,Y)
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_333_linorder__less__linear) ).

fof(fact_334_linorder__antisym__conv3,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [Y_1,X_1] :
          ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1))
         => ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
          <=> ti(X_b,X_1) = ti(X_b,Y_1) ) ) ),
    file('theBenchmark.p',fact_334_linorder__antisym__conv3) ).

fof(fact_335_linorder__neqE,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( ti(X_a,X) != ti(X_a,Y)
         => ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ),
    file('theBenchmark.p',fact_335_linorder__neqE) ).

fof(fact_336_less__imp__neq,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ti(X_a,X) != ti(X_a,Y) ) ),
    file('theBenchmark.p',fact_336_less__imp__neq) ).

fof(fact_337_order__less__not__sym,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ),
    file('theBenchmark.p',fact_337_order__less__not__sym) ).

fof(fact_338_order__less__imp__not__less,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ),
    file('theBenchmark.p',fact_338_order__less__imp__not__less) ).

fof(fact_339_order__less__imp__not__eq,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ti(X_a,X) != ti(X_a,Y) ) ),
    file('theBenchmark.p',fact_339_order__less__imp__not__eq) ).

fof(fact_340_order__less__imp__not__eq2,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ti(X_a,Y) != ti(X_a,X) ) ),
    file('theBenchmark.p',fact_340_order__less__imp__not__eq2) ).

fof(fact_341_order__less__imp__triv,axiom,
    ! [X_b] :
      ( preorder(X_b)
     => ! [Pa,X_1,Y_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1))
           => hBOOL(Pa) ) ) ),
    file('theBenchmark.p',fact_341_order__less__imp__triv) ).

fof(fact_342_order__less__asym_H,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1)) ) ),
    file('theBenchmark.p',fact_342_order__less__asym_H) ).

fof(fact_343_xt1_I9_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [B_1,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) ) ),
    file('theBenchmark.p',fact_343_xt1_I9_J) ).

fof(fact_344_ord__eq__less__trans,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [C,A_1,B_1] :
          ( A_1 = B_1
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C)) ) ) ),
    file('theBenchmark.p',fact_344_ord__eq__less__trans) ).

fof(fact_345_xt1_I1_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [C,A_1,B_1] :
          ( ti(X_a,A_1) = ti(X_a,B_1)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1)) ) ) ),
    file('theBenchmark.p',fact_345_xt1_I1_J) ).

fof(fact_346_ord__less__eq__trans,axiom,
    ! [X_a] :
      ( ord(X_a)
     => ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))
         => ( B_1 = C
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C)) ) ) ),
    file('theBenchmark.p',fact_346_ord__less__eq__trans) ).

fof(fact_347_xt1_I2_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [C,B_1,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1))
         => ( ti(X_a,B_1) = ti(X_a,C)
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1)) ) ) ),
    file('theBenchmark.p',fact_347_xt1_I2_J) ).

fof(fact_348_order__less__trans,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)) ) ) ),
    file('theBenchmark.p',fact_348_order__less__trans) ).

fof(fact_349_xt1_I10_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)) ) ) ),
    file('theBenchmark.p',fact_349_xt1_I10_J) ).

fof(fact_350_order__less__asym,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ),
    file('theBenchmark.p',fact_350_order__less__asym) ).

fof(fact_351_linorder__cases,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ( ti(X_a,X) != ti(X_a,Y)
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ),
    file('theBenchmark.p',fact_351_linorder__cases) ).

fof(fact_352_termination__basic__simps_I5_J,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) ),
    file('theBenchmark.p',fact_352_termination__basic__simps_I5_J) ).

fof(fact_353_less__not__refl,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)),
    file('theBenchmark.p',fact_353_less__not__refl) ).

fof(fact_354_nat__neq__iff,axiom,
    ! [M_1,Na] :
      ( M_1 != Na
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) ),
    file('theBenchmark.p',fact_354_nat__neq__iff) ).

fof(fact_355_linorder__neqE__nat,axiom,
    ! [X,Y] :
      ( X != Y
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X)) ) ),
    file('theBenchmark.p',fact_355_linorder__neqE__nat) ).

fof(fact_356_less__irrefl__nat,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)),
    file('theBenchmark.p',fact_356_less__irrefl__nat) ).

fof(fact_357_less__not__refl2,axiom,
    ! [N,M] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M))
     => M != N ),
    file('theBenchmark.p',fact_357_less__not__refl2) ).

fof(fact_358_less__not__refl3,axiom,
    ! [S,T_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3))
     => S != T_3 ),
    file('theBenchmark.p',fact_358_less__not__refl3) ).

fof(fact_359_nat__less__cases,axiom,
    ! [Pa,M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_1)) )
     => ( ( M_1 = Na
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_1)) )
       => ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1))
           => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_1)) )
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_1)) ) ) ),
    file('theBenchmark.p',fact_359_nat__less__cases) ).

fof(fact_360_not__less__bot,axiom,
    ! [X_a] :
      ( bot(X_a)
     => ! [A_1] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),bot_bot(X_a))) ),
    file('theBenchmark.p',fact_360_not__less__bot) ).

fof(fact_361_bot__less,axiom,
    ! [X_b] :
      ( bot(X_b)
     => ! [A_2] :
          ( ti(X_b,A_2) != bot_bot(X_b)
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),bot_bot(X_b)),A_2)) ) ),
    file('theBenchmark.p',fact_361_bot__less) ).

fof(fact_362_linorder__not__less,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [X_1,Y_1] :
          ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)) ) ),
    file('theBenchmark.p',fact_362_linorder__not__less) ).

fof(fact_363_linorder__not__le,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [X_1,Y_1] :
          ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) ) ),
    file('theBenchmark.p',fact_363_linorder__not__le) ).

fof(fact_364_linorder__le__less__linear,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_364_linorder__le__less__linear) ).

fof(fact_365_order__less__le,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [X_1,Y_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
        <=> ( ti(X_b,X_1) != ti(X_b,Y_1)
            & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) ) ) ),
    file('theBenchmark.p',fact_365_order__less__le) ).

fof(fact_366_less__le__not__le,axiom,
    ! [X_b] :
      ( preorder(X_b)
     => ! [X_1,Y_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
        <=> ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1))
            & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) ) ) ),
    file('theBenchmark.p',fact_366_less__le__not__le) ).

fof(fact_367_order__le__less,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [X_1,Y_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1))
        <=> ( ti(X_b,X_1) = ti(X_b,Y_1)
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) ) ) ),
    file('theBenchmark.p',fact_367_order__le__less) ).

fof(fact_368_leI,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [X,Y] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) ) ),
    file('theBenchmark.p',fact_368_leI) ).

fof(fact_369_not__leE,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [Y,X] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_369_not__leE) ).

fof(fact_370_linorder__antisym__conv1,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [X_1,Y_1] :
          ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1))
          <=> ti(X_b,X_1) = ti(X_b,Y_1) ) ) ),
    file('theBenchmark.p',fact_370_linorder__antisym__conv1) ).

fof(fact_371_order__neq__le__trans,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [A_1,B_1] :
          ( ti(X_a,A_1) != ti(X_a,B_1)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) ) ) ),
    file('theBenchmark.p',fact_371_order__neq__le__trans) ).

fof(fact_372_xt1_I12_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [A_1,B_1] :
          ( ti(X_a,A_1) != ti(X_a,B_1)
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_372_xt1_I12_J) ).

fof(fact_373_leD,axiom,
    ! [X_a] :
      ( linorder(X_a)
     => ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_373_leD) ).

fof(fact_374_order__less__imp__le,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) ) ),
    file('theBenchmark.p',fact_374_order__less__imp__le) ).

fof(fact_375_linorder__antisym__conv2,axiom,
    ! [X_b] :
      ( linorder(X_b)
     => ! [X_1,Y_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1))
         => ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
          <=> ti(X_b,X_1) = ti(X_b,Y_1) ) ) ),
    file('theBenchmark.p',fact_375_linorder__antisym__conv2) ).

fof(fact_376_order__le__imp__less__or__eq,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => ( ti(X_a,X) = ti(X_a,Y)
            | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) ) ) ),
    file('theBenchmark.p',fact_376_order__le__imp__less__or__eq) ).

fof(fact_377_order__le__neq__trans,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1))
         => ( ti(X_a,A_1) != ti(X_a,B_1)
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) ) ) ),
    file('theBenchmark.p',fact_377_order__le__neq__trans) ).

fof(fact_378_xt1_I11_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [B_1,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_1))
         => ( ti(X_a,A_1) != ti(X_a,B_1)
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1)) ) ) ),
    file('theBenchmark.p',fact_378_xt1_I11_J) ).

fof(fact_379_order__less__le__trans,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)) ) ) ),
    file('theBenchmark.p',fact_379_order__less__le__trans) ).

fof(fact_380_xt1_I7_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)) ) ) ),
    file('theBenchmark.p',fact_380_xt1_I7_J) ).

fof(fact_381_order__le__less__trans,axiom,
    ! [X_a] :
      ( preorder(X_a)
     => ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z)) ) ) ),
    file('theBenchmark.p',fact_381_order__le__less__trans) ).

fof(fact_382_xt1_I8_J,axiom,
    ! [X_a] :
      ( order(X_a)
     => ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X)) ) ) ),
    file('theBenchmark.p',fact_382_xt1_I8_J) ).

fof(fact_383_finite__nat__set__iff__bounded,axiom,
    ! [N_1] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_1))
    <=> ? [M_2] :
        ! [X_2] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_1))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2)) ) ),
    file('theBenchmark.p',fact_383_finite__nat__set__iff__bounded) ).

fof(fact_384_nat__seg__image__imp__finite,axiom,
    ! [X_b,A_3,F,Na] :
      ( ti(fun(X_b,bool),A_3) = hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na)))
     => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    file('theBenchmark.p',fact_384_nat__seg__image__imp__finite) ).

fof(fact_385_card__Collect__less__nat,axiom,
    ! [Na] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na))) = Na,
    file('theBenchmark.p',fact_385_card__Collect__less__nat) ).

fof(fact_386_finite__M__bounded__by__nat,axiom,
    ! [Pa,I_1] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),Pa)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1))))),
    file('theBenchmark.p',fact_386_finite__M__bounded__by__nat) ).

fof(fact_387_add__le__less__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C,D,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ),
    file('theBenchmark.p',fact_387_add__le__less__mono) ).

fof(fact_388_add__less__le__mono,axiom,
    ! [X_a] :
      ( ordere223160158up_add(X_a)
     => ! [C,D,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D))) ) ) ),
    file('theBenchmark.p',fact_388_add__less__le__mono) ).

fof(fact_389_less__add__Suc1,axiom,
    ! [I,M] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),M)))),
    file('theBenchmark.p',fact_389_less__add__Suc1) ).

fof(fact_390_less__add__Suc2,axiom,
    ! [I,M] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I)))),
    file('theBenchmark.p',fact_390_less__add__Suc2) ).

fof(fact_391_less__iff__Suc__add,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
    <=> ? [K_1] : Na = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)) ),
    file('theBenchmark.p',fact_391_less__iff__Suc__add) ).

fof(fact_392_less__eq__Suc__le,axiom,
    ! [Na,M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_1)) ),
    file('theBenchmark.p',fact_392_less__eq__Suc__le) ).

fof(fact_393_less__Suc__eq__le,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,Na)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ),
    file('theBenchmark.p',fact_393_less__Suc__eq__le) ).

fof(fact_394_Suc__le__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),Na))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ),
    file('theBenchmark.p',fact_394_Suc__le__eq) ).

fof(fact_395_le__imp__less__Suc,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) ),
    file('theBenchmark.p',fact_395_le__imp__less__Suc) ).

fof(fact_396_Suc__leI,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) ),
    file('theBenchmark.p',fact_396_Suc__leI) ).

fof(fact_397_le__less__Suc__eq,axiom,
    ! [M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_1)))
      <=> Na = M_1 ) ),
    file('theBenchmark.p',fact_397_le__less__Suc__eq) ).

fof(fact_398_Suc__le__lessD,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ),
    file('theBenchmark.p',fact_398_Suc__le__lessD) ).

fof(fact_399_diff__less__Suc,axiom,
    ! [M,N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),hAPP(nat,nat,suc,M))),
    file('theBenchmark.p',fact_399_diff__less__Suc) ).

fof(fact_400_add__diff__inverse,axiom,
    ! [M,N] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M ),
    file('theBenchmark.p',fact_400_add__diff__inverse) ).

fof(fact_401_less__diff__conv,axiom,
    ! [I_1,J_1,K_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_2)),J_1)) ),
    file('theBenchmark.p',fact_401_less__diff__conv) ).

fof(fact_402_diff__less__mono,axiom,
    ! [C,A_1,B_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B_1),C))) ) ),
    file('theBenchmark.p',fact_402_diff__less__mono) ).

fof(fact_403_less__diff__iff,axiom,
    ! [Na,K_2,M_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),M_1))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K_2)))
        <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) ) ),
    file('theBenchmark.p',fact_403_less__diff__iff) ).

fof(fact_404_less__eq__Suc__le__raw,axiom,
    ! [X_2] : hAPP(nat,fun(nat,bool),ord_less(nat),X_2) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_2)),
    file('theBenchmark.p',fact_404_less__eq__Suc__le__raw) ).

fof(fact_405_mono__nat__linear__lb,axiom,
    ! [M_1,K_2,F] :
      ( ! [M_2,N_2] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_2))) )
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M_1)),K_2)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2)))) ),
    file('theBenchmark.p',fact_405_mono__nat__linear__lb) ).

fof(fact_406_inc__induct,axiom,
    ! [Pa,I_1,J_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1))
     => ( hBOOL(hAPP(nat,bool,Pa,J_1))
       => ( ! [I_2] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1))
             => ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,I_2)))
               => hBOOL(hAPP(nat,bool,Pa,I_2)) ) )
         => hBOOL(hAPP(nat,bool,Pa,I_1)) ) ) ),
    file('theBenchmark.p',fact_406_inc__induct) ).

fof(fact_407_less__imp__Suc__add,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
     => ? [K_1] : N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1)) ),
    file('theBenchmark.p',fact_407_less__imp__Suc__add) ).

fof(fact_408_subset__psubset__trans,axiom,
    ! [X_b,C_2,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_2),C_2))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2)) ) ),
    file('theBenchmark.p',fact_408_subset__psubset__trans) ).

fof(fact_409_psubset__subset__trans,axiom,
    ! [X_b,C_2,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),C_2))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2)) ) ),
    file('theBenchmark.p',fact_409_psubset__subset__trans) ).

fof(fact_410_psubset__imp__subset,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
     => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    file('theBenchmark.p',fact_410_psubset__imp__subset) ).

fof(fact_411_subset__iff__psubset__eq,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
    <=> ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)
        | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) ) ),
    file('theBenchmark.p',fact_411_subset__iff__psubset__eq) ).

fof(fact_412_psubset__eq,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
    <=> ( ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_2)
        & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ),
    file('theBenchmark.p',fact_412_psubset__eq) ).

fof(fact_413_not__psubset__empty,axiom,
    ! [X_b,A_3] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))),
    file('theBenchmark.p',fact_413_not__psubset__empty) ).

fof(fact_414_less__fun__def,axiom,
    ! [X_b,X_c] :
      ( ord(X_c)
     => ! [F,G] :
          ( hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less(fun(X_b,X_c)),F),G))
        <=> ( ~ hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),G),F))
            & hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) ) ) ),
    file('theBenchmark.p',fact_414_less__fun__def) ).

fof(fact_415_psubset__card__mono,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))) ) ),
    file('theBenchmark.p',fact_415_psubset__card__mono) ).

fof(fact_416_psubset__insert__iff,axiom,
    ! [X_b,A_3,X_1,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2)))
    <=> ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
         => ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
             => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) )
            & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
             => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_2)) ) ) )
        & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) ) ) ),
    file('theBenchmark.p',fact_416_psubset__insert__iff) ).

fof(fact_417_card__psubset,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)))
         => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) ) ) ),
    file('theBenchmark.p',fact_417_card__psubset) ).

fof(fact_418_finite__conv__nat__seg__image,axiom,
    ! [X_b,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
    <=> ? [N_2,F_1] : ti(fun(X_b,bool),A_3) = hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F_1),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2))) ),
    file('theBenchmark.p',fact_418_finite__conv__nat__seg__image) ).

fof(fact_419_lift__Suc__mono__less,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [Na,N_3,F] :
          ( ! [N_2] : hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_2)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_2))))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),N_3))
           => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3))) ) ) ),
    file('theBenchmark.p',fact_419_lift__Suc__mono__less) ).

fof(fact_420_psubsetD,axiom,
    ! [X_b,C_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2)) ) ),
    file('theBenchmark.p',fact_420_psubsetD) ).

fof(fact_421_psubset__trans,axiom,
    ! [X_b,C_2,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
     => ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_2),C_2))
       => hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2)) ) ),
    file('theBenchmark.p',fact_421_psubset__trans) ).

fof(fact_422_lift__Suc__mono__less__iff,axiom,
    ! [X_b] :
      ( order(X_b)
     => ! [Na,M_1,F] :
          ( ! [N_2] : hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_2)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_2))))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,M_1)))
          <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1)) ) ) ),
    file('theBenchmark.p',fact_422_lift__Suc__mono__less__iff) ).

fof(fact_423_less__add__one,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ! [A_1] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a)))) ),
    file('theBenchmark.p',fact_423_less__add__one) ).

fof(fact_424_linorder__neqE__linordered__idom,axiom,
    ! [X_a] :
      ( linordered_idom(X_a)
     => ! [X,Y] :
          ( ti(X_a,X) != ti(X_a,Y)
         => ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) ) ) ),
    file('theBenchmark.p',fact_424_linorder__neqE__linordered__idom) ).

fof(fact_425_bounded__nat__set__is__finite,axiom,
    ! [Na,N_1] :
      ( ! [X_2] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_1))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),Na)) )
     => hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_1)) ),
    file('theBenchmark.p',fact_425_bounded__nat__set__is__finite) ).

fof(fact_426_psubset__imp__ex__mem,axiom,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
     => ? [B_3] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),A_3))) ),
    file('theBenchmark.p',fact_426_psubset__imp__ex__mem) ).

fof(fact_427_less__mono__imp__le__mono,axiom,
    ! [I_1,J_1,F] :
      ( ! [I_2,J] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J))) )
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1))) ) ),
    file('theBenchmark.p',fact_427_less__mono__imp__le__mono) ).

fof(fact_428_Suc__lessE,axiom,
    ! [I,K] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K))
     => ~ ! [J] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))
           => K != hAPP(nat,nat,suc,J) ) ),
    file('theBenchmark.p',fact_428_Suc__lessE) ).

fof(fact_429_lessE,axiom,
    ! [I,K] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K))
     => ( K != hAPP(nat,nat,suc,I)
       => ~ ! [J] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J))
             => K != hAPP(nat,nat,suc,J) ) ) ),
    file('theBenchmark.p',fact_429_lessE) ).

fof(fact_430_xt6,axiom,
    ! [X_c,X_b] :
      ( ( ord(X_c)
        & order(X_b) )
     => ! [C_1,F,B,A_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,B)),A_2))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),B))
           => ( ! [X_2,Y_2] :
                  ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Y_2),X_2))
                 => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Y_2)),hAPP(X_c,X_b,F,X_2))) )
             => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,C_1)),A_2)) ) ) ) ),
    file('theBenchmark.p',fact_430_xt6) ).

fof(fact_431_dense__le,axiom,
    ! [X_a] :
      ( dense_linorder(X_a)
     => ! [Z,Y] :
          ( ! [X_2] :
              ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y))
             => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z)) )
         => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) ) ),
    file('theBenchmark.p',fact_431_dense__le) ).

fof(fact_432_dense__le__bounded,axiom,
    ! [X_a] :
      ( dense_linorder(X_a)
     => ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
         => ( ! [W] :
                ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W))
               => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Y))
                 => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z)) ) )
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) ) ) ),
    file('theBenchmark.p',fact_432_dense__le__bounded) ).

fof(fact_433_xt4,axiom,
    ! [X_c,X_b] :
      ( ( order(X_c)
        & order(X_b) )
     => ! [C_1,F,B,A_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,B)),A_2))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),C_1),B))
           => ( ! [X_2,Y_2] :
                  ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Y_2),X_2))
                 => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Y_2)),hAPP(X_c,X_b,F,X_2))) )
             => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,C_1)),A_2)) ) ) ) ),
    file('theBenchmark.p',fact_433_xt4) ).

fof(fact_434_order__le__less__subst1,axiom,
    ! [X_b,X_c] :
      ( ( order(X_b)
        & order(X_c) )
     => ! [C_1,A_2,F,B] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),hAPP(X_c,X_b,F,B)))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),B),C_1))
           => ( ! [X_2,Y_2] :
                  ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),X_2),Y_2))
                 => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_2))) )
             => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1))) ) ) ) ),
    file('theBenchmark.p',fact_434_order__le__less__subst1) ).

fof(fact_435_xt5,axiom,
    ! [X_c,X_b] :
      ( ( order(X_c)
        & order(X_b) )
     => ! [C_1,F,B,A_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B),A_2))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),C_1),hAPP(X_b,X_c,F,B)))
           => ( ! [X_2,Y_2] :
                  ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_2))
                 => hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,Y_2)),hAPP(X_b,X_c,F,X_2))) )
             => hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2))) ) ) ) ),
    file('theBenchmark.p',fact_435_xt5) ).

fof(fact_436_xt7,axiom,
    ! [X_c,X_b] :
      ( ( order(X_c)
        & order(X_b) )
     => ! [C_1,F,B,A_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B),A_2))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,B)))
           => ( ! [X_2,Y_2] :
                  ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_2))
                 => hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,Y_2)),hAPP(X_b,X_c,F,X_2))) )
             => hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2))) ) ) ) ),
    file('theBenchmark.p',fact_436_xt7) ).

fof(fact_437_order__less__le__subst1,axiom,
    ! [X_b,X_c] :
      ( ( order(X_b)
        & order(X_c) )
     => ! [C_1,A_2,F,B] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,B)))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),B),C_1))
           => ( ! [X_2,Y_2] :
                  ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),X_2),Y_2))
                 => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_2))) )
             => hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1))) ) ) ) ),
    file('theBenchmark.p',fact_437_order__less__le__subst1) ).

fof(fact_438_order__le__less__subst2,axiom,
    ! [X_b,X_c] :
      ( ( order(X_b)
        & order(X_c) )
     => ! [F,C_1,A_2,B] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,B)),C_1))
           => ( ! [X_2,Y_2] :
                  ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_2))
                 => hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_2))) )
             => hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1)) ) ) ) ),
    file('theBenchmark.p',fact_438_order__le__less__subst2) ).

fof(fact_439_order__less__le__subst2,axiom,
    ! [X_b,X_c] :
      ( ( order(X_b)
        & order(X_c) )
     => ! [F,C_1,A_2,B] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B))
         => ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,B)),C_1))
           => ( ! [X_2,Y_2] :
                  ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_2))
                 => hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_2))) )
             => hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1)) ) ) ) ),
    file('theBenchmark.p',fact_439_order__less__le__subst2) ).

fof(fact_440_card__Plus,axiom,
    ! [X_c,X_b,B_2,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
       => hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_2)) ) ),
    file('theBenchmark.p',fact_440_card__Plus) ).

fof(fact_441_finite__Plus__iff,axiom,
    ! [X_b,X_c,A_3,B_2] :
      ( hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)))
    <=> ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
        & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ) ),
    file('theBenchmark.p',fact_441_finite__Plus__iff) ).

fof(fact_442_finite__Plus,axiom,
    ! [X_c,X_b,B_2,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
       => hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2))) ) ),
    file('theBenchmark.p',fact_442_finite__Plus) ).

fof(fact_443_finite__PlusD_I1_J,axiom,
    ! [X_b,X_c,A_3,B_2] :
      ( hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)))
     => hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    file('theBenchmark.p',fact_443_finite__PlusD_I1_J) ).

fof(fact_444_finite__PlusD_I2_J,axiom,
    ! [X_b,X_c,A_3,B_2] :
      ( hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)))
     => hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2)) ),
    file('theBenchmark.p',fact_444_finite__PlusD_I2_J) ).

fof(fact_445_Plus__eq__empty__conv,axiom,
    ! [X_c,X_b,A_3,B_2] :
      ( hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2) = bot_bot(fun(sum_sum(X_b,X_c),bool))
    <=> ( ti(fun(X_c,bool),B_2) = bot_bot(fun(X_c,bool))
        & ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) ) ),
    file('theBenchmark.p',fact_445_Plus__eq__empty__conv) ).

fof(fact_446_card__Plus__conv__if,axiom,
    ! [X_c,X_b,B_2,A_3] :
      ( ( ~ ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
            & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) )
       => hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)) = zero_zero(nat) )
      & ( ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
          & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) )
       => hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_2)) ) ),
    file('theBenchmark.p',fact_446_card__Plus__conv__if) ).

fof(fact_447_less__zeroE,axiom,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))),
    file('theBenchmark.p',fact_447_less__zeroE) ).

fof(fact_448_le0,axiom,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N)),
    file('theBenchmark.p',fact_448_le0) ).

fof(fact_449_zero__less__Suc,axiom,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))),
    file('theBenchmark.p',fact_449_zero__less__Suc) ).

fof(fact_450_card__infinite,axiom,
    ! [X_b,A_3] :
      ( ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
     => hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat) ),
    file('theBenchmark.p',fact_450_card__infinite) ).

fof(fact_451_card_Oempty,axiom,
    ! [X_b] : hAPP(fun(X_b,bool),nat,finite_card(X_b),bot_bot(fun(X_b,bool))) = zero_zero(nat),
    file('theBenchmark.p',fact_451_card_Oempty) ).

fof(fact_452_zero__less__one,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))) ),
    file('theBenchmark.p',fact_452_zero__less__one) ).

fof(fact_453_not__one__less__zero,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))) ),
    file('theBenchmark.p',fact_453_not__one__less__zero) ).

fof(fact_454_pos__add__strict,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ! [B_1,C,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))) ) ) ),
    file('theBenchmark.p',fact_454_pos__add__strict) ).

fof(fact_455_not__one__le__zero,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),zero_zero(X_a))) ),
    file('theBenchmark.p',fact_455_not__one__le__zero) ).

fof(fact_456_zero__le__one,axiom,
    ! [X_a] :
      ( linordered_semidom(X_a)
     => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),one_one(X_a))) ),
    file('theBenchmark.p',fact_456_zero__le__one) ).

fof(fact_457_one__neq__zero,axiom,
    ! [X_a] :
      ( zero_neq_one(X_a)
     => one_one(X_a) != zero_zero(X_a) ),
    file('theBenchmark.p',fact_457_one__neq__zero) ).

fof(fact_458_zero__neq__one,axiom,
    ! [X_a] :
      ( zero_neq_one(X_a)
     => zero_zero(X_a) != one_one(X_a) ),
    file('theBenchmark.p',fact_458_zero__neq__one) ).

fof(fact_459_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [X_b] :
      ( linord219039673up_add(X_b)
     => ! [A_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),A_2)) ) ),
    file('theBenchmark.p',fact_459_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_460_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [X_b] :
      ( linord219039673up_add(X_b)
     => ! [A_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b)))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),zero_zero(X_b))) ) ),
    file('theBenchmark.p',fact_460_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_461_add__nonneg__nonneg,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1))) ) ) ),
    file('theBenchmark.p',fact_461_add__nonneg__nonneg) ).

fof(fact_462_add__nonneg__eq__0__iff,axiom,
    ! [X_b] :
      ( ordere216010020id_add(X_b)
     => ! [Y_1,X_1] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),X_1))
         => ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),Y_1))
           => ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_1),Y_1) = zero_zero(X_b)
            <=> ( ti(X_b,Y_1) = zero_zero(X_b)
                & ti(X_b,X_1) = zero_zero(X_b) ) ) ) ) ),
    file('theBenchmark.p',fact_462_add__nonneg__eq__0__iff) ).

fof(fact_463_add__increasing,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,C,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))) ) ) ),
    file('theBenchmark.p',fact_463_add__increasing) ).

fof(fact_464_add__increasing2,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,A_1,C] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_1))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C))) ) ) ),
    file('theBenchmark.p',fact_464_add__increasing2) ).

fof(fact_465_add__nonpos__nonpos,axiom,
    ! [X_a] :
      ( ordere216010020id_add(X_a)
     => ! [B_1,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a)))
         => ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
           => hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1)),zero_zero(X_a))) ) ) ),
    file('theBenchmark.p',fact_465_add__nonpos__nonpos) ).

fof(fact_466_le__iff__diff__le__0,axiom,
    ! [X_b] :
      ( ordered_ab_group_add(X_b)
     => ! [A_2,B] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B))
        <=> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B)),zero_zero(X_b))) ) ),
    file('theBenchmark.p',fact_466_le__iff__diff__le__0) ).

fof(fact_467_add__is__1,axiom,
    ! [M_1,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),Na) = hAPP(nat,nat,suc,zero_zero(nat))
    <=> ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M_1 = zero_zero(nat) )
        | ( Na = zero_zero(nat)
          & M_1 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    file('theBenchmark.p',fact_467_add__is__1) ).

fof(fact_468_one__is__add,axiom,
    ! [M_1,Na] :
      ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),Na)
    <=> ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M_1 = zero_zero(nat) )
        | ( Na = zero_zero(nat)
          & M_1 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    file('theBenchmark.p',fact_468_one__is__add) ).

fof(fact_469_diff__add__0,axiom,
    ! [N,M] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)) = zero_zero(nat),
    file('theBenchmark.p',fact_469_diff__add__0) ).

fof(fact_470_diff__is__0__eq_H,axiom,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
     => hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = zero_zero(nat) ),
    file('theBenchmark.p',fact_470_diff__is__0__eq_H) ).

fof(fact_471_diff__is__0__eq,axiom,
    ! [M_1,Na] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),Na) = zero_zero(nat)
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ),
    file('theBenchmark.p',fact_471_diff__is__0__eq) ).

fof(fact_472_One__nat__def,axiom,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    file('theBenchmark.p',fact_472_One__nat__def) ).

fof(fact_473_diffs0__imp__equal,axiom,
    ! [M,N] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = zero_zero(nat)
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M) = zero_zero(nat)
       => M = N ) ),
    file('theBenchmark.p',fact_473_diffs0__imp__equal) ).

fof(fact_474_diff__self__eq__0,axiom,
    ! [M] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M) = zero_zero(nat),
    file('theBenchmark.p',fact_474_diff__self__eq__0) ).

fof(fact_475_minus__nat_Odiff__0,axiom,
    ! [M] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat)) = M,
    file('theBenchmark.p',fact_475_minus__nat_Odiff__0) ).

fof(fact_476_diff__0__eq__0,axiom,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N) = zero_zero(nat),
    file('theBenchmark.p',fact_476_diff__0__eq__0) ).

fof(fact_477_diff__0__right,axiom,
    ! [X_a] :
      ( group_add(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_477_diff__0__right) ).

fof(fact_478_diff__self,axiom,
    ! [X_a] :
      ( group_add(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1) = zero_zero(X_a) ),
    file('theBenchmark.p',fact_478_diff__self) ).

fof(fact_479_eq__iff__diff__eq__0,axiom,
    ! [X_b] :
      ( ab_group_add(X_b)
     => ! [A_2,B] :
          ( ti(X_b,A_2) = ti(X_b,B)
        <=> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) = zero_zero(X_b) ) ),
    file('theBenchmark.p',fact_479_eq__iff__diff__eq__0) ).

fof(fact_480_right__minus__eq,axiom,
    ! [X_b] :
      ( group_add(X_b)
     => ! [A_2,B] :
          ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) = zero_zero(X_b)
        <=> ti(X_b,A_2) = ti(X_b,B) ) ),
    file('theBenchmark.p',fact_480_right__minus__eq) ).

fof(fact_481_Suc__neq__Zero,axiom,
    ! [M] : hAPP(nat,nat,suc,M) != zero_zero(nat),
    file('theBenchmark.p',fact_481_Suc__neq__Zero) ).

fof(fact_482_Zero__neq__Suc,axiom,
    ! [M] : zero_zero(nat) != hAPP(nat,nat,suc,M),
    file('theBenchmark.p',fact_482_Zero__neq__Suc) ).

fof(fact_483_nat_Osimps_I3_J,axiom,
    ! [Nat_1] : hAPP(nat,nat,suc,Nat_1) != zero_zero(nat),
    file('theBenchmark.p',fact_483_nat_Osimps_I3_J) ).

fof(fact_484_Suc__not__Zero,axiom,
    ! [M] : hAPP(nat,nat,suc,M) != zero_zero(nat),
    file('theBenchmark.p',fact_484_Suc__not__Zero) ).

fof(fact_485_nat_Osimps_I2_J,axiom,
    ! [Nat] : zero_zero(nat) != hAPP(nat,nat,suc,Nat),
    file('theBenchmark.p',fact_485_nat_Osimps_I2_J) ).

fof(fact_486_Zero__not__Suc,axiom,
    ! [M] : zero_zero(nat) != hAPP(nat,nat,suc,M),
    file('theBenchmark.p',fact_486_Zero__not__Suc) ).

fof(fact_487_zero__reorient,axiom,
    ! [X_b] :
      ( zero(X_b)
     => ! [X_1] :
          ( zero_zero(X_b) = ti(X_b,X_1)
        <=> ti(X_b,X_1) = zero_zero(X_b) ) ),
    file('theBenchmark.p',fact_487_zero__reorient) ).

fof(fact_488_bot__nat__def,axiom,
    bot_bot(nat) = zero_zero(nat),
    file('theBenchmark.p',fact_488_bot__nat__def) ).

fof(fact_489_le__0__eq,axiom,
    ! [Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),zero_zero(nat)))
    <=> Na = zero_zero(nat) ),
    file('theBenchmark.p',fact_489_le__0__eq) ).

fof(fact_490_less__eq__nat_Osimps_I1_J,axiom,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N)),
    file('theBenchmark.p',fact_490_less__eq__nat_Osimps_I1_J) ).

fof(fact_491_nat__case__0,axiom,
    ! [X_b,F1,F2] : hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),zero_zero(nat)) = ti(X_b,F1),
    file('theBenchmark.p',fact_491_nat__case__0) ).

fof(fact_492_add__0__left,axiom,
    ! [X_a] :
      ( monoid_add(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_492_add__0__left) ).

fof(fact_493_add__0,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_493_add__0) ).

fof(fact_494_double__zero__sym,axiom,
    ! [X_b] :
      ( linord219039673up_add(X_b)
     => ! [A_2] :
          ( zero_zero(X_b) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)
        <=> ti(X_b,A_2) = zero_zero(X_b) ) ),
    file('theBenchmark.p',fact_494_double__zero__sym) ).

fof(fact_495_add__0__right,axiom,
    ! [X_a] :
      ( monoid_add(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_495_add__0__right) ).

fof(fact_496_add_Ocomm__neutral,axiom,
    ! [X_a] :
      ( comm_monoid_add(X_a)
     => ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1) ),
    file('theBenchmark.p',fact_496_add_Ocomm__neutral) ).

fof(arity_fun___Orderings_Opreorder,axiom,
    ! [T_2,T_1] :
      ( preorder(T_1)
     => preorder(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Orderings_Opreorder) ).

fof(arity_fun___Finite__Set_Ofinite,axiom,
    ! [T_2,T_1] :
      ( ( finite_finite_1(T_2)
        & finite_finite_1(T_1) )
     => finite_finite_1(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).

fof(arity_fun___Orderings_Oorder,axiom,
    ! [T_2,T_1] :
      ( order(T_1)
     => order(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Orderings_Oorder) ).

fof(arity_fun___Orderings_Oord,axiom,
    ! [T_2,T_1] :
      ( ord(T_1)
     => ord(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Orderings_Oord) ).

fof(arity_fun___Orderings_Obot,axiom,
    ! [T_2,T_1] :
      ( bot(T_1)
     => bot(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Orderings_Obot) ).

fof(arity_fun___Groups_Ominus,axiom,
    ! [T_2,T_1] :
      ( minus(T_1)
     => minus(fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun___Groups_Ominus) ).

fof(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
    ordere223160158up_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    ordere236663937imp_le(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
    ordere779506340up_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).

fof(arity_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
    ordere216010020id_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).

fof(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
    cancel146912293up_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
    cancel_semigroup_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).

fof(arity_Nat_Onat___Rings_Olinordered__semidom,axiom,
    linordered_semidom(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).

fof(arity_Nat_Onat___Groups_Oab__semigroup__add,axiom,
    ab_semigroup_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).

fof(arity_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
    comm_monoid_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).

fof(arity_Nat_Onat___Rings_Ozero__neq__one,axiom,
    zero_neq_one(nat),
    file('theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).

fof(arity_Nat_Onat___Orderings_Opreorder,axiom,
    preorder(nat),
    file('theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).

fof(arity_Nat_Onat___Orderings_Olinorder,axiom,
    linorder(nat),
    file('theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).

fof(arity_Nat_Onat___Groups_Omonoid__add,axiom,
    monoid_add(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).

fof(arity_Nat_Onat___Orderings_Oorder,axiom,
    order(nat),
    file('theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).

fof(arity_Nat_Onat___Orderings_Oord,axiom,
    ord(nat),
    file('theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).

fof(arity_Nat_Onat___Orderings_Obot,axiom,
    bot(nat),
    file('theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).

fof(arity_Nat_Onat___Groups_Ominus,axiom,
    minus(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Ominus) ).

fof(arity_Nat_Onat___Groups_Ozero,axiom,
    zero(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).

fof(arity_Nat_Onat___Groups_Oone,axiom,
    one(nat),
    file('theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).

fof(arity_HOL_Obool___Orderings_Opreorder,axiom,
    preorder(bool),
    file('theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).

fof(arity_HOL_Obool___Finite__Set_Ofinite,axiom,
    finite_finite_1(bool),
    file('theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).

fof(arity_HOL_Obool___Orderings_Oorder,axiom,
    order(bool),
    file('theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).

fof(arity_HOL_Obool___Orderings_Oord,axiom,
    ord(bool),
    file('theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).

fof(arity_HOL_Obool___Orderings_Obot,axiom,
    bot(bool),
    file('theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).

fof(arity_HOL_Obool___Groups_Ominus,axiom,
    minus(bool),
    file('theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).

fof(arity_sum___Finite__Set_Ofinite,axiom,
    ! [T_2,T_1] :
      ( ( finite_finite_1(T_2)
        & finite_finite_1(T_1) )
     => finite_finite_1(sum_sum(T_2,T_1)) ),
    file('theBenchmark.p',arity_sum___Finite__Set_Ofinite) ).

fof(help_ti_idem,axiom,
    ! [T,A] : ti(T,ti(T,A)) = ti(T,A),
    file('theBenchmark.p',help_ti_idem) ).

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_COMBB_1_1_U,axiom,
    ! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_U) ).

fof(help_COMBC_1_1_U,axiom,
    ! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_U) ).

fof(help_COMBI_1_1_U,axiom,
    ! [X_a,P] : hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P),
    file('theBenchmark.p',help_COMBI_1_1_U) ).

fof(help_COMBK_1_1_U,axiom,
    ! [X_b,X_a,P,Q] : hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P),
    file('theBenchmark.p',help_COMBK_1_1_U) ).

fof(help_COMBS_1_1_U,axiom,
    ! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_U) ).

fof(help_fconj_1_1_U,axiom,
    ! [Q,P] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,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(bool,fun(bool,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(bool,fun(bool,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(bool,fun(bool,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(bool,fun(bool,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(bool,fun(bool,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] :
      ( ti(bool,P) = fFalse
      | ti(bool,P) = fTrue ),
    file('theBenchmark.p',help_fFalse_1_1_T) ).

fof(help_fequal_1_1_T,axiom,
    ! [X_a,X,Y] :
      ( ti(X_a,X) = ti(X_a,Y)
      | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) ),
    file('theBenchmark.p',help_fequal_1_1_T) ).

fof(help_fequal_2_1_T,axiom,
    ! [X_a,X,Y] :
      ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y))
      | ti(X_a,X) != ti(X_a,Y) ),
    file('theBenchmark.p',help_fequal_2_1_T) ).

fof(help_fimplies_1_1_U,axiom,
    ! [Q,P] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,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(bool,fun(bool,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(bool,fun(bool,bool),fimplies,P),Q)) ),
    file('theBenchmark.p',help_fimplies_3_1_U) ).

fof(conj_0,hypothesis,
    hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
    file('theBenchmark.p',conj_0) ).

fof(conj_1,hypothesis,
    hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    file('theBenchmark.p',conj_1) ).

fof(conj_2,hypothesis,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))),
    file('theBenchmark.p',conj_2) ).

fof(conj_3,hypothesis,
    hAPP(fun(x_a,bool),nat,finite_card(x_a),g) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)),
    file('theBenchmark.p',conj_3) ).

fof(conj_4,hypothesis,
    hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
    file('theBenchmark.p',conj_4) ).

fof(conj_5,hypothesis,
    ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),
    file('theBenchmark.p',conj_5) ).

fof(conj_6,conjecture,
    hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    file('theBenchmark.p',conj_6) ).

fof(f_1_1,plain,
    ! [X_b,X_c,X_a] : ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a)) = combb(X_b,X_c,X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_COMBB_res]) ).

fof(f_1_2,plain,
    ! [U_2,U_1,U_0] : ti(fun(fun(U_2,U_1),fun(fun(U_0,U_2),fun(U_0,U_1))),combb(U_2,U_1,U_0)) = combb(U_2,U_1,U_0),
    inference(variable_rename,[status(thm)],[f_1_1]) ).

fof(f_1_3,plain,
    ! [U_0,U_2,U_1] : ti(fun(fun(U_2,U_1),fun(fun(U_0,U_2),fun(U_0,U_1))),combb(U_2,U_1,U_0)) = combb(U_2,U_1,U_0),
    inference(definitional_conversion,[status(esa)],[f_1_2]) ).

cnf(f_1_4,plain,
    ti(fun(fun(U_2,U_1),fun(fun(U_0,U_2),fun(U_0,U_1))),combb(U_2,U_1,U_0)) = combb(U_2,U_1,U_0),
    inference(clausify,[status(thm)],[f_1_3]) ).

fof(f_2_1,plain,
    ! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c),
    inference(fof_nnf,[status(thm)],[tsy_c_COMBC_res]) ).

fof(f_2_2,plain,
    ! [U_5,U_4,U_3] : ti(fun(fun(U_5,fun(U_4,U_3)),fun(U_4,fun(U_5,U_3))),combc(U_5,U_4,U_3)) = combc(U_5,U_4,U_3),
    inference(variable_rename,[status(thm)],[f_2_1]) ).

fof(f_2_3,plain,
    ! [U_3,U_4,U_5] : ti(fun(fun(U_5,fun(U_4,U_3)),fun(U_4,fun(U_5,U_3))),combc(U_5,U_4,U_3)) = combc(U_5,U_4,U_3),
    inference(definitional_conversion,[status(esa)],[f_2_2]) ).

cnf(f_2_4,plain,
    ti(fun(fun(U_5,fun(U_4,U_3)),fun(U_4,fun(U_5,U_3))),combc(U_5,U_4,U_3)) = combc(U_5,U_4,U_3),
    inference(clausify,[status(thm)],[f_2_3]) ).

fof(f_3_1,plain,
    ! [X_a] : ti(fun(X_a,X_a),combi(X_a)) = combi(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_COMBI_res]) ).

fof(f_3_2,plain,
    ! [U_6] : ti(fun(U_6,U_6),combi(U_6)) = combi(U_6),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

fof(f_3_3,plain,
    ! [U_6] : ti(fun(U_6,U_6),combi(U_6)) = combi(U_6),
    inference(definitional_conversion,[status(esa)],[f_3_2]) ).

cnf(f_3_4,plain,
    ti(fun(U_6,U_6),combi(U_6)) = combi(U_6),
    inference(clausify,[status(thm)],[f_3_3]) ).

fof(f_4_1,plain,
    ! [X_a,X_b] : ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_COMBK_res]) ).

fof(f_4_2,plain,
    ! [U_8,U_7] : ti(fun(U_8,fun(U_7,U_8)),combk(U_8,U_7)) = combk(U_8,U_7),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

fof(f_4_3,plain,
    ! [U_7,U_8] : ti(fun(U_8,fun(U_7,U_8)),combk(U_8,U_7)) = combk(U_8,U_7),
    inference(definitional_conversion,[status(esa)],[f_4_2]) ).

cnf(f_4_4,plain,
    ti(fun(U_8,fun(U_7,U_8)),combk(U_8,U_7)) = combk(U_8,U_7),
    inference(clausify,[status(thm)],[f_4_3]) ).

fof(f_5_1,plain,
    ! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c)) = combs(X_a,X_b,X_c),
    inference(fof_nnf,[status(thm)],[tsy_c_COMBS_res]) ).

fof(f_5_2,plain,
    ! [U_11,U_10,U_9] : ti(fun(fun(U_11,fun(U_10,U_9)),fun(fun(U_11,U_10),fun(U_11,U_9))),combs(U_11,U_10,U_9)) = combs(U_11,U_10,U_9),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

fof(f_5_3,plain,
    ! [U_9,U_10,U_11] : ti(fun(fun(U_11,fun(U_10,U_9)),fun(fun(U_11,U_10),fun(U_11,U_9))),combs(U_11,U_10,U_9)) = combs(U_11,U_10,U_9),
    inference(definitional_conversion,[status(esa)],[f_5_2]) ).

cnf(f_5_4,plain,
    ti(fun(fun(U_11,fun(U_10,U_9)),fun(fun(U_11,U_10),fun(U_11,U_9))),combs(U_11,U_10,U_9)) = combs(U_11,U_10,U_9),
    inference(clausify,[status(thm)],[f_5_3]) ).

fof(f_6_1,plain,
    ti(fun(pname,option(com)),body) = body,
    inference(fof_nnf,[status(thm)],[tsy_c_Com_Obody_res]) ).

fof(f_6_2,plain,
    ti(fun(pname,option(com)),body) = body,
    inference(definitional_conversion,[status(esa)],[f_6_1]) ).

cnf(f_6_3,plain,
    ti(fun(pname,option(com)),body) = body,
    inference(clausify,[status(thm)],[f_6_2]) ).

fof(f_7_1,plain,
    ! [X_c] : ti(fun(fun(X_c,bool),nat),finite_card(X_c)) = finite_card(X_c),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ocard_res]) ).

fof(f_7_2,plain,
    ! [U_12] : ti(fun(fun(U_12,bool),nat),finite_card(U_12)) = finite_card(U_12),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

fof(f_7_3,plain,
    ! [U_12] : ti(fun(fun(U_12,bool),nat),finite_card(U_12)) = finite_card(U_12),
    inference(definitional_conversion,[status(esa)],[f_7_2]) ).

cnf(f_7_4,plain,
    ti(fun(fun(U_12,bool),nat),finite_card(U_12)) = finite_card(U_12),
    inference(clausify,[status(thm)],[f_7_3]) ).

fof(f_8_1,plain,
    ! [X_b,X_c] : ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite_comp_fun_idem(X_b,X_c)) = finite_comp_fun_idem(X_b,X_c),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ocomp__fun__idem_res]) ).

fof(f_8_2,plain,
    ! [U_14,U_13] : ti(fun(fun(U_14,fun(U_13,U_13)),bool),finite_comp_fun_idem(U_14,U_13)) = finite_comp_fun_idem(U_14,U_13),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ! [U_13,U_14] : ti(fun(fun(U_14,fun(U_13,U_13)),bool),finite_comp_fun_idem(U_14,U_13)) = finite_comp_fun_idem(U_14,U_13),
    inference(definitional_conversion,[status(esa)],[f_8_2]) ).

cnf(f_8_4,plain,
    ti(fun(fun(U_14,fun(U_13,U_13)),bool),finite_comp_fun_idem(U_14,U_13)) = finite_comp_fun_idem(U_14,U_13),
    inference(clausify,[status(thm)],[f_8_3]) ).

fof(f_9_1,plain,
    ! [X_b] : ti(fun(fun(X_b,bool),bool),finite_finite(X_b)) = finite_finite(X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofinite_res]) ).

fof(f_9_2,plain,
    ! [U_15] : ti(fun(fun(U_15,bool),bool),finite_finite(U_15)) = finite_finite(U_15),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

fof(f_9_3,plain,
    ! [U_15] : ti(fun(fun(U_15,bool),bool),finite_finite(U_15)) = finite_finite(U_15),
    inference(definitional_conversion,[status(esa)],[f_9_2]) ).

cnf(f_9_4,plain,
    ti(fun(fun(U_15,bool),bool),finite_finite(U_15)) = finite_finite(U_15),
    inference(clausify,[status(thm)],[f_9_3]) ).

fof(f_10_1,plain,
    ! [X_b,X_c] : ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite1357897459simple(X_b,X_c)) = finite1357897459simple(X_b,X_c),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofolding__image__simple_res]) ).

fof(f_10_2,plain,
    ! [U_17,U_16] : ti(fun(fun(U_17,fun(U_17,U_17)),fun(U_17,fun(fun(U_16,U_17),fun(fun(fun(U_16,bool),U_17),bool)))),finite1357897459simple(U_17,U_16)) = finite1357897459simple(U_17,U_16),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

fof(f_10_3,plain,
    ! [U_16,U_17] : ti(fun(fun(U_17,fun(U_17,U_17)),fun(U_17,fun(fun(U_16,U_17),fun(fun(fun(U_16,bool),U_17),bool)))),finite1357897459simple(U_17,U_16)) = finite1357897459simple(U_17,U_16),
    inference(definitional_conversion,[status(esa)],[f_10_2]) ).

cnf(f_10_4,plain,
    ti(fun(fun(U_17,fun(U_17,U_17)),fun(U_17,fun(fun(U_16,U_17),fun(fun(fun(U_16,bool),U_17),bool)))),finite1357897459simple(U_17,U_16)) = finite1357897459simple(U_17,U_16),
    inference(clausify,[status(thm)],[f_10_3]) ).

fof(f_11_1,plain,
    ! [X_b] : ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite_folding_one(X_b)) = finite_folding_one(X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofolding__one_res]) ).

fof(f_11_2,plain,
    ! [U_18] : ti(fun(fun(U_18,fun(U_18,U_18)),fun(fun(fun(U_18,bool),U_18),bool)),finite_folding_one(U_18)) = finite_folding_one(U_18),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ! [U_18] : ti(fun(fun(U_18,fun(U_18,U_18)),fun(fun(fun(U_18,bool),U_18),bool)),finite_folding_one(U_18)) = finite_folding_one(U_18),
    inference(definitional_conversion,[status(esa)],[f_11_2]) ).

cnf(f_11_4,plain,
    ti(fun(fun(U_18,fun(U_18,U_18)),fun(fun(fun(U_18,bool),U_18),bool)),finite_folding_one(U_18)) = finite_folding_one(U_18),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_1,plain,
    ! [X_b] : ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite2073411215e_idem(X_b)) = finite2073411215e_idem(X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofolding__one__idem_res]) ).

fof(f_12_2,plain,
    ! [U_19] : ti(fun(fun(U_19,fun(U_19,U_19)),fun(fun(fun(U_19,bool),U_19),bool)),finite2073411215e_idem(U_19)) = finite2073411215e_idem(U_19),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

fof(f_12_3,plain,
    ! [U_19] : ti(fun(fun(U_19,fun(U_19,U_19)),fun(fun(fun(U_19,bool),U_19),bool)),finite2073411215e_idem(U_19)) = finite2073411215e_idem(U_19),
    inference(definitional_conversion,[status(esa)],[f_12_2]) ).

cnf(f_12_4,plain,
    ti(fun(fun(U_19,fun(U_19,U_19)),fun(fun(fun(U_19,bool),U_19),bool)),finite2073411215e_idem(U_19)) = finite2073411215e_idem(U_19),
    inference(clausify,[status(thm)],[f_12_3]) ).

fof(f_13_1,plain,
    ! [X_c] :
      ( ti(fun(X_c,fun(X_c,X_c)),minus_minus(X_c)) = minus_minus(X_c)
      | ~ minus(X_c) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Ominus__class_Ominus_res]) ).

fof(f_13_2,plain,
    ! [U_20] :
      ( ti(fun(U_20,fun(U_20,U_20)),minus_minus(U_20)) = minus_minus(U_20)
      | ~ minus(U_20) ),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

fof(f_13_3,plain,
    ! [U_20] :
      ( ti(fun(U_20,fun(U_20,U_20)),minus_minus(U_20)) = minus_minus(U_20)
      | ~ minus(U_20) ),
    inference(definitional_conversion,[status(esa)],[f_13_2]) ).

cnf(f_13_4,plain,
    ( ti(fun(U_20,fun(U_20,U_20)),minus_minus(U_20)) = minus_minus(U_20)
    | ~ minus(U_20) ),
    inference(clausify,[status(thm)],[f_13_3]) ).

fof(f_14_1,plain,
    ! [X_b] :
      ( ti(X_b,one_one(X_b)) = one_one(X_b)
      | ~ one(X_b) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oone__class_Oone_res]) ).

fof(f_14_2,plain,
    ! [U_21] :
      ( ti(U_21,one_one(U_21)) = one_one(U_21)
      | ~ one(U_21) ),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

fof(f_14_3,plain,
    ! [U_21] :
      ( ti(U_21,one_one(U_21)) = one_one(U_21)
      | ~ one(U_21) ),
    inference(definitional_conversion,[status(esa)],[f_14_2]) ).

cnf(f_14_4,plain,
    ( ti(U_21,one_one(U_21)) = one_one(U_21)
    | ~ one(U_21) ),
    inference(clausify,[status(thm)],[f_14_3]) ).

fof(f_15_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a)
      | ~ monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_0_res]) ).

fof(f_15_2,plain,
    ! [U_22] :
      ( ti(fun(U_22,fun(U_22,U_22)),plus_plus(U_22)) = plus_plus(U_22)
      | ~ monoid_add(U_22) ),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

fof(f_15_3,plain,
    ! [U_22] :
      ( ti(fun(U_22,fun(U_22,U_22)),plus_plus(U_22)) = plus_plus(U_22)
      | ~ monoid_add(U_22) ),
    inference(definitional_conversion,[status(esa)],[f_15_2]) ).

cnf(f_15_4,plain,
    ( ti(fun(U_22,fun(U_22,U_22)),plus_plus(U_22)) = plus_plus(U_22)
    | ~ monoid_add(U_22) ),
    inference(clausify,[status(thm)],[f_15_3]) ).

fof(f_16_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a)
      | ~ ab_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_1_res]) ).

fof(f_16_2,plain,
    ! [U_23] :
      ( ti(fun(U_23,fun(U_23,U_23)),plus_plus(U_23)) = plus_plus(U_23)
      | ~ ab_semigroup_add(U_23) ),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

fof(f_16_3,plain,
    ! [U_23] :
      ( ti(fun(U_23,fun(U_23,U_23)),plus_plus(U_23)) = plus_plus(U_23)
      | ~ ab_semigroup_add(U_23) ),
    inference(definitional_conversion,[status(esa)],[f_16_2]) ).

cnf(f_16_4,plain,
    ( ti(fun(U_23,fun(U_23,U_23)),plus_plus(U_23)) = plus_plus(U_23)
    | ~ ab_semigroup_add(U_23) ),
    inference(clausify,[status(thm)],[f_16_3]) ).

fof(f_17_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a)
      | ~ cancel_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Oplus__class_Oplus_2_res]) ).

fof(f_17_2,plain,
    ! [U_24] :
      ( ti(fun(U_24,fun(U_24,U_24)),plus_plus(U_24)) = plus_plus(U_24)
      | ~ cancel_semigroup_add(U_24) ),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

fof(f_17_3,plain,
    ! [U_24] :
      ( ti(fun(U_24,fun(U_24,U_24)),plus_plus(U_24)) = plus_plus(U_24)
      | ~ cancel_semigroup_add(U_24) ),
    inference(definitional_conversion,[status(esa)],[f_17_2]) ).

cnf(f_17_4,plain,
    ( ti(fun(U_24,fun(U_24,U_24)),plus_plus(U_24)) = plus_plus(U_24)
    | ~ cancel_semigroup_add(U_24) ),
    inference(clausify,[status(thm)],[f_17_3]) ).

fof(f_18_1,plain,
    ! [X_b] :
      ( ti(X_b,zero_zero(X_b)) = zero_zero(X_b)
      | ~ zero(X_b) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Groups_Ozero__class_Ozero_res]) ).

fof(f_18_2,plain,
    ! [U_25] :
      ( ti(U_25,zero_zero(U_25)) = zero_zero(U_25)
      | ~ zero(U_25) ),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

fof(f_18_3,plain,
    ! [U_25] :
      ( ti(U_25,zero_zero(U_25)) = zero_zero(U_25)
      | ~ zero(U_25) ),
    inference(definitional_conversion,[status(esa)],[f_18_2]) ).

cnf(f_18_4,plain,
    ( ti(U_25,zero_zero(U_25)) = zero_zero(U_25)
    | ~ zero(U_25) ),
    inference(clausify,[status(thm)],[f_18_3]) ).

fof(f_19_1,plain,
    ! [X_b] : ti(fun(fun(X_b,bool),X_b),the(X_b)) = the(X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_HOL_OThe_res]) ).

fof(f_19_2,plain,
    ! [U_26] : ti(fun(fun(U_26,bool),U_26),the(U_26)) = the(U_26),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

fof(f_19_3,plain,
    ! [U_26] : ti(fun(fun(U_26,bool),U_26),the(U_26)) = the(U_26),
    inference(definitional_conversion,[status(esa)],[f_19_2]) ).

cnf(f_19_4,plain,
    ti(fun(fun(U_26,bool),U_26),the(U_26)) = the(U_26),
    inference(clausify,[status(thm)],[f_19_3]) ).

fof(f_20_1,plain,
    ! [X_a] : ti(X_a,undefined(X_a)) = undefined(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_HOL_Oundefined_res]) ).

fof(f_20_2,plain,
    ! [U_27] : ti(U_27,undefined(U_27)) = undefined(U_27),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

fof(f_20_3,plain,
    ! [U_27] : ti(U_27,undefined(U_27)) = undefined(U_27),
    inference(definitional_conversion,[status(esa)],[f_20_2]) ).

cnf(f_20_4,plain,
    ti(U_27,undefined(U_27)) = undefined(U_27),
    inference(clausify,[status(thm)],[f_20_3]) ).

fof(f_21_1,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(fof_nnf,[status(thm)],[tsy_c_Nat_OSuc_res]) ).

fof(f_21_2,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(definitional_conversion,[status(esa)],[f_21_1]) ).

cnf(f_21_3,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(clausify,[status(thm)],[f_21_2]) ).

fof(f_22_1,plain,
    ! [X_b] : ti(fun(X_b,fun(fun(nat,X_b),fun(nat,X_b))),nat_case(X_b)) = nat_case(X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Nat_Onat_Onat__case_res]) ).

fof(f_22_2,plain,
    ! [U_28] : ti(fun(U_28,fun(fun(nat,U_28),fun(nat,U_28))),nat_case(U_28)) = nat_case(U_28),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

fof(f_22_3,plain,
    ! [U_28] : ti(fun(U_28,fun(fun(nat,U_28),fun(nat,U_28))),nat_case(U_28)) = nat_case(U_28),
    inference(definitional_conversion,[status(esa)],[f_22_2]) ).

cnf(f_22_4,plain,
    ti(fun(U_28,fun(fun(nat,U_28),fun(nat,U_28))),nat_case(U_28)) = nat_case(U_28),
    inference(clausify,[status(thm)],[f_22_3]) ).

fof(f_23_1,plain,
    ti(fun(option(com),com),the_1(com)) = the_1(com),
    inference(fof_nnf,[status(thm)],[tsy_c_Option_Othe_res]) ).

fof(f_23_2,plain,
    ti(fun(option(com),com),the_1(com)) = the_1(com),
    inference(definitional_conversion,[status(esa)],[f_23_1]) ).

cnf(f_23_3,plain,
    ti(fun(option(com),com),the_1(com)) = the_1(com),
    inference(clausify,[status(thm)],[f_23_2]) ).

fof(f_24_1,plain,
    ! [X_c] :
      ( ti(X_c,bot_bot(X_c)) = bot_bot(X_c)
      | ~ bot(X_c) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Obot__class_Obot_res]) ).

fof(f_24_2,plain,
    ! [U_29] :
      ( ti(U_29,bot_bot(U_29)) = bot_bot(U_29)
      | ~ bot(U_29) ),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

fof(f_24_3,plain,
    ! [U_29] :
      ( ti(U_29,bot_bot(U_29)) = bot_bot(U_29)
      | ~ bot(U_29) ),
    inference(definitional_conversion,[status(esa)],[f_24_2]) ).

cnf(f_24_4,plain,
    ( ti(U_29,bot_bot(U_29)) = bot_bot(U_29)
    | ~ bot(U_29) ),
    inference(clausify,[status(thm)],[f_24_3]) ).

fof(f_25_1,plain,
    ! [X_a] :
      ( ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a)
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless_res]) ).

fof(f_25_2,plain,
    ! [U_30] :
      ( ti(fun(U_30,fun(U_30,bool)),ord_less(U_30)) = ord_less(U_30)
      | ~ ord(U_30) ),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

fof(f_25_3,plain,
    ! [U_30] :
      ( ti(fun(U_30,fun(U_30,bool)),ord_less(U_30)) = ord_less(U_30)
      | ~ ord(U_30) ),
    inference(definitional_conversion,[status(esa)],[f_25_2]) ).

cnf(f_25_4,plain,
    ( ti(fun(U_30,fun(U_30,bool)),ord_less(U_30)) = ord_less(U_30)
    | ~ ord(U_30) ),
    inference(clausify,[status(thm)],[f_25_3]) ).

fof(f_26_1,plain,
    ! [X_c] :
      ( ti(fun(X_c,fun(X_c,bool)),ord_less_eq(X_c)) = ord_less_eq(X_c)
      | ~ ord(X_c) ),
    inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless__eq_res]) ).

fof(f_26_2,plain,
    ! [U_31] :
      ( ti(fun(U_31,fun(U_31,bool)),ord_less_eq(U_31)) = ord_less_eq(U_31)
      | ~ ord(U_31) ),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

fof(f_26_3,plain,
    ! [U_31] :
      ( ti(fun(U_31,fun(U_31,bool)),ord_less_eq(U_31)) = ord_less_eq(U_31)
      | ~ ord(U_31) ),
    inference(definitional_conversion,[status(esa)],[f_26_2]) ).

cnf(f_26_4,plain,
    ( ti(fun(U_31,fun(U_31,bool)),ord_less_eq(U_31)) = ord_less_eq(U_31)
    | ~ ord(U_31) ),
    inference(clausify,[status(thm)],[f_26_3]) ).

fof(f_27_1,plain,
    ! [X_b] : ti(fun(X_b,fun(fun(X_b,bool),X_b)),partial_flat_lub(X_b)) = partial_flat_lub(X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Partial__Function_Oflat__lub_res]) ).

fof(f_27_2,plain,
    ! [U_32] : ti(fun(U_32,fun(fun(U_32,bool),U_32)),partial_flat_lub(U_32)) = partial_flat_lub(U_32),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

fof(f_27_3,plain,
    ! [U_32] : ti(fun(U_32,fun(fun(U_32,bool),U_32)),partial_flat_lub(U_32)) = partial_flat_lub(U_32),
    inference(definitional_conversion,[status(esa)],[f_27_2]) ).

cnf(f_27_4,plain,
    ti(fun(U_32,fun(fun(U_32,bool),U_32)),partial_flat_lub(U_32)) = partial_flat_lub(U_32),
    inference(clausify,[status(thm)],[f_27_3]) ).

fof(f_28_1,plain,
    ! [X_b] : ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b)) = collect(X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Set_OCollect_res]) ).

fof(f_28_2,plain,
    ! [U_33] : ti(fun(fun(U_33,bool),fun(U_33,bool)),collect(U_33)) = collect(U_33),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

fof(f_28_3,plain,
    ! [U_33] : ti(fun(fun(U_33,bool),fun(U_33,bool)),collect(U_33)) = collect(U_33),
    inference(definitional_conversion,[status(esa)],[f_28_2]) ).

cnf(f_28_4,plain,
    ti(fun(fun(U_33,bool),fun(U_33,bool)),collect(U_33)) = collect(U_33),
    inference(clausify,[status(thm)],[f_28_3]) ).

fof(f_29_1,plain,
    ! [X_b,X_c] : ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool))),image(X_b,X_c)) = image(X_b,X_c),
    inference(fof_nnf,[status(thm)],[tsy_c_Set_Oimage_res]) ).

fof(f_29_2,plain,
    ! [U_35,U_34] : ti(fun(fun(U_35,U_34),fun(fun(U_35,bool),fun(U_34,bool))),image(U_35,U_34)) = image(U_35,U_34),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

fof(f_29_3,plain,
    ! [U_34,U_35] : ti(fun(fun(U_35,U_34),fun(fun(U_35,bool),fun(U_34,bool))),image(U_35,U_34)) = image(U_35,U_34),
    inference(definitional_conversion,[status(esa)],[f_29_2]) ).

cnf(f_29_4,plain,
    ti(fun(fun(U_35,U_34),fun(fun(U_35,bool),fun(U_34,bool))),image(U_35,U_34)) = image(U_35,U_34),
    inference(clausify,[status(thm)],[f_29_3]) ).

fof(f_30_1,plain,
    ! [X_b] : ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b)) = insert(X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Set_Oinsert_res]) ).

fof(f_30_2,plain,
    ! [U_36] : ti(fun(U_36,fun(fun(U_36,bool),fun(U_36,bool))),insert(U_36)) = insert(U_36),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

fof(f_30_3,plain,
    ! [U_36] : ti(fun(U_36,fun(fun(U_36,bool),fun(U_36,bool))),insert(U_36)) = insert(U_36),
    inference(definitional_conversion,[status(esa)],[f_30_2]) ).

cnf(f_30_4,plain,
    ti(fun(U_36,fun(fun(U_36,bool),fun(U_36,bool))),insert(U_36)) = insert(U_36),
    inference(clausify,[status(thm)],[f_30_3]) ).

fof(f_31_1,plain,
    ! [X_b] : ti(fun(fun(X_b,bool),X_b),the_elem(X_b)) = the_elem(X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_Set_Othe__elem_res]) ).

fof(f_31_2,plain,
    ! [U_37] : ti(fun(fun(U_37,bool),U_37),the_elem(U_37)) = the_elem(U_37),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

fof(f_31_3,plain,
    ! [U_37] : ti(fun(fun(U_37,bool),U_37),the_elem(U_37)) = the_elem(U_37),
    inference(definitional_conversion,[status(esa)],[f_31_2]) ).

cnf(f_31_4,plain,
    ti(fun(fun(U_37,bool),U_37),the_elem(U_37)) = the_elem(U_37),
    inference(clausify,[status(thm)],[f_31_3]) ).

fof(f_32_1,plain,
    ! [X_b,X_c] : ti(fun(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool))),sum_Plus(X_b,X_c)) = sum_Plus(X_b,X_c),
    inference(fof_nnf,[status(thm)],[tsy_c_Sum__Type_OPlus_res]) ).

fof(f_32_2,plain,
    ! [U_39,U_38] : ti(fun(fun(U_39,bool),fun(fun(U_38,bool),fun(sum_sum(U_39,U_38),bool))),sum_Plus(U_39,U_38)) = sum_Plus(U_39,U_38),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

fof(f_32_3,plain,
    ! [U_38,U_39] : ti(fun(fun(U_39,bool),fun(fun(U_38,bool),fun(sum_sum(U_39,U_38),bool))),sum_Plus(U_39,U_38)) = sum_Plus(U_39,U_38),
    inference(definitional_conversion,[status(esa)],[f_32_2]) ).

cnf(f_32_4,plain,
    ti(fun(fun(U_39,bool),fun(fun(U_38,bool),fun(sum_sum(U_39,U_38),bool))),sum_Plus(U_39,U_38)) = sum_Plus(U_39,U_38),
    inference(clausify,[status(thm)],[f_32_3]) ).

fof(f_33_1,plain,
    ti(bool,fFalse) = fFalse,
    inference(fof_nnf,[status(thm)],[tsy_c_fFalse_res]) ).

fof(f_33_2,plain,
    ti(bool,fFalse) = fFalse,
    inference(definitional_conversion,[status(esa)],[f_33_1]) ).

cnf(f_33_3,plain,
    ti(bool,fFalse) = fFalse,
    inference(clausify,[status(thm)],[f_33_2]) ).

fof(f_34_1,plain,
    ti(fun(bool,bool),fNot) = fNot,
    inference(fof_nnf,[status(thm)],[tsy_c_fNot_res]) ).

fof(f_34_2,plain,
    ti(fun(bool,bool),fNot) = fNot,
    inference(definitional_conversion,[status(esa)],[f_34_1]) ).

cnf(f_34_3,plain,
    ti(fun(bool,bool),fNot) = fNot,
    inference(clausify,[status(thm)],[f_34_2]) ).

fof(f_35_1,plain,
    ti(bool,fTrue) = fTrue,
    inference(fof_nnf,[status(thm)],[tsy_c_fTrue_res]) ).

fof(f_35_2,plain,
    ti(bool,fTrue) = fTrue,
    inference(definitional_conversion,[status(esa)],[f_35_1]) ).

cnf(f_35_3,plain,
    ti(bool,fTrue) = fTrue,
    inference(clausify,[status(thm)],[f_35_2]) ).

fof(f_36_1,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(fof_nnf,[status(thm)],[tsy_c_fconj_res]) ).

fof(f_36_2,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(definitional_conversion,[status(esa)],[f_36_1]) ).

cnf(f_36_3,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(clausify,[status(thm)],[f_36_2]) ).

fof(f_37_1,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(fof_nnf,[status(thm)],[tsy_c_fdisj_res]) ).

fof(f_37_2,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(definitional_conversion,[status(esa)],[f_37_1]) ).

cnf(f_37_3,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(clausify,[status(thm)],[f_37_2]) ).

fof(f_38_1,plain,
    ! [X_a] : ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a),
    inference(fof_nnf,[status(thm)],[tsy_c_fequal_res]) ).

fof(f_38_2,plain,
    ! [U_40] : ti(fun(U_40,fun(U_40,bool)),fequal(U_40)) = fequal(U_40),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

fof(f_38_3,plain,
    ! [U_40] : ti(fun(U_40,fun(U_40,bool)),fequal(U_40)) = fequal(U_40),
    inference(definitional_conversion,[status(esa)],[f_38_2]) ).

cnf(f_38_4,plain,
    ti(fun(U_40,fun(U_40,bool)),fequal(U_40)) = fequal(U_40),
    inference(clausify,[status(thm)],[f_38_3]) ).

fof(f_39_1,plain,
    ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
    inference(fof_nnf,[status(thm)],[tsy_c_fimplies_res]) ).

fof(f_39_2,plain,
    ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
    inference(definitional_conversion,[status(esa)],[f_39_1]) ).

cnf(f_39_3,plain,
    ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
    inference(clausify,[status(thm)],[f_39_2]) ).

fof(f_40_1,plain,
    ! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1),
    inference(fof_nnf,[status(thm)],[tsy_c_hAPP_arg1]) ).

fof(f_40_2,plain,
    ! [U_44,U_43,U_42,U_41] : hAPP(U_44,U_43,ti(fun(U_44,U_43),U_42),U_41) = hAPP(U_44,U_43,U_42,U_41),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

fof(f_40_3,plain,
    ! [U_43,U_41,U_42,U_44] : hAPP(U_44,U_43,ti(fun(U_44,U_43),U_42),U_41) = hAPP(U_44,U_43,U_42,U_41),
    inference(definitional_conversion,[status(esa)],[f_40_2]) ).

cnf(f_40_4,plain,
    hAPP(U_44,U_43,ti(fun(U_44,U_43),U_42),U_41) = hAPP(U_44,U_43,U_42,U_41),
    inference(clausify,[status(thm)],[f_40_3]) ).

fof(f_41_1,plain,
    ! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
    inference(fof_nnf,[status(thm)],[tsy_c_hAPP_arg2]) ).

fof(f_41_2,plain,
    ! [U_48,U_47,U_46,U_45] : hAPP(U_48,U_47,U_46,ti(U_48,U_45)) = hAPP(U_48,U_47,U_46,U_45),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

fof(f_41_3,plain,
    ! [U_46,U_48,U_47,U_45] : hAPP(U_48,U_47,U_46,ti(U_48,U_45)) = hAPP(U_48,U_47,U_46,U_45),
    inference(definitional_conversion,[status(esa)],[f_41_2]) ).

cnf(f_41_4,plain,
    hAPP(U_48,U_47,U_46,ti(U_48,U_45)) = hAPP(U_48,U_47,U_46,U_45),
    inference(clausify,[status(thm)],[f_41_3]) ).

fof(f_42_1,plain,
    ! [X_c,X_a,B_1_1,B_2_1] : ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
    inference(fof_nnf,[status(thm)],[tsy_c_hAPP_res]) ).

fof(f_42_2,plain,
    ! [U_52,U_51,U_50,U_49] : ti(U_52,hAPP(U_51,U_52,U_50,U_49)) = hAPP(U_51,U_52,U_50,U_49),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

fof(f_42_3,plain,
    ! [U_50,U_49,U_51,U_52] : ti(U_52,hAPP(U_51,U_52,U_50,U_49)) = hAPP(U_51,U_52,U_50,U_49),
    inference(definitional_conversion,[status(esa)],[f_42_2]) ).

cnf(f_42_4,plain,
    ti(U_52,hAPP(U_51,U_52,U_50,U_49)) = hAPP(U_51,U_52,U_50,U_49),
    inference(clausify,[status(thm)],[f_42_3]) ).

fof(f_43_1,plain,
    ! [B_1_1] :
      ( ( hBOOL(ti(bool,B_1_1))
        | ~ hBOOL(B_1_1) )
      & ( hBOOL(B_1_1)
        | ~ hBOOL(ti(bool,B_1_1)) ) ),
    inference(fof_nnf,[status(thm)],[tsy_c_hBOOL_arg1]) ).

fof(f_43_2,plain,
    ! [U_53] :
      ( ( hBOOL(ti(bool,U_53))
        | ~ hBOOL(U_53) )
      & ( hBOOL(U_53)
        | ~ hBOOL(ti(bool,U_53)) ) ),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

fof(f_43_3,plain,
    ( ! [U_55] :
        ( hBOOL(ti(bool,U_55))
        | ~ hBOOL(U_55) )
    & ! [U_54] :
        ( hBOOL(U_54)
        | ~ hBOOL(ti(bool,U_54)) ) ),
    inference(miniscope,[status(thm)],[f_43_2]) ).

fof(f_43_4,plain,
    ( ! [U_55] :
        ( hBOOL(ti(bool,U_55))
        | ~ hBOOL(U_55) )
    & ! [U_54] :
        ( hBOOL(U_54)
        | ~ hBOOL(ti(bool,U_54)) ) ),
    inference(definitional_conversion,[status(esa)],[f_43_3]) ).

cnf(f_43_5,plain,
    ( hBOOL(U_54)
    | ~ hBOOL(ti(bool,U_54)) ),
    inference(clausify,[status(thm)],[f_43_4]) ).

cnf(f_43_6,plain,
    ( hBOOL(ti(bool,U_55))
    | ~ hBOOL(U_55) ),
    inference(clausify,[status(thm)],[f_43_4]) ).

fof(f_44_1,plain,
    ! [X_b] : ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b),
    inference(fof_nnf,[status(thm)],[tsy_c_member_res]) ).

fof(f_44_2,plain,
    ! [U_56] : ti(fun(U_56,fun(fun(U_56,bool),bool)),member(U_56)) = member(U_56),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

fof(f_44_3,plain,
    ! [U_56] : ti(fun(U_56,fun(fun(U_56,bool),bool)),member(U_56)) = member(U_56),
    inference(definitional_conversion,[status(esa)],[f_44_2]) ).

cnf(f_44_4,plain,
    ti(fun(U_56,fun(fun(U_56,bool),bool)),member(U_56)) = member(U_56),
    inference(clausify,[status(thm)],[f_44_3]) ).

fof(f_45_1,plain,
    ti(fun(x_a,bool),g) = g,
    inference(fof_nnf,[status(thm)],[tsy_v_G_res]) ).

fof(f_45_2,plain,
    ti(fun(x_a,bool),g) = g,
    inference(definitional_conversion,[status(esa)],[f_45_1]) ).

cnf(f_45_3,plain,
    ti(fun(x_a,bool),g) = g,
    inference(clausify,[status(thm)],[f_45_2]) ).

fof(f_46_1,plain,
    ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
    inference(fof_nnf,[status(thm)],[tsy_v_P_res]) ).

fof(f_46_2,plain,
    ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
    inference(definitional_conversion,[status(esa)],[f_46_1]) ).

cnf(f_46_3,plain,
    ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p) = p,
    inference(clausify,[status(thm)],[f_46_2]) ).

fof(f_47_1,plain,
    ti(fun(pname,bool),u) = u,
    inference(fof_nnf,[status(thm)],[tsy_v_U_res]) ).

fof(f_47_2,plain,
    ti(fun(pname,bool),u) = u,
    inference(definitional_conversion,[status(esa)],[f_47_1]) ).

cnf(f_47_3,plain,
    ti(fun(pname,bool),u) = u,
    inference(clausify,[status(thm)],[f_47_2]) ).

fof(f_48_1,plain,
    ti(fun(com,x_a),mgt) = mgt,
    inference(fof_nnf,[status(thm)],[tsy_v_mgt_res]) ).

fof(f_48_2,plain,
    ti(fun(com,x_a),mgt) = mgt,
    inference(definitional_conversion,[status(esa)],[f_48_1]) ).

cnf(f_48_3,plain,
    ti(fun(com,x_a),mgt) = mgt,
    inference(clausify,[status(thm)],[f_48_2]) ).

fof(f_49_1,plain,
    ti(fun(pname,x_a),mgt_call) = mgt_call,
    inference(fof_nnf,[status(thm)],[tsy_v_mgt__call_res]) ).

fof(f_49_2,plain,
    ti(fun(pname,x_a),mgt_call) = mgt_call,
    inference(definitional_conversion,[status(esa)],[f_49_1]) ).

cnf(f_49_3,plain,
    ti(fun(pname,x_a),mgt_call) = mgt_call,
    inference(clausify,[status(thm)],[f_49_2]) ).

fof(f_50_1,plain,
    ti(nat,na) = na,
    inference(fof_nnf,[status(thm)],[tsy_v_na_res]) ).

fof(f_50_2,plain,
    ti(nat,na) = na,
    inference(definitional_conversion,[status(esa)],[f_50_1]) ).

cnf(f_50_3,plain,
    ti(nat,na) = na,
    inference(clausify,[status(thm)],[f_50_2]) ).

fof(f_51_1,plain,
    ti(pname,pn) = pn,
    inference(fof_nnf,[status(thm)],[tsy_v_pn_res]) ).

fof(f_51_2,plain,
    ti(pname,pn) = pn,
    inference(definitional_conversion,[status(esa)],[f_51_1]) ).

cnf(f_51_3,plain,
    ti(pname,pn) = pn,
    inference(clausify,[status(thm)],[f_51_2]) ).

fof(f_52_1,plain,
    ti(fun(com,bool),wt) = wt,
    inference(fof_nnf,[status(thm)],[tsy_v_wt_res]) ).

fof(f_52_2,plain,
    ti(fun(com,bool),wt) = wt,
    inference(definitional_conversion,[status(esa)],[f_52_1]) ).

cnf(f_52_3,plain,
    ti(fun(com,bool),wt) = wt,
    inference(clausify,[status(thm)],[f_52_2]) ).

fof(f_53_1,plain,
    ! [Ts,G_1] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),Ts))
      | ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),Ts),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_0_assms_I1_J]) ).

fof(f_53_2,plain,
    ! [U_58,U_57] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_57),U_58))
      | ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),U_58),U_57)) ),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

fof(f_53_3,plain,
    ! [U_57,U_58] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_57),U_58))
      | ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),U_58),U_57)) ),
    inference(definitional_conversion,[status(esa)],[f_53_2]) ).

cnf(f_53_4,plain,
    ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_57),U_58))
    | ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),U_58),U_57)) ),
    inference(clausify,[status(thm)],[f_53_3]) ).

fof(f_54_1,plain,
    ! [X_b,A_3] :
      ( hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite(fun(X_b,bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,bool),bool),collect(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),combc(fun(X_b,bool),fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool))),A_3))))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_1_finite__Collect__subsets]) ).

fof(f_54_2,plain,
    ! [U_60,U_59] :
      ( hBOOL(hAPP(fun(fun(U_60,bool),bool),bool,finite_finite(fun(U_60,bool)),hAPP(fun(fun(U_60,bool),bool),fun(fun(U_60,bool),bool),collect(fun(U_60,bool)),hAPP(fun(U_60,bool),fun(fun(U_60,bool),bool),hAPP(fun(fun(U_60,bool),fun(fun(U_60,bool),bool)),fun(fun(U_60,bool),fun(fun(U_60,bool),bool)),combc(fun(U_60,bool),fun(U_60,bool),bool),ord_less_eq(fun(U_60,bool))),U_59))))
      | ~ hBOOL(hAPP(fun(U_60,bool),bool,finite_finite(U_60),U_59)) ),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

fof(f_54_3,plain,
    ! [U_60,U_59] :
      ( hBOOL(hAPP(fun(fun(U_60,bool),bool),bool,finite_finite(fun(U_60,bool)),hAPP(fun(fun(U_60,bool),bool),fun(fun(U_60,bool),bool),collect(fun(U_60,bool)),hAPP(fun(U_60,bool),fun(fun(U_60,bool),bool),hAPP(fun(fun(U_60,bool),fun(fun(U_60,bool),bool)),fun(fun(U_60,bool),fun(fun(U_60,bool),bool)),combc(fun(U_60,bool),fun(U_60,bool),bool),ord_less_eq(fun(U_60,bool))),U_59))))
      | ~ hBOOL(hAPP(fun(U_60,bool),bool,finite_finite(U_60),U_59)) ),
    inference(definitional_conversion,[status(esa)],[f_54_2]) ).

cnf(f_54_4,plain,
    ( hBOOL(hAPP(fun(fun(U_60,bool),bool),bool,finite_finite(fun(U_60,bool)),hAPP(fun(fun(U_60,bool),bool),fun(fun(U_60,bool),bool),collect(fun(U_60,bool)),hAPP(fun(U_60,bool),fun(fun(U_60,bool),bool),hAPP(fun(fun(U_60,bool),fun(fun(U_60,bool),bool)),fun(fun(U_60,bool),fun(fun(U_60,bool),bool)),combc(fun(U_60,bool),fun(U_60,bool),bool),ord_less_eq(fun(U_60,bool))),U_59))))
    | ~ hBOOL(hAPP(fun(U_60,bool),bool,finite_finite(U_60),U_59)) ),
    inference(clausify,[status(thm)],[f_54_3]) ).

fof(f_55_1,plain,
    ! [X_c,X_b,H,F_2] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),H),F_2)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_2_finite__imageI]) ).

fof(f_55_2,plain,
    ! [U_64,U_63,U_62,U_61] :
      ( hBOOL(hAPP(fun(U_64,bool),bool,finite_finite(U_64),hAPP(fun(U_63,bool),fun(U_64,bool),hAPP(fun(U_63,U_64),fun(fun(U_63,bool),fun(U_64,bool)),image(U_63,U_64),U_62),U_61)))
      | ~ hBOOL(hAPP(fun(U_63,bool),bool,finite_finite(U_63),U_61)) ),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

fof(f_55_3,plain,
    ! [U_61,U_63,U_62,U_64] :
      ( hBOOL(hAPP(fun(U_64,bool),bool,finite_finite(U_64),hAPP(fun(U_63,bool),fun(U_64,bool),hAPP(fun(U_63,U_64),fun(fun(U_63,bool),fun(U_64,bool)),image(U_63,U_64),U_62),U_61)))
      | ~ hBOOL(hAPP(fun(U_63,bool),bool,finite_finite(U_63),U_61)) ),
    inference(definitional_conversion,[status(esa)],[f_55_2]) ).

cnf(f_55_4,plain,
    ( hBOOL(hAPP(fun(U_64,bool),bool,finite_finite(U_64),hAPP(fun(U_63,bool),fun(U_64,bool),hAPP(fun(U_63,U_64),fun(fun(U_63,bool),fun(U_64,bool)),image(U_63,U_64),U_62),U_61)))
    | ~ hBOOL(hAPP(fun(U_63,bool),bool,finite_finite(U_63),U_61)) ),
    inference(clausify,[status(thm)],[f_55_3]) ).

fof(f_56_1,plain,
    ! [X_b,A_2,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_3_finite_OinsertI]) ).

fof(f_56_2,plain,
    ! [U_67,U_66,U_65] :
      ( hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),hAPP(U_67,fun(fun(U_67,bool),fun(U_67,bool)),insert(U_67),U_66),U_65)))
      | ~ hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),U_65)) ),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

fof(f_56_3,plain,
    ! [U_65,U_67,U_66] :
      ( hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),hAPP(U_67,fun(fun(U_67,bool),fun(U_67,bool)),insert(U_67),U_66),U_65)))
      | ~ hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),U_65)) ),
    inference(definitional_conversion,[status(esa)],[f_56_2]) ).

cnf(f_56_4,plain,
    ( hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),hAPP(fun(U_67,bool),fun(U_67,bool),hAPP(U_67,fun(fun(U_67,bool),fun(U_67,bool)),insert(U_67),U_66),U_65)))
    | ~ hBOOL(hAPP(fun(U_67,bool),bool,finite_finite(U_67),U_65)) ),
    inference(clausify,[status(thm)],[f_56_3]) ).

fof(f_57_1,plain,
    ! [X_c,X_b,F,A_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_c,bool),nat,finite_card(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_4_card__image__le]) ).

fof(f_57_2,plain,
    ! [U_71,U_70,U_69,U_68] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_71,bool),nat,finite_card(U_71),hAPP(fun(U_70,bool),fun(U_71,bool),hAPP(fun(U_70,U_71),fun(fun(U_70,bool),fun(U_71,bool)),image(U_70,U_71),U_69),U_68))),hAPP(fun(U_70,bool),nat,finite_card(U_70),U_68)))
      | ~ hBOOL(hAPP(fun(U_70,bool),bool,finite_finite(U_70),U_68)) ),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

fof(f_57_3,plain,
    ! [U_68,U_70,U_69,U_71] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_71,bool),nat,finite_card(U_71),hAPP(fun(U_70,bool),fun(U_71,bool),hAPP(fun(U_70,U_71),fun(fun(U_70,bool),fun(U_71,bool)),image(U_70,U_71),U_69),U_68))),hAPP(fun(U_70,bool),nat,finite_card(U_70),U_68)))
      | ~ hBOOL(hAPP(fun(U_70,bool),bool,finite_finite(U_70),U_68)) ),
    inference(definitional_conversion,[status(esa)],[f_57_2]) ).

cnf(f_57_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_71,bool),nat,finite_card(U_71),hAPP(fun(U_70,bool),fun(U_71,bool),hAPP(fun(U_70,U_71),fun(fun(U_70,bool),fun(U_71,bool)),image(U_70,U_71),U_69),U_68))),hAPP(fun(U_70,bool),nat,finite_card(U_70),U_68)))
    | ~ hBOOL(hAPP(fun(U_70,bool),bool,finite_finite(U_70),U_68)) ),
    inference(clausify,[status(thm)],[f_57_3]) ).

fof(f_58_1,plain,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_5_card__mono]) ).

fof(f_58_2,plain,
    ! [U_74,U_73,U_72] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_74,bool),nat,finite_card(U_74),U_73)),hAPP(fun(U_74,bool),nat,finite_card(U_74),U_72)))
      | ~ hBOOL(hAPP(fun(U_74,bool),bool,hAPP(fun(U_74,bool),fun(fun(U_74,bool),bool),ord_less_eq(fun(U_74,bool)),U_73),U_72))
      | ~ hBOOL(hAPP(fun(U_74,bool),bool,finite_finite(U_74),U_72)) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

fof(f_58_3,plain,
    ! [U_72,U_73,U_74] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_74,bool),nat,finite_card(U_74),U_73)),hAPP(fun(U_74,bool),nat,finite_card(U_74),U_72)))
      | ~ hBOOL(hAPP(fun(U_74,bool),bool,hAPP(fun(U_74,bool),fun(fun(U_74,bool),bool),ord_less_eq(fun(U_74,bool)),U_73),U_72))
      | ~ hBOOL(hAPP(fun(U_74,bool),bool,finite_finite(U_74),U_72)) ),
    inference(definitional_conversion,[status(esa)],[f_58_2]) ).

cnf(f_58_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_74,bool),nat,finite_card(U_74),U_73)),hAPP(fun(U_74,bool),nat,finite_card(U_74),U_72)))
    | ~ hBOOL(hAPP(fun(U_74,bool),bool,hAPP(fun(U_74,bool),fun(fun(U_74,bool),bool),ord_less_eq(fun(U_74,bool)),U_73),U_72))
    | ~ hBOOL(hAPP(fun(U_74,bool),bool,finite_finite(U_74),U_72)) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

fof(f_59_1,plain,
    ! [X_b,A_3,B_2] :
      ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_6_card__seteq]) ).

fof(f_59_2,plain,
    ! [U_77,U_76,U_75] :
      ( ti(fun(U_77,bool),U_76) = ti(fun(U_77,bool),U_75)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_77,bool),nat,finite_card(U_77),U_75)),hAPP(fun(U_77,bool),nat,finite_card(U_77),U_76)))
      | ~ hBOOL(hAPP(fun(U_77,bool),bool,hAPP(fun(U_77,bool),fun(fun(U_77,bool),bool),ord_less_eq(fun(U_77,bool)),U_76),U_75))
      | ~ hBOOL(hAPP(fun(U_77,bool),bool,finite_finite(U_77),U_75)) ),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

fof(f_59_3,plain,
    ! [U_75,U_76,U_77] :
      ( ti(fun(U_77,bool),U_76) = ti(fun(U_77,bool),U_75)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_77,bool),nat,finite_card(U_77),U_75)),hAPP(fun(U_77,bool),nat,finite_card(U_77),U_76)))
      | ~ hBOOL(hAPP(fun(U_77,bool),bool,hAPP(fun(U_77,bool),fun(fun(U_77,bool),bool),ord_less_eq(fun(U_77,bool)),U_76),U_75))
      | ~ hBOOL(hAPP(fun(U_77,bool),bool,finite_finite(U_77),U_75)) ),
    inference(definitional_conversion,[status(esa)],[f_59_2]) ).

cnf(f_59_4,plain,
    ( ti(fun(U_77,bool),U_76) = ti(fun(U_77,bool),U_75)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_77,bool),nat,finite_card(U_77),U_75)),hAPP(fun(U_77,bool),nat,finite_card(U_77),U_76)))
    | ~ hBOOL(hAPP(fun(U_77,bool),bool,hAPP(fun(U_77,bool),fun(fun(U_77,bool),bool),ord_less_eq(fun(U_77,bool)),U_76),U_75))
    | ~ hBOOL(hAPP(fun(U_77,bool),bool,finite_finite(U_77),U_75)) ),
    inference(clausify,[status(thm)],[f_59_3]) ).

fof(f_60_1,plain,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3))))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_7_card__insert__le]) ).

fof(f_60_2,plain,
    ! [U_80,U_79,U_78] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_80,bool),nat,finite_card(U_80),U_78)),hAPP(fun(U_80,bool),nat,finite_card(U_80),hAPP(fun(U_80,bool),fun(U_80,bool),hAPP(U_80,fun(fun(U_80,bool),fun(U_80,bool)),insert(U_80),U_79),U_78))))
      | ~ hBOOL(hAPP(fun(U_80,bool),bool,finite_finite(U_80),U_78)) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

fof(f_60_3,plain,
    ! [U_80,U_78,U_79] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_80,bool),nat,finite_card(U_80),U_78)),hAPP(fun(U_80,bool),nat,finite_card(U_80),hAPP(fun(U_80,bool),fun(U_80,bool),hAPP(U_80,fun(fun(U_80,bool),fun(U_80,bool)),insert(U_80),U_79),U_78))))
      | ~ hBOOL(hAPP(fun(U_80,bool),bool,finite_finite(U_80),U_78)) ),
    inference(definitional_conversion,[status(esa)],[f_60_2]) ).

cnf(f_60_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_80,bool),nat,finite_card(U_80),U_78)),hAPP(fun(U_80,bool),nat,finite_card(U_80),hAPP(fun(U_80,bool),fun(U_80,bool),hAPP(U_80,fun(fun(U_80,bool),fun(U_80,bool)),insert(U_80),U_79),U_78))))
    | ~ hBOOL(hAPP(fun(U_80,bool),bool,finite_finite(U_80),U_78)) ),
    inference(clausify,[status(thm)],[f_60_3]) ).

fof(f_61_1,plain,
    ! [X_b,X_1,A_3] :
      ( ( ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))
          | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) )
        & ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_8_card__insert__if]) ).

fof(f_61_2,plain,
    ! [U_83,U_82,U_81] :
      ( ( ( hAPP(fun(U_83,bool),nat,finite_card(U_83),hAPP(fun(U_83,bool),fun(U_83,bool),hAPP(U_83,fun(fun(U_83,bool),fun(U_83,bool)),insert(U_83),U_82),U_81)) = hAPP(nat,nat,suc,hAPP(fun(U_83,bool),nat,finite_card(U_83),U_81))
          | hBOOL(hAPP(fun(U_83,bool),bool,hAPP(U_83,fun(fun(U_83,bool),bool),member(U_83),U_82),U_81)) )
        & ( hAPP(fun(U_83,bool),nat,finite_card(U_83),hAPP(fun(U_83,bool),fun(U_83,bool),hAPP(U_83,fun(fun(U_83,bool),fun(U_83,bool)),insert(U_83),U_82),U_81)) = hAPP(fun(U_83,bool),nat,finite_card(U_83),U_81)
          | ~ hBOOL(hAPP(fun(U_83,bool),bool,hAPP(U_83,fun(fun(U_83,bool),bool),member(U_83),U_82),U_81)) ) )
      | ~ hBOOL(hAPP(fun(U_83,bool),bool,finite_finite(U_83),U_81)) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

fof(f_61_3,plain,
    ( ! [U_81,U_83,U_82] :
        ( hAPP(fun(U_83,bool),nat,finite_card(U_83),hAPP(fun(U_83,bool),fun(U_83,bool),hAPP(U_83,fun(fun(U_83,bool),fun(U_83,bool)),insert(U_83),U_82),U_81)) = hAPP(nat,nat,suc,hAPP(fun(U_83,bool),nat,finite_card(U_83),U_81))
        | hBOOL(hAPP(fun(U_83,bool),bool,hAPP(U_83,fun(fun(U_83,bool),bool),member(U_83),U_82),U_81))
        | ~ sP0(U_81,U_83,U_82) )
    & ! [U_81,U_83,U_82] :
        ( hAPP(fun(U_83,bool),nat,finite_card(U_83),hAPP(fun(U_83,bool),fun(U_83,bool),hAPP(U_83,fun(fun(U_83,bool),fun(U_83,bool)),insert(U_83),U_82),U_81)) = hAPP(fun(U_83,bool),nat,finite_card(U_83),U_81)
        | ~ hBOOL(hAPP(fun(U_83,bool),bool,hAPP(U_83,fun(fun(U_83,bool),bool),member(U_83),U_82),U_81))
        | ~ sP0(U_81,U_83,U_82) )
    & ! [U_81,U_83,U_82] :
        ( sP0(U_81,U_83,U_82)
        | ~ hBOOL(hAPP(fun(U_83,bool),bool,finite_finite(U_83),U_81)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_61_2]) ).

cnf(f_61_4,plain,
    ( sP0(U_81,U_83,U_82)
    | ~ hBOOL(hAPP(fun(U_83,bool),bool,finite_finite(U_83),U_81)) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

cnf(f_61_5,plain,
    ( hAPP(fun(U_83,bool),nat,finite_card(U_83),hAPP(fun(U_83,bool),fun(U_83,bool),hAPP(U_83,fun(fun(U_83,bool),fun(U_83,bool)),insert(U_83),U_82),U_81)) = hAPP(fun(U_83,bool),nat,finite_card(U_83),U_81)
    | ~ hBOOL(hAPP(fun(U_83,bool),bool,hAPP(U_83,fun(fun(U_83,bool),bool),member(U_83),U_82),U_81))
    | ~ sP0(U_81,U_83,U_82) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

cnf(f_61_6,plain,
    ( hAPP(fun(U_83,bool),nat,finite_card(U_83),hAPP(fun(U_83,bool),fun(U_83,bool),hAPP(U_83,fun(fun(U_83,bool),fun(U_83,bool)),insert(U_83),U_82),U_81)) = hAPP(nat,nat,suc,hAPP(fun(U_83,bool),nat,finite_card(U_83),U_81))
    | hBOOL(hAPP(fun(U_83,bool),bool,hAPP(U_83,fun(fun(U_83,bool),bool),member(U_83),U_82),U_81))
    | ~ sP0(U_81,U_83,U_82) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

fof(f_62_1,plain,
    ! [X_b,X_1,A_3] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_9_card__insert__disjoint]) ).

fof(f_62_2,plain,
    ! [U_86,U_85,U_84] :
      ( hAPP(fun(U_86,bool),nat,finite_card(U_86),hAPP(fun(U_86,bool),fun(U_86,bool),hAPP(U_86,fun(fun(U_86,bool),fun(U_86,bool)),insert(U_86),U_85),U_84)) = hAPP(nat,nat,suc,hAPP(fun(U_86,bool),nat,finite_card(U_86),U_84))
      | hBOOL(hAPP(fun(U_86,bool),bool,hAPP(U_86,fun(fun(U_86,bool),bool),member(U_86),U_85),U_84))
      | ~ hBOOL(hAPP(fun(U_86,bool),bool,finite_finite(U_86),U_84)) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

fof(f_62_3,plain,
    ! [U_85,U_86,U_84] :
      ( hAPP(fun(U_86,bool),nat,finite_card(U_86),hAPP(fun(U_86,bool),fun(U_86,bool),hAPP(U_86,fun(fun(U_86,bool),fun(U_86,bool)),insert(U_86),U_85),U_84)) = hAPP(nat,nat,suc,hAPP(fun(U_86,bool),nat,finite_card(U_86),U_84))
      | hBOOL(hAPP(fun(U_86,bool),bool,hAPP(U_86,fun(fun(U_86,bool),bool),member(U_86),U_85),U_84))
      | ~ hBOOL(hAPP(fun(U_86,bool),bool,finite_finite(U_86),U_84)) ),
    inference(definitional_conversion,[status(esa)],[f_62_2]) ).

cnf(f_62_4,plain,
    ( hAPP(fun(U_86,bool),nat,finite_card(U_86),hAPP(fun(U_86,bool),fun(U_86,bool),hAPP(U_86,fun(fun(U_86,bool),fun(U_86,bool)),insert(U_86),U_85),U_84)) = hAPP(nat,nat,suc,hAPP(fun(U_86,bool),nat,finite_card(U_86),U_84))
    | hBOOL(hAPP(fun(U_86,bool),bool,hAPP(U_86,fun(fun(U_86,bool),bool),member(U_86),U_85),U_84))
    | ~ hBOOL(hAPP(fun(U_86,bool),bool,finite_finite(U_86),U_84)) ),
    inference(clausify,[status(thm)],[f_62_3]) ).

fof(f_63_1,plain,
    ! [X_b,Q_1,Pa] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Q_1))))
      | ( ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1)))
        & ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_10_finite__Collect__conjI]) ).

fof(f_63_2,plain,
    ! [U_89,U_88,U_87] :
      ( hBOOL(hAPP(fun(U_89,bool),bool,finite_finite(U_89),hAPP(fun(U_89,bool),fun(U_89,bool),collect(U_89),hAPP(fun(U_89,bool),fun(U_89,bool),hAPP(fun(U_89,fun(bool,bool)),fun(fun(U_89,bool),fun(U_89,bool)),combs(U_89,bool,bool),hAPP(fun(U_89,bool),fun(U_89,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_89,bool),fun(U_89,fun(bool,bool))),combb(bool,fun(bool,bool),U_89),fconj),U_87)),U_88))))
      | ( ~ hBOOL(hAPP(fun(U_89,bool),bool,finite_finite(U_89),hAPP(fun(U_89,bool),fun(U_89,bool),collect(U_89),U_88)))
        & ~ hBOOL(hAPP(fun(U_89,bool),bool,finite_finite(U_89),hAPP(fun(U_89,bool),fun(U_89,bool),collect(U_89),U_87))) ) ),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

fof(f_63_3,plain,
    ( ! [U_87,U_89,U_88] :
        ( ~ hBOOL(hAPP(fun(U_89,bool),bool,finite_finite(U_89),hAPP(fun(U_89,bool),fun(U_89,bool),collect(U_89),U_88)))
        | ~ sP1(U_87,U_89,U_88) )
    & ! [U_87,U_89,U_88] :
        ( ~ hBOOL(hAPP(fun(U_89,bool),bool,finite_finite(U_89),hAPP(fun(U_89,bool),fun(U_89,bool),collect(U_89),U_87)))
        | ~ sP1(U_87,U_89,U_88) )
    & ! [U_87,U_89,U_88] :
        ( hBOOL(hAPP(fun(U_89,bool),bool,finite_finite(U_89),hAPP(fun(U_89,bool),fun(U_89,bool),collect(U_89),hAPP(fun(U_89,bool),fun(U_89,bool),hAPP(fun(U_89,fun(bool,bool)),fun(fun(U_89,bool),fun(U_89,bool)),combs(U_89,bool,bool),hAPP(fun(U_89,bool),fun(U_89,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_89,bool),fun(U_89,fun(bool,bool))),combb(bool,fun(bool,bool),U_89),fconj),U_87)),U_88))))
        | sP1(U_87,U_89,U_88) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_63_2]) ).

cnf(f_63_4,plain,
    ( hBOOL(hAPP(fun(U_89,bool),bool,finite_finite(U_89),hAPP(fun(U_89,bool),fun(U_89,bool),collect(U_89),hAPP(fun(U_89,bool),fun(U_89,bool),hAPP(fun(U_89,fun(bool,bool)),fun(fun(U_89,bool),fun(U_89,bool)),combs(U_89,bool,bool),hAPP(fun(U_89,bool),fun(U_89,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_89,bool),fun(U_89,fun(bool,bool))),combb(bool,fun(bool,bool),U_89),fconj),U_87)),U_88))))
    | sP1(U_87,U_89,U_88) ),
    inference(clausify,[status(thm)],[f_63_3]) ).

cnf(f_63_5,plain,
    ( ~ hBOOL(hAPP(fun(U_89,bool),bool,finite_finite(U_89),hAPP(fun(U_89,bool),fun(U_89,bool),collect(U_89),U_87)))
    | ~ sP1(U_87,U_89,U_88) ),
    inference(clausify,[status(thm)],[f_63_3]) ).

cnf(f_63_6,plain,
    ( ~ hBOOL(hAPP(fun(U_89,bool),bool,finite_finite(U_89),hAPP(fun(U_89,bool),fun(U_89,bool),collect(U_89),U_88)))
    | ~ sP1(U_87,U_89,U_88) ),
    inference(clausify,[status(thm)],[f_63_3]) ).

fof(f_64_1,plain,
    ! [N,M] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) ),
    inference(fof_nnf,[status(thm)],[fact_11_Suc__diff__le]) ).

fof(f_64_2,plain,
    ! [U_91,U_90] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_90)),U_91) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_90),U_91))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_91),U_90)) ),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

fof(f_64_3,plain,
    ! [U_90,U_91] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_90)),U_91) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_90),U_91))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_91),U_90)) ),
    inference(definitional_conversion,[status(esa)],[f_64_2]) ).

cnf(f_64_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_90)),U_91) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_90),U_91))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_91),U_90)) ),
    inference(clausify,[status(thm)],[f_64_3]) ).

fof(f_65_1,plain,
    ! [K_2] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),K_2)))),
    inference(fof_nnf,[status(thm)],[fact_12_finite__Collect__le__nat]) ).

fof(f_65_2,plain,
    ! [U_92] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),U_92)))),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

fof(f_65_3,plain,
    ! [U_92] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),U_92)))),
    inference(definitional_conversion,[status(esa)],[f_65_2]) ).

cnf(f_65_4,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),U_92)))),
    inference(clausify,[status(thm)],[f_65_3]) ).

fof(f_66_1,plain,
    ! [Na] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),Na))) = hAPP(nat,nat,suc,Na),
    inference(fof_nnf,[status(thm)],[fact_13_card__Collect__le__nat]) ).

fof(f_66_2,plain,
    ! [U_93] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),U_93))) = hAPP(nat,nat,suc,U_93),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

fof(f_66_3,plain,
    ! [U_93] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),U_93))) = hAPP(nat,nat,suc,U_93),
    inference(definitional_conversion,[status(esa)],[f_66_2]) ).

cnf(f_66_4,plain,
    hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),U_93))) = hAPP(nat,nat,suc,U_93),
    inference(clausify,[status(thm)],[f_66_3]) ).

fof(f_67_1,plain,
    ! [X_b] :
      ( ! [A_3] : hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ~ finite_finite_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_14_finite__code]) ).

fof(f_67_2,plain,
    ! [U_95] :
      ( ! [U_94] : hBOOL(hAPP(fun(U_95,bool),bool,finite_finite(U_95),U_94))
      | ~ finite_finite_1(U_95) ),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

fof(f_67_3,plain,
    ! [U_94,U_95] :
      ( hBOOL(hAPP(fun(U_95,bool),bool,finite_finite(U_95),U_94))
      | ~ finite_finite_1(U_95) ),
    inference(definitional_conversion,[status(esa)],[f_67_2]) ).

cnf(f_67_4,plain,
    ( hBOOL(hAPP(fun(U_95,bool),bool,finite_finite(U_95),U_94))
    | ~ finite_finite_1(U_95) ),
    inference(clausify,[status(thm)],[f_67_3]) ).

fof(f_68_1,plain,
    ! [X_b] :
      ( ! [A_3] : hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ~ finite_finite_1(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_15_finite]) ).

fof(f_68_2,plain,
    ! [U_97] :
      ( ! [U_96] : hBOOL(hAPP(fun(U_97,bool),bool,finite_finite(U_97),U_96))
      | ~ finite_finite_1(U_97) ),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

fof(f_68_3,plain,
    ! [U_96,U_97] :
      ( hBOOL(hAPP(fun(U_97,bool),bool,finite_finite(U_97),U_96))
      | ~ finite_finite_1(U_97) ),
    inference(definitional_conversion,[status(esa)],[f_68_2]) ).

cnf(f_68_4,plain,
    ( hBOOL(hAPP(fun(U_97,bool),bool,finite_finite(U_97),U_96))
    | ~ finite_finite_1(U_97) ),
    inference(clausify,[status(thm)],[f_68_3]) ).

fof(f_69_1,plain,
    ! [X,Y] :
      ( X = Y
      | hAPP(nat,nat,suc,X) != hAPP(nat,nat,suc,Y) ),
    inference(fof_nnf,[status(thm)],[fact_16_Suc__inject]) ).

fof(f_69_2,plain,
    ! [U_99,U_98] :
      ( U_99 = U_98
      | hAPP(nat,nat,suc,U_99) != hAPP(nat,nat,suc,U_98) ),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

fof(f_69_3,plain,
    ! [U_98,U_99] :
      ( U_99 = U_98
      | hAPP(nat,nat,suc,U_99) != hAPP(nat,nat,suc,U_98) ),
    inference(definitional_conversion,[status(esa)],[f_69_2]) ).

cnf(f_69_4,plain,
    ( U_99 = U_98
    | hAPP(nat,nat,suc,U_99) != hAPP(nat,nat,suc,U_98) ),
    inference(clausify,[status(thm)],[f_69_3]) ).

fof(f_70_1,plain,
    ! [Nat_2,Nat_3] :
      ( ( hAPP(nat,nat,suc,Nat_2) = hAPP(nat,nat,suc,Nat_3)
        | Nat_2 != Nat_3 )
      & ( Nat_2 = Nat_3
        | hAPP(nat,nat,suc,Nat_2) != hAPP(nat,nat,suc,Nat_3) ) ),
    inference(fof_nnf,[status(thm)],[fact_17_nat_Oinject]) ).

fof(f_70_2,plain,
    ! [U_101,U_100] :
      ( ( hAPP(nat,nat,suc,U_101) = hAPP(nat,nat,suc,U_100)
        | U_101 != U_100 )
      & ( U_101 = U_100
        | hAPP(nat,nat,suc,U_101) != hAPP(nat,nat,suc,U_100) ) ),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

fof(f_70_3,plain,
    ( ! [U_105,U_103] :
        ( hAPP(nat,nat,suc,U_105) = hAPP(nat,nat,suc,U_103)
        | U_105 != U_103 )
    & ! [U_104,U_102] :
        ( U_104 = U_102
        | hAPP(nat,nat,suc,U_104) != hAPP(nat,nat,suc,U_102) ) ),
    inference(miniscope,[status(thm)],[f_70_2]) ).

fof(f_70_4,plain,
    ( ! [U_105,U_103] :
        ( hAPP(nat,nat,suc,U_105) = hAPP(nat,nat,suc,U_103)
        | U_105 != U_103 )
    & ! [U_102,U_104] :
        ( U_104 = U_102
        | hAPP(nat,nat,suc,U_104) != hAPP(nat,nat,suc,U_102) ) ),
    inference(definitional_conversion,[status(esa)],[f_70_3]) ).

cnf(f_70_5,plain,
    ( U_104 = U_102
    | hAPP(nat,nat,suc,U_104) != hAPP(nat,nat,suc,U_102) ),
    inference(clausify,[status(thm)],[f_70_4]) ).

cnf(f_70_6,plain,
    ( hAPP(nat,nat,suc,U_105) = hAPP(nat,nat,suc,U_103)
    | U_105 != U_103 ),
    inference(clausify,[status(thm)],[f_70_4]) ).

fof(f_71_1,plain,
    ! [N] : hAPP(nat,nat,suc,N) != N,
    inference(fof_nnf,[status(thm)],[fact_18_Suc__n__not__n]) ).

fof(f_71_2,plain,
    ! [U_106] : hAPP(nat,nat,suc,U_106) != U_106,
    inference(variable_rename,[status(thm)],[f_71_1]) ).

fof(f_71_3,plain,
    ! [U_106] : hAPP(nat,nat,suc,U_106) != U_106,
    inference(definitional_conversion,[status(esa)],[f_71_2]) ).

cnf(f_71_4,plain,
    hAPP(nat,nat,suc,U_106) != U_106,
    inference(clausify,[status(thm)],[f_71_3]) ).

fof(f_72_1,plain,
    ! [N] : N != hAPP(nat,nat,suc,N),
    inference(fof_nnf,[status(thm)],[fact_19_n__not__Suc__n]) ).

fof(f_72_2,plain,
    ! [U_107] : U_107 != hAPP(nat,nat,suc,U_107),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

fof(f_72_3,plain,
    ! [U_107] : U_107 != hAPP(nat,nat,suc,U_107),
    inference(definitional_conversion,[status(esa)],[f_72_2]) ).

cnf(f_72_4,plain,
    U_107 != hAPP(nat,nat,suc,U_107),
    inference(clausify,[status(thm)],[f_72_3]) ).

fof(f_73_1,plain,
    ! [M,N] :
      ( M = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_20_le__antisym]) ).

fof(f_73_2,plain,
    ! [U_109,U_108] :
      ( U_109 = U_108
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_108),U_109))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_109),U_108)) ),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

fof(f_73_3,plain,
    ! [U_108,U_109] :
      ( U_109 = U_108
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_108),U_109))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_109),U_108)) ),
    inference(definitional_conversion,[status(esa)],[f_73_2]) ).

cnf(f_73_4,plain,
    ( U_109 = U_108
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_108),U_109))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_109),U_108)) ),
    inference(clausify,[status(thm)],[f_73_3]) ).

fof(f_74_1,plain,
    ! [K,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),K))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_21_le__trans]) ).

fof(f_74_2,plain,
    ! [U_112,U_111,U_110] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_111),U_112))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_110),U_112))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_111),U_110)) ),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

fof(f_74_3,plain,
    ! [U_111,U_110,U_112] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_111),U_112))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_110),U_112))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_111),U_110)) ),
    inference(definitional_conversion,[status(esa)],[f_74_2]) ).

cnf(f_74_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_111),U_112))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_110),U_112))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_111),U_110)) ),
    inference(clausify,[status(thm)],[f_74_3]) ).

fof(f_75_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
      | M != N ),
    inference(fof_nnf,[status(thm)],[fact_22_eq__imp__le]) ).

fof(f_75_2,plain,
    ! [U_114,U_113] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_114),U_113))
      | U_114 != U_113 ),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

fof(f_75_3,plain,
    ! [U_113,U_114] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_114),U_113))
      | U_114 != U_113 ),
    inference(definitional_conversion,[status(esa)],[f_75_2]) ).

cnf(f_75_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_114),U_113))
    | U_114 != U_113 ),
    inference(clausify,[status(thm)],[f_75_3]) ).

fof(f_76_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_23_nat__le__linear]) ).

fof(f_76_2,plain,
    ! [U_116,U_115] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_115),U_116))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_116),U_115)) ),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

fof(f_76_3,plain,
    ! [U_115,U_116] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_115),U_116))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_116),U_115)) ),
    inference(definitional_conversion,[status(esa)],[f_76_2]) ).

cnf(f_76_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_115),U_116))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_116),U_115)) ),
    inference(clausify,[status(thm)],[f_76_3]) ).

fof(f_77_1,plain,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N)),
    inference(fof_nnf,[status(thm)],[fact_24_le__refl]) ).

fof(f_77_2,plain,
    ! [U_117] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_117),U_117)),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ! [U_117] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_117),U_117)),
    inference(definitional_conversion,[status(esa)],[f_77_2]) ).

cnf(f_77_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_117),U_117)),
    inference(clausify,[status(thm)],[f_77_3]) ).

fof(f_78_1,plain,
    ! [I,J_2,K] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_2)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),K)),J_2),
    inference(fof_nnf,[status(thm)],[fact_25_diff__commute]) ).

fof(f_78_2,plain,
    ! [U_120,U_119,U_118] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_120),U_119)),U_118) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_120),U_118)),U_119),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

fof(f_78_3,plain,
    ! [U_118,U_119,U_120] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_120),U_119)),U_118) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_120),U_118)),U_119),
    inference(definitional_conversion,[status(esa)],[f_78_2]) ).

cnf(f_78_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_120),U_119)),U_118) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_120),U_118)),U_119),
    inference(clausify,[status(thm)],[f_78_3]) ).

fof(f_79_1,plain,
    ! [X_b,Pa,Q_1] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_1))))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1)))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) )
      & ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1)))
          & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) )
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_26_finite__Collect__disjI]) ).

fof(f_79_2,plain,
    ! [U_123,U_122,U_121] :
      ( ( hBOOL(hAPP(fun(U_123,bool),bool,finite_finite(U_123),hAPP(fun(U_123,bool),fun(U_123,bool),collect(U_123),hAPP(fun(U_123,bool),fun(U_123,bool),hAPP(fun(U_123,fun(bool,bool)),fun(fun(U_123,bool),fun(U_123,bool)),combs(U_123,bool,bool),hAPP(fun(U_123,bool),fun(U_123,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_123,bool),fun(U_123,fun(bool,bool))),combb(bool,fun(bool,bool),U_123),fdisj),U_122)),U_121))))
        | ~ hBOOL(hAPP(fun(U_123,bool),bool,finite_finite(U_123),hAPP(fun(U_123,bool),fun(U_123,bool),collect(U_123),U_121)))
        | ~ hBOOL(hAPP(fun(U_123,bool),bool,finite_finite(U_123),hAPP(fun(U_123,bool),fun(U_123,bool),collect(U_123),U_122))) )
      & ( ( hBOOL(hAPP(fun(U_123,bool),bool,finite_finite(U_123),hAPP(fun(U_123,bool),fun(U_123,bool),collect(U_123),U_121)))
          & hBOOL(hAPP(fun(U_123,bool),bool,finite_finite(U_123),hAPP(fun(U_123,bool),fun(U_123,bool),collect(U_123),U_122))) )
        | ~ hBOOL(hAPP(fun(U_123,bool),bool,finite_finite(U_123),hAPP(fun(U_123,bool),fun(U_123,bool),collect(U_123),hAPP(fun(U_123,bool),fun(U_123,bool),hAPP(fun(U_123,fun(bool,bool)),fun(fun(U_123,bool),fun(U_123,bool)),combs(U_123,bool,bool),hAPP(fun(U_123,bool),fun(U_123,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_123,bool),fun(U_123,fun(bool,bool))),combb(bool,fun(bool,bool),U_123),fdisj),U_122)),U_121)))) ) ),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

fof(f_79_3,plain,
    ( ! [U_129,U_127,U_125] :
        ( hBOOL(hAPP(fun(U_129,bool),bool,finite_finite(U_129),hAPP(fun(U_129,bool),fun(U_129,bool),collect(U_129),hAPP(fun(U_129,bool),fun(U_129,bool),hAPP(fun(U_129,fun(bool,bool)),fun(fun(U_129,bool),fun(U_129,bool)),combs(U_129,bool,bool),hAPP(fun(U_129,bool),fun(U_129,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_129,bool),fun(U_129,fun(bool,bool))),combb(bool,fun(bool,bool),U_129),fdisj),U_127)),U_125))))
        | ~ hBOOL(hAPP(fun(U_129,bool),bool,finite_finite(U_129),hAPP(fun(U_129,bool),fun(U_129,bool),collect(U_129),U_125)))
        | ~ hBOOL(hAPP(fun(U_129,bool),bool,finite_finite(U_129),hAPP(fun(U_129,bool),fun(U_129,bool),collect(U_129),U_127))) )
    & ! [U_128,U_126,U_124] :
        ( ( hBOOL(hAPP(fun(U_128,bool),bool,finite_finite(U_128),hAPP(fun(U_128,bool),fun(U_128,bool),collect(U_128),U_124)))
          & hBOOL(hAPP(fun(U_128,bool),bool,finite_finite(U_128),hAPP(fun(U_128,bool),fun(U_128,bool),collect(U_128),U_126))) )
        | ~ hBOOL(hAPP(fun(U_128,bool),bool,finite_finite(U_128),hAPP(fun(U_128,bool),fun(U_128,bool),collect(U_128),hAPP(fun(U_128,bool),fun(U_128,bool),hAPP(fun(U_128,fun(bool,bool)),fun(fun(U_128,bool),fun(U_128,bool)),combs(U_128,bool,bool),hAPP(fun(U_128,bool),fun(U_128,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_128,bool),fun(U_128,fun(bool,bool))),combb(bool,fun(bool,bool),U_128),fdisj),U_126)),U_124)))) ) ),
    inference(miniscope,[status(thm)],[f_79_2]) ).

fof(f_79_4,plain,
    ( ! [U_128,U_124,U_126] :
        ( hBOOL(hAPP(fun(U_128,bool),bool,finite_finite(U_128),hAPP(fun(U_128,bool),fun(U_128,bool),collect(U_128),U_124)))
        | ~ sP2(U_128,U_124,U_126) )
    & ! [U_128,U_124,U_126] :
        ( hBOOL(hAPP(fun(U_128,bool),bool,finite_finite(U_128),hAPP(fun(U_128,bool),fun(U_128,bool),collect(U_128),U_126)))
        | ~ sP2(U_128,U_124,U_126) )
    & ! [U_129,U_127,U_125] :
        ( hBOOL(hAPP(fun(U_129,bool),bool,finite_finite(U_129),hAPP(fun(U_129,bool),fun(U_129,bool),collect(U_129),hAPP(fun(U_129,bool),fun(U_129,bool),hAPP(fun(U_129,fun(bool,bool)),fun(fun(U_129,bool),fun(U_129,bool)),combs(U_129,bool,bool),hAPP(fun(U_129,bool),fun(U_129,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_129,bool),fun(U_129,fun(bool,bool))),combb(bool,fun(bool,bool),U_129),fdisj),U_127)),U_125))))
        | ~ hBOOL(hAPP(fun(U_129,bool),bool,finite_finite(U_129),hAPP(fun(U_129,bool),fun(U_129,bool),collect(U_129),U_125)))
        | ~ hBOOL(hAPP(fun(U_129,bool),bool,finite_finite(U_129),hAPP(fun(U_129,bool),fun(U_129,bool),collect(U_129),U_127))) )
    & ! [U_128,U_124,U_126] :
        ( sP2(U_128,U_124,U_126)
        | ~ hBOOL(hAPP(fun(U_128,bool),bool,finite_finite(U_128),hAPP(fun(U_128,bool),fun(U_128,bool),collect(U_128),hAPP(fun(U_128,bool),fun(U_128,bool),hAPP(fun(U_128,fun(bool,bool)),fun(fun(U_128,bool),fun(U_128,bool)),combs(U_128,bool,bool),hAPP(fun(U_128,bool),fun(U_128,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_128,bool),fun(U_128,fun(bool,bool))),combb(bool,fun(bool,bool),U_128),fdisj),U_126)),U_124)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_79_3]) ).

cnf(f_79_5,plain,
    ( sP2(U_128,U_124,U_126)
    | ~ hBOOL(hAPP(fun(U_128,bool),bool,finite_finite(U_128),hAPP(fun(U_128,bool),fun(U_128,bool),collect(U_128),hAPP(fun(U_128,bool),fun(U_128,bool),hAPP(fun(U_128,fun(bool,bool)),fun(fun(U_128,bool),fun(U_128,bool)),combs(U_128,bool,bool),hAPP(fun(U_128,bool),fun(U_128,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_128,bool),fun(U_128,fun(bool,bool))),combb(bool,fun(bool,bool),U_128),fdisj),U_126)),U_124)))) ),
    inference(clausify,[status(thm)],[f_79_4]) ).

cnf(f_79_6,plain,
    ( hBOOL(hAPP(fun(U_129,bool),bool,finite_finite(U_129),hAPP(fun(U_129,bool),fun(U_129,bool),collect(U_129),hAPP(fun(U_129,bool),fun(U_129,bool),hAPP(fun(U_129,fun(bool,bool)),fun(fun(U_129,bool),fun(U_129,bool)),combs(U_129,bool,bool),hAPP(fun(U_129,bool),fun(U_129,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_129,bool),fun(U_129,fun(bool,bool))),combb(bool,fun(bool,bool),U_129),fdisj),U_127)),U_125))))
    | ~ hBOOL(hAPP(fun(U_129,bool),bool,finite_finite(U_129),hAPP(fun(U_129,bool),fun(U_129,bool),collect(U_129),U_125)))
    | ~ hBOOL(hAPP(fun(U_129,bool),bool,finite_finite(U_129),hAPP(fun(U_129,bool),fun(U_129,bool),collect(U_129),U_127))) ),
    inference(clausify,[status(thm)],[f_79_4]) ).

cnf(f_79_7,plain,
    ( hBOOL(hAPP(fun(U_128,bool),bool,finite_finite(U_128),hAPP(fun(U_128,bool),fun(U_128,bool),collect(U_128),U_126)))
    | ~ sP2(U_128,U_124,U_126) ),
    inference(clausify,[status(thm)],[f_79_4]) ).

cnf(f_79_8,plain,
    ( hBOOL(hAPP(fun(U_128,bool),bool,finite_finite(U_128),hAPP(fun(U_128,bool),fun(U_128,bool),collect(U_128),U_124)))
    | ~ sP2(U_128,U_124,U_126) ),
    inference(clausify,[status(thm)],[f_79_4]) ).

fof(f_80_1,plain,
    ! [X_b,A_2,A_3] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) )
      & ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_27_finite__insert]) ).

fof(f_80_2,plain,
    ! [U_132,U_131,U_130] :
      ( ( hBOOL(hAPP(fun(U_132,bool),bool,finite_finite(U_132),hAPP(fun(U_132,bool),fun(U_132,bool),hAPP(U_132,fun(fun(U_132,bool),fun(U_132,bool)),insert(U_132),U_131),U_130)))
        | ~ hBOOL(hAPP(fun(U_132,bool),bool,finite_finite(U_132),U_130)) )
      & ( hBOOL(hAPP(fun(U_132,bool),bool,finite_finite(U_132),U_130))
        | ~ hBOOL(hAPP(fun(U_132,bool),bool,finite_finite(U_132),hAPP(fun(U_132,bool),fun(U_132,bool),hAPP(U_132,fun(fun(U_132,bool),fun(U_132,bool)),insert(U_132),U_131),U_130))) ) ),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

fof(f_80_3,plain,
    ( ! [U_138,U_136,U_134] :
        ( hBOOL(hAPP(fun(U_138,bool),bool,finite_finite(U_138),hAPP(fun(U_138,bool),fun(U_138,bool),hAPP(U_138,fun(fun(U_138,bool),fun(U_138,bool)),insert(U_138),U_136),U_134)))
        | ~ hBOOL(hAPP(fun(U_138,bool),bool,finite_finite(U_138),U_134)) )
    & ! [U_137,U_135,U_133] :
        ( hBOOL(hAPP(fun(U_137,bool),bool,finite_finite(U_137),U_133))
        | ~ hBOOL(hAPP(fun(U_137,bool),bool,finite_finite(U_137),hAPP(fun(U_137,bool),fun(U_137,bool),hAPP(U_137,fun(fun(U_137,bool),fun(U_137,bool)),insert(U_137),U_135),U_133))) ) ),
    inference(miniscope,[status(thm)],[f_80_2]) ).

fof(f_80_4,plain,
    ( ! [U_134,U_138,U_136] :
        ( hBOOL(hAPP(fun(U_138,bool),bool,finite_finite(U_138),hAPP(fun(U_138,bool),fun(U_138,bool),hAPP(U_138,fun(fun(U_138,bool),fun(U_138,bool)),insert(U_138),U_136),U_134)))
        | ~ hBOOL(hAPP(fun(U_138,bool),bool,finite_finite(U_138),U_134)) )
    & ! [U_137,U_133,U_135] :
        ( hBOOL(hAPP(fun(U_137,bool),bool,finite_finite(U_137),U_133))
        | ~ hBOOL(hAPP(fun(U_137,bool),bool,finite_finite(U_137),hAPP(fun(U_137,bool),fun(U_137,bool),hAPP(U_137,fun(fun(U_137,bool),fun(U_137,bool)),insert(U_137),U_135),U_133))) ) ),
    inference(definitional_conversion,[status(esa)],[f_80_3]) ).

cnf(f_80_5,plain,
    ( hBOOL(hAPP(fun(U_137,bool),bool,finite_finite(U_137),U_133))
    | ~ hBOOL(hAPP(fun(U_137,bool),bool,finite_finite(U_137),hAPP(fun(U_137,bool),fun(U_137,bool),hAPP(U_137,fun(fun(U_137,bool),fun(U_137,bool)),insert(U_137),U_135),U_133))) ),
    inference(clausify,[status(thm)],[f_80_4]) ).

cnf(f_80_6,plain,
    ( hBOOL(hAPP(fun(U_138,bool),bool,finite_finite(U_138),hAPP(fun(U_138,bool),fun(U_138,bool),hAPP(U_138,fun(fun(U_138,bool),fun(U_138,bool)),insert(U_138),U_136),U_134)))
    | ~ hBOOL(hAPP(fun(U_138,bool),bool,finite_finite(U_138),U_134)) ),
    inference(clausify,[status(thm)],[f_80_4]) ).

fof(f_81_1,plain,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_28_finite__subset]) ).

fof(f_81_2,plain,
    ! [U_141,U_140,U_139] :
      ( hBOOL(hAPP(fun(U_141,bool),bool,finite_finite(U_141),U_140))
      | ~ hBOOL(hAPP(fun(U_141,bool),bool,finite_finite(U_141),U_139))
      | ~ hBOOL(hAPP(fun(U_141,bool),bool,hAPP(fun(U_141,bool),fun(fun(U_141,bool),bool),ord_less_eq(fun(U_141,bool)),U_140),U_139)) ),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

fof(f_81_3,plain,
    ! [U_139,U_141,U_140] :
      ( hBOOL(hAPP(fun(U_141,bool),bool,finite_finite(U_141),U_140))
      | ~ hBOOL(hAPP(fun(U_141,bool),bool,finite_finite(U_141),U_139))
      | ~ hBOOL(hAPP(fun(U_141,bool),bool,hAPP(fun(U_141,bool),fun(fun(U_141,bool),bool),ord_less_eq(fun(U_141,bool)),U_140),U_139)) ),
    inference(definitional_conversion,[status(esa)],[f_81_2]) ).

cnf(f_81_4,plain,
    ( hBOOL(hAPP(fun(U_141,bool),bool,finite_finite(U_141),U_140))
    | ~ hBOOL(hAPP(fun(U_141,bool),bool,finite_finite(U_141),U_139))
    | ~ hBOOL(hAPP(fun(U_141,bool),bool,hAPP(fun(U_141,bool),fun(fun(U_141,bool),bool),ord_less_eq(fun(U_141,bool)),U_140),U_139)) ),
    inference(clausify,[status(thm)],[f_81_3]) ).

fof(f_82_1,plain,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_29_rev__finite__subset]) ).

fof(f_82_2,plain,
    ! [U_144,U_143,U_142] :
      ( hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),U_143))
      | ~ hBOOL(hAPP(fun(U_144,bool),bool,hAPP(fun(U_144,bool),fun(fun(U_144,bool),bool),ord_less_eq(fun(U_144,bool)),U_143),U_142))
      | ~ hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),U_142)) ),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

fof(f_82_3,plain,
    ! [U_144,U_143,U_142] :
      ( hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),U_143))
      | ~ hBOOL(hAPP(fun(U_144,bool),bool,hAPP(fun(U_144,bool),fun(fun(U_144,bool),bool),ord_less_eq(fun(U_144,bool)),U_143),U_142))
      | ~ hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),U_142)) ),
    inference(definitional_conversion,[status(esa)],[f_82_2]) ).

cnf(f_82_4,plain,
    ( hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),U_143))
    | ~ hBOOL(hAPP(fun(U_144,bool),bool,hAPP(fun(U_144,bool),fun(fun(U_144,bool),bool),ord_less_eq(fun(U_144,bool)),U_143),U_142))
    | ~ hBOOL(hAPP(fun(U_144,bool),bool,finite_finite(U_144),U_142)) ),
    inference(clausify,[status(thm)],[f_82_3]) ).

fof(f_83_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_30_Suc__leD]) ).

fof(f_83_2,plain,
    ! [U_146,U_145] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_146),U_145))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_146)),U_145)) ),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

fof(f_83_3,plain,
    ! [U_145,U_146] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_146),U_145))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_146)),U_145)) ),
    inference(definitional_conversion,[status(esa)],[f_83_2]) ).

cnf(f_83_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_146),U_145))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_146)),U_145)) ),
    inference(clausify,[status(thm)],[f_83_3]) ).

fof(f_84_1,plain,
    ! [M,N] :
      ( M = hAPP(nat,nat,suc,N)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_31_le__SucE]) ).

fof(f_84_2,plain,
    ! [U_148,U_147] :
      ( U_148 = hAPP(nat,nat,suc,U_147)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_148),U_147))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_148),hAPP(nat,nat,suc,U_147))) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

fof(f_84_3,plain,
    ! [U_148,U_147] :
      ( U_148 = hAPP(nat,nat,suc,U_147)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_148),U_147))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_148),hAPP(nat,nat,suc,U_147))) ),
    inference(definitional_conversion,[status(esa)],[f_84_2]) ).

cnf(f_84_4,plain,
    ( U_148 = hAPP(nat,nat,suc,U_147)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_148),U_147))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_148),hAPP(nat,nat,suc,U_147))) ),
    inference(clausify,[status(thm)],[f_84_3]) ).

fof(f_85_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_32_le__SucI]) ).

fof(f_85_2,plain,
    ! [U_150,U_149] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_150),hAPP(nat,nat,suc,U_149)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_150),U_149)) ),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

fof(f_85_3,plain,
    ! [U_150,U_149] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_150),hAPP(nat,nat,suc,U_149)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_150),U_149)) ),
    inference(definitional_conversion,[status(esa)],[f_85_2]) ).

cnf(f_85_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_150),hAPP(nat,nat,suc,U_149)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_150),U_149)) ),
    inference(clausify,[status(thm)],[f_85_3]) ).

fof(f_86_1,plain,
    ! [Na,M_1] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_1)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_1)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_1))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_33_Suc__le__mono]) ).

fof(f_86_2,plain,
    ! [U_152,U_151] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_152)),hAPP(nat,nat,suc,U_151)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_152),U_151)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_152),U_151))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_152)),hAPP(nat,nat,suc,U_151))) ) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

fof(f_86_3,plain,
    ( ! [U_156,U_154] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_156)),hAPP(nat,nat,suc,U_154)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_156),U_154)) )
    & ! [U_155,U_153] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_155),U_153))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_155)),hAPP(nat,nat,suc,U_153))) ) ),
    inference(miniscope,[status(thm)],[f_86_2]) ).

fof(f_86_4,plain,
    ( ! [U_154,U_156] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_156)),hAPP(nat,nat,suc,U_154)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_156),U_154)) )
    & ! [U_155,U_153] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_155),U_153))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_155)),hAPP(nat,nat,suc,U_153))) ) ),
    inference(definitional_conversion,[status(esa)],[f_86_3]) ).

cnf(f_86_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_155),U_153))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_155)),hAPP(nat,nat,suc,U_153))) ),
    inference(clausify,[status(thm)],[f_86_4]) ).

cnf(f_86_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_156)),hAPP(nat,nat,suc,U_154)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_156),U_154)) ),
    inference(clausify,[status(thm)],[f_86_4]) ).

fof(f_87_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,Na)))
        | ( M_1 != hAPP(nat,nat,suc,Na)
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ) )
      & ( M_1 = hAPP(nat,nat,suc,Na)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_34_le__Suc__eq]) ).

fof(f_87_2,plain,
    ! [U_158,U_157] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_158),hAPP(nat,nat,suc,U_157)))
        | ( U_158 != hAPP(nat,nat,suc,U_157)
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_158),U_157)) ) )
      & ( U_158 = hAPP(nat,nat,suc,U_157)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_158),U_157))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_158),hAPP(nat,nat,suc,U_157))) ) ),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

fof(f_87_3,plain,
    ( ! [U_162,U_160] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_162),hAPP(nat,nat,suc,U_160)))
        | ( U_162 != hAPP(nat,nat,suc,U_160)
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_162),U_160)) ) )
    & ! [U_161,U_159] :
        ( U_161 = hAPP(nat,nat,suc,U_159)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_161),U_159))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_161),hAPP(nat,nat,suc,U_159))) ) ),
    inference(miniscope,[status(thm)],[f_87_2]) ).

fof(f_87_4,plain,
    ( ! [U_162,U_160] :
        ( U_162 != hAPP(nat,nat,suc,U_160)
        | ~ sP3(U_162,U_160) )
    & ! [U_162,U_160] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_162),U_160))
        | ~ sP3(U_162,U_160) )
    & ! [U_162,U_160] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_162),hAPP(nat,nat,suc,U_160)))
        | sP3(U_162,U_160) )
    & ! [U_159,U_161] :
        ( U_161 = hAPP(nat,nat,suc,U_159)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_161),U_159))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_161),hAPP(nat,nat,suc,U_159))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_87_3]) ).

cnf(f_87_5,plain,
    ( U_161 = hAPP(nat,nat,suc,U_159)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_161),U_159))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_161),hAPP(nat,nat,suc,U_159))) ),
    inference(clausify,[status(thm)],[f_87_4]) ).

cnf(f_87_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_162),hAPP(nat,nat,suc,U_160)))
    | sP3(U_162,U_160) ),
    inference(clausify,[status(thm)],[f_87_4]) ).

cnf(f_87_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_162),U_160))
    | ~ sP3(U_162,U_160) ),
    inference(clausify,[status(thm)],[f_87_4]) ).

cnf(f_87_8,plain,
    ( U_162 != hAPP(nat,nat,suc,U_160)
    | ~ sP3(U_162,U_160) ),
    inference(clausify,[status(thm)],[f_87_4]) ).

fof(f_88_1,plain,
    ! [M_1,Na] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_1)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_1))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_35_not__less__eq__eq]) ).

fof(f_88_2,plain,
    ! [U_164,U_163] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_164),U_163))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_163)),U_164)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_163)),U_164))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_164),U_163)) ) ),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

fof(f_88_3,plain,
    ( ! [U_168,U_166] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_168),U_166))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_166)),U_168)) )
    & ! [U_167,U_165] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_165)),U_167))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_167),U_165)) ) ),
    inference(miniscope,[status(thm)],[f_88_2]) ).

fof(f_88_4,plain,
    ( ! [U_168,U_166] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_168),U_166))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_166)),U_168)) )
    & ! [U_167,U_165] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_165)),U_167))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_167),U_165)) ) ),
    inference(definitional_conversion,[status(esa)],[f_88_3]) ).

cnf(f_88_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_165)),U_167))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_167),U_165)) ),
    inference(clausify,[status(thm)],[f_88_4]) ).

cnf(f_88_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_168),U_166))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_166)),U_168)) ),
    inference(clausify,[status(thm)],[f_88_4]) ).

fof(f_89_1,plain,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),N)),
    inference(fof_nnf,[status(thm)],[fact_36_Suc__n__not__le__n]) ).

fof(f_89_2,plain,
    ! [U_169] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_169)),U_169)),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

fof(f_89_3,plain,
    ! [U_169] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_169)),U_169)),
    inference(definitional_conversion,[status(esa)],[f_89_2]) ).

cnf(f_89_4,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_169)),U_169)),
    inference(clausify,[status(thm)],[f_89_3]) ).

fof(f_90_1,plain,
    ! [M,N,K] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,suc,K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),K),
    inference(fof_nnf,[status(thm)],[fact_37_Suc__diff__diff]) ).

fof(f_90_2,plain,
    ! [U_172,U_171,U_170] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_172)),U_171)),hAPP(nat,nat,suc,U_170)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_172),U_171)),U_170),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

fof(f_90_3,plain,
    ! [U_170,U_171,U_172] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_172)),U_171)),hAPP(nat,nat,suc,U_170)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_172),U_171)),U_170),
    inference(definitional_conversion,[status(esa)],[f_90_2]) ).

cnf(f_90_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_172)),U_171)),hAPP(nat,nat,suc,U_170)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_172),U_171)),U_170),
    inference(clausify,[status(thm)],[f_90_3]) ).

fof(f_91_1,plain,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N),
    inference(fof_nnf,[status(thm)],[fact_38_diff__Suc__Suc]) ).

fof(f_91_2,plain,
    ! [U_174,U_173] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_174)),hAPP(nat,nat,suc,U_173)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_174),U_173),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

fof(f_91_3,plain,
    ! [U_174,U_173] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_174)),hAPP(nat,nat,suc,U_173)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_174),U_173),
    inference(definitional_conversion,[status(esa)],[f_91_2]) ).

cnf(f_91_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_174)),hAPP(nat,nat,suc,U_173)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_174),U_173),
    inference(clausify,[status(thm)],[f_91_3]) ).

fof(f_92_1,plain,
    ! [Na,K_2,M_1] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K_2)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K_2))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_39_le__diff__iff]) ).

fof(f_92_2,plain,
    ! [U_177,U_176,U_175] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_175),U_176)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_177),U_176)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_175),U_177)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_175),U_177))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_175),U_176)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_177),U_176))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_176),U_177))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_176),U_175)) ),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

fof(f_92_3,plain,
    ( ! [U_176,U_177,U_175] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_175),U_176)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_177),U_176)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_175),U_177))
        | ~ sP4(U_176,U_177,U_175) )
    & ! [U_176,U_177,U_175] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_175),U_177))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_175),U_176)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_177),U_176)))
        | ~ sP4(U_176,U_177,U_175) )
    & ! [U_176,U_177,U_175] :
        ( sP4(U_176,U_177,U_175)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_176),U_177))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_176),U_175)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_92_2]) ).

cnf(f_92_4,plain,
    ( sP4(U_176,U_177,U_175)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_176),U_177))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_176),U_175)) ),
    inference(clausify,[status(thm)],[f_92_3]) ).

cnf(f_92_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_175),U_177))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_175),U_176)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_177),U_176)))
    | ~ sP4(U_176,U_177,U_175) ),
    inference(clausify,[status(thm)],[f_92_3]) ).

cnf(f_92_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_175),U_176)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_177),U_176)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_175),U_177))
    | ~ sP4(U_176,U_177,U_175) ),
    inference(clausify,[status(thm)],[f_92_3]) ).

fof(f_93_1,plain,
    ! [N,K,M] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M)) ),
    inference(fof_nnf,[status(thm)],[fact_40_Nat_Odiff__diff__eq]) ).

fof(f_93_2,plain,
    ! [U_180,U_179,U_178] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_178),U_179)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_180),U_179)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_178),U_180)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_179),U_180))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_179),U_178)) ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

fof(f_93_3,plain,
    ! [U_180,U_179,U_178] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_178),U_179)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_180),U_179)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_178),U_180)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_179),U_180))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_179),U_178)) ),
    inference(definitional_conversion,[status(esa)],[f_93_2]) ).

cnf(f_93_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_178),U_179)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_180),U_179)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_178),U_180)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_179),U_180))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_179),U_178)) ),
    inference(clausify,[status(thm)],[f_93_3]) ).

fof(f_94_1,plain,
    ! [Na,K_2,M_1] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K_2)
          | M_1 != Na )
        & ( M_1 = Na
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K_2) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_41_eq__diff__iff]) ).

fof(f_94_2,plain,
    ! [U_183,U_182,U_181] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_181),U_182) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_183),U_182)
          | U_181 != U_183 )
        & ( U_181 = U_183
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_181),U_182) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_183),U_182) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_182),U_183))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_182),U_181)) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

fof(f_94_3,plain,
    ( ! [U_182,U_181,U_183] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_181),U_182) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_183),U_182)
        | U_181 != U_183
        | ~ sP5(U_182,U_181,U_183) )
    & ! [U_182,U_181,U_183] :
        ( U_181 = U_183
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_181),U_182) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_183),U_182)
        | ~ sP5(U_182,U_181,U_183) )
    & ! [U_182,U_181,U_183] :
        ( sP5(U_182,U_181,U_183)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_182),U_183))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_182),U_181)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_94_2]) ).

cnf(f_94_4,plain,
    ( sP5(U_182,U_181,U_183)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_182),U_183))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_182),U_181)) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

cnf(f_94_5,plain,
    ( U_181 = U_183
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_181),U_182) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_183),U_182)
    | ~ sP5(U_182,U_181,U_183) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

cnf(f_94_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_181),U_182) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_183),U_182)
    | U_181 != U_183
    | ~ sP5(U_182,U_181,U_183) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

fof(f_95_1,plain,
    ! [I,N] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),I)) = I
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),N)) ),
    inference(fof_nnf,[status(thm)],[fact_42_diff__diff__cancel]) ).

fof(f_95_2,plain,
    ! [U_185,U_184] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_184),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_184),U_185)) = U_185
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_185),U_184)) ),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

fof(f_95_3,plain,
    ! [U_185,U_184] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_184),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_184),U_185)) = U_185
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_185),U_184)) ),
    inference(definitional_conversion,[status(esa)],[f_95_2]) ).

cnf(f_95_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_184),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_184),U_185)) = U_185
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_185),U_184)) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

fof(f_96_1,plain,
    ! [L,M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_43_diff__le__mono]) ).

fof(f_96_2,plain,
    ! [U_188,U_187,U_186] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_187),U_188)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_186),U_188)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_187),U_186)) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ! [U_186,U_187,U_188] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_187),U_188)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_186),U_188)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_187),U_186)) ),
    inference(definitional_conversion,[status(esa)],[f_96_2]) ).

cnf(f_96_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_187),U_188)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_186),U_188)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_187),U_186)) ),
    inference(clausify,[status(thm)],[f_96_3]) ).

fof(f_97_1,plain,
    ! [L,M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_44_diff__le__mono2]) ).

fof(f_97_2,plain,
    ! [U_191,U_190,U_189] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_191),U_189)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_191),U_190)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_190),U_189)) ),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

fof(f_97_3,plain,
    ! [U_189,U_190,U_191] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_191),U_189)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_191),U_190)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_190),U_189)) ),
    inference(definitional_conversion,[status(esa)],[f_97_2]) ).

cnf(f_97_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_191),U_189)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_191),U_190)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_190),U_189)) ),
    inference(clausify,[status(thm)],[f_97_3]) ).

fof(f_98_1,plain,
    ! [M,N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M)),
    inference(fof_nnf,[status(thm)],[fact_45_diff__le__self]) ).

fof(f_98_2,plain,
    ! [U_193,U_192] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_193),U_192)),U_193)),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

fof(f_98_3,plain,
    ! [U_192,U_193] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_193),U_192)),U_193)),
    inference(definitional_conversion,[status(esa)],[f_98_2]) ).

cnf(f_98_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_193),U_192)),U_193)),
    inference(clausify,[status(thm)],[f_98_3]) ).

fof(f_99_1,plain,
    ! [X_c,X_b,B_2,F,A_3] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),B_2),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_46_finite__surj]) ).

fof(f_99_2,plain,
    ! [U_198,U_197,U_196,U_195,U_194] :
      ( hBOOL(hAPP(fun(U_198,bool),bool,finite_finite(U_198),U_196))
      | ~ hBOOL(hAPP(fun(U_198,bool),bool,hAPP(fun(U_198,bool),fun(fun(U_198,bool),bool),ord_less_eq(fun(U_198,bool)),U_196),hAPP(fun(U_197,bool),fun(U_198,bool),hAPP(fun(U_197,U_198),fun(fun(U_197,bool),fun(U_198,bool)),image(U_197,U_198),U_195),U_194)))
      | ~ hBOOL(hAPP(fun(U_197,bool),bool,finite_finite(U_197),U_194)) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

fof(f_99_3,plain,
    ! [U_197,U_194,U_196,U_195,U_198] :
      ( hBOOL(hAPP(fun(U_198,bool),bool,finite_finite(U_198),U_196))
      | ~ hBOOL(hAPP(fun(U_198,bool),bool,hAPP(fun(U_198,bool),fun(fun(U_198,bool),bool),ord_less_eq(fun(U_198,bool)),U_196),hAPP(fun(U_197,bool),fun(U_198,bool),hAPP(fun(U_197,U_198),fun(fun(U_197,bool),fun(U_198,bool)),image(U_197,U_198),U_195),U_194)))
      | ~ hBOOL(hAPP(fun(U_197,bool),bool,finite_finite(U_197),U_194)) ),
    inference(definitional_conversion,[status(esa)],[f_99_2]) ).

cnf(f_99_4,plain,
    ( hBOOL(hAPP(fun(U_198,bool),bool,finite_finite(U_198),U_196))
    | ~ hBOOL(hAPP(fun(U_198,bool),bool,hAPP(fun(U_198,bool),fun(fun(U_198,bool),bool),ord_less_eq(fun(U_198,bool)),U_196),hAPP(fun(U_197,bool),fun(U_198,bool),hAPP(fun(U_197,U_198),fun(fun(U_197,bool),fun(U_198,bool)),image(U_197,U_198),U_195),U_194)))
    | ~ hBOOL(hAPP(fun(U_197,bool),bool,finite_finite(U_197),U_194)) ),
    inference(clausify,[status(thm)],[f_99_3]) ).

fof(f_100_1,plain,
    ! [X_c,X_b,F,A_3,B_2] :
      ( ? [C_3] :
          ( ti(fun(X_b,bool),B_2) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),C_3)
          & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),C_3))
          & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),C_3),A_3)) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_47_finite__subset__image]) ).

fof(f_100_2,plain,
    ! [U_204,U_203,U_202,U_201,U_200] :
      ( ? [U_199] :
          ( ti(fun(U_203,bool),U_200) = hAPP(fun(U_204,bool),fun(U_203,bool),hAPP(fun(U_204,U_203),fun(fun(U_204,bool),fun(U_203,bool)),image(U_204,U_203),U_202),U_199)
          & hBOOL(hAPP(fun(U_204,bool),bool,finite_finite(U_204),U_199))
          & hBOOL(hAPP(fun(U_204,bool),bool,hAPP(fun(U_204,bool),fun(fun(U_204,bool),bool),ord_less_eq(fun(U_204,bool)),U_199),U_201)) )
      | ~ hBOOL(hAPP(fun(U_203,bool),bool,hAPP(fun(U_203,bool),fun(fun(U_203,bool),bool),ord_less_eq(fun(U_203,bool)),U_200),hAPP(fun(U_204,bool),fun(U_203,bool),hAPP(fun(U_204,U_203),fun(fun(U_204,bool),fun(U_203,bool)),image(U_204,U_203),U_202),U_201)))
      | ~ hBOOL(hAPP(fun(U_203,bool),bool,finite_finite(U_203),U_200)) ),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

fof(f_100_3,plain,
    ! [U_204,U_203,U_202,U_201,U_200] :
      ( ( ti(fun(U_203,bool),U_200) = hAPP(fun(U_204,bool),fun(U_203,bool),hAPP(fun(U_204,U_203),fun(fun(U_204,bool),fun(U_203,bool)),image(U_204,U_203),U_202),sK1(U_204,U_203,U_202,U_201,U_200))
        & hBOOL(hAPP(fun(U_204,bool),bool,finite_finite(U_204),sK1(U_204,U_203,U_202,U_201,U_200)))
        & hBOOL(hAPP(fun(U_204,bool),bool,hAPP(fun(U_204,bool),fun(fun(U_204,bool),bool),ord_less_eq(fun(U_204,bool)),sK1(U_204,U_203,U_202,U_201,U_200)),U_201)) )
      | ~ hBOOL(hAPP(fun(U_203,bool),bool,hAPP(fun(U_203,bool),fun(fun(U_203,bool),bool),ord_less_eq(fun(U_203,bool)),U_200),hAPP(fun(U_204,bool),fun(U_203,bool),hAPP(fun(U_204,U_203),fun(fun(U_204,bool),fun(U_203,bool)),image(U_204,U_203),U_202),U_201)))
      | ~ hBOOL(hAPP(fun(U_203,bool),bool,finite_finite(U_203),U_200)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_199,sK1(U_204,U_203,U_202,U_201,U_200))],[f_100_2]) ).

fof(f_100_4,plain,
    ( ! [U_203,U_202,U_201,U_200,U_204] :
        ( ti(fun(U_203,bool),U_200) = hAPP(fun(U_204,bool),fun(U_203,bool),hAPP(fun(U_204,U_203),fun(fun(U_204,bool),fun(U_203,bool)),image(U_204,U_203),U_202),sK1(U_204,U_203,U_202,U_201,U_200))
        | ~ sP6(U_203,U_202,U_201,U_200,U_204) )
    & ! [U_203,U_202,U_201,U_200,U_204] :
        ( hBOOL(hAPP(fun(U_204,bool),bool,finite_finite(U_204),sK1(U_204,U_203,U_202,U_201,U_200)))
        | ~ sP6(U_203,U_202,U_201,U_200,U_204) )
    & ! [U_203,U_202,U_201,U_200,U_204] :
        ( hBOOL(hAPP(fun(U_204,bool),bool,hAPP(fun(U_204,bool),fun(fun(U_204,bool),bool),ord_less_eq(fun(U_204,bool)),sK1(U_204,U_203,U_202,U_201,U_200)),U_201))
        | ~ sP6(U_203,U_202,U_201,U_200,U_204) )
    & ! [U_203,U_202,U_201,U_200,U_204] :
        ( sP6(U_203,U_202,U_201,U_200,U_204)
        | ~ hBOOL(hAPP(fun(U_203,bool),bool,hAPP(fun(U_203,bool),fun(fun(U_203,bool),bool),ord_less_eq(fun(U_203,bool)),U_200),hAPP(fun(U_204,bool),fun(U_203,bool),hAPP(fun(U_204,U_203),fun(fun(U_204,bool),fun(U_203,bool)),image(U_204,U_203),U_202),U_201)))
        | ~ hBOOL(hAPP(fun(U_203,bool),bool,finite_finite(U_203),U_200)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_100_3]) ).

cnf(f_100_5,plain,
    ( sP6(U_203,U_202,U_201,U_200,U_204)
    | ~ hBOOL(hAPP(fun(U_203,bool),bool,hAPP(fun(U_203,bool),fun(fun(U_203,bool),bool),ord_less_eq(fun(U_203,bool)),U_200),hAPP(fun(U_204,bool),fun(U_203,bool),hAPP(fun(U_204,U_203),fun(fun(U_204,bool),fun(U_203,bool)),image(U_204,U_203),U_202),U_201)))
    | ~ hBOOL(hAPP(fun(U_203,bool),bool,finite_finite(U_203),U_200)) ),
    inference(clausify,[status(thm)],[f_100_4]) ).

cnf(f_100_6,plain,
    ( hBOOL(hAPP(fun(U_204,bool),bool,hAPP(fun(U_204,bool),fun(fun(U_204,bool),bool),ord_less_eq(fun(U_204,bool)),sK1(U_204,U_203,U_202,U_201,U_200)),U_201))
    | ~ sP6(U_203,U_202,U_201,U_200,U_204) ),
    inference(clausify,[status(thm)],[f_100_4]) ).

cnf(f_100_7,plain,
    ( hBOOL(hAPP(fun(U_204,bool),bool,finite_finite(U_204),sK1(U_204,U_203,U_202,U_201,U_200)))
    | ~ sP6(U_203,U_202,U_201,U_200,U_204) ),
    inference(clausify,[status(thm)],[f_100_4]) ).

cnf(f_100_8,plain,
    ( ti(fun(U_203,bool),U_200) = hAPP(fun(U_204,bool),fun(U_203,bool),hAPP(fun(U_204,U_203),fun(fun(U_204,bool),fun(U_203,bool)),image(U_204,U_203),U_202),sK1(U_204,U_203,U_202,U_201,U_200))
    | ~ sP6(U_203,U_202,U_201,U_200,U_204) ),
    inference(clausify,[status(thm)],[f_100_4]) ).

fof(f_101_1,plain,
    ! [X_b] :
      ( ! [Na,N_3,F] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_3))
          | ? [N_2] : ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,N_2)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_2)))) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_48_lift__Suc__mono__le]) ).

fof(f_101_2,plain,
    ! [U_209] :
      ( ! [U_208,U_207,U_206] :
          ( hBOOL(hAPP(U_209,bool,hAPP(U_209,fun(U_209,bool),ord_less_eq(U_209),hAPP(nat,U_209,U_206,U_208)),hAPP(nat,U_209,U_206,U_207)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_208),U_207))
          | ? [U_205] : ~ hBOOL(hAPP(U_209,bool,hAPP(U_209,fun(U_209,bool),ord_less_eq(U_209),hAPP(nat,U_209,U_206,U_205)),hAPP(nat,U_209,U_206,hAPP(nat,nat,suc,U_205)))) )
      | ~ order(U_209) ),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

fof(f_101_3,plain,
    ! [U_209] :
      ( ! [U_208,U_207,U_206] :
          ( hBOOL(hAPP(U_209,bool,hAPP(U_209,fun(U_209,bool),ord_less_eq(U_209),hAPP(nat,U_209,U_206,U_208)),hAPP(nat,U_209,U_206,U_207)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_208),U_207))
          | ~ hBOOL(hAPP(U_209,bool,hAPP(U_209,fun(U_209,bool),ord_less_eq(U_209),hAPP(nat,U_209,U_206,sK2(U_209,U_208,U_207,U_206))),hAPP(nat,U_209,U_206,hAPP(nat,nat,suc,sK2(U_209,U_208,U_207,U_206))))) )
      | ~ order(U_209) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_205,sK2(U_209,U_208,U_207,U_206))],[f_101_2]) ).

fof(f_101_4,plain,
    ! [U_208,U_206,U_209,U_207] :
      ( hBOOL(hAPP(U_209,bool,hAPP(U_209,fun(U_209,bool),ord_less_eq(U_209),hAPP(nat,U_209,U_206,U_208)),hAPP(nat,U_209,U_206,U_207)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_208),U_207))
      | ~ hBOOL(hAPP(U_209,bool,hAPP(U_209,fun(U_209,bool),ord_less_eq(U_209),hAPP(nat,U_209,U_206,sK2(U_209,U_208,U_207,U_206))),hAPP(nat,U_209,U_206,hAPP(nat,nat,suc,sK2(U_209,U_208,U_207,U_206)))))
      | ~ order(U_209) ),
    inference(definitional_conversion,[status(esa)],[f_101_3]) ).

cnf(f_101_5,plain,
    ( hBOOL(hAPP(U_209,bool,hAPP(U_209,fun(U_209,bool),ord_less_eq(U_209),hAPP(nat,U_209,U_206,U_208)),hAPP(nat,U_209,U_206,U_207)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_208),U_207))
    | ~ hBOOL(hAPP(U_209,bool,hAPP(U_209,fun(U_209,bool),ord_less_eq(U_209),hAPP(nat,U_209,U_206,sK2(U_209,U_208,U_207,U_206))),hAPP(nat,U_209,U_206,hAPP(nat,nat,suc,sK2(U_209,U_208,U_207,U_206)))))
    | ~ order(U_209) ),
    inference(clausify,[status(thm)],[f_101_4]) ).

fof(f_102_1,plain,
    ! [X_c,X_b,F,A_3] :
      ( ? [X_2] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_b),fequal(X_c)),F)),hAPP(X_b,X_c,F,X_2))))))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) )
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
      | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_49_pigeonhole__infinite]) ).

fof(f_102_2,plain,
    ! [U_214,U_213,U_212,U_211] :
      ( ? [U_210] :
          ( ~ hBOOL(hAPP(fun(U_213,bool),bool,finite_finite(U_213),hAPP(fun(U_213,bool),fun(U_213,bool),collect(U_213),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(fun(U_213,fun(bool,bool)),fun(fun(U_213,bool),fun(U_213,bool)),combs(U_213,bool,bool),hAPP(fun(U_213,bool),fun(U_213,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_213,bool),fun(U_213,fun(bool,bool))),combb(bool,fun(bool,bool),U_213),fconj),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(fun(U_213,fun(fun(U_213,bool),bool)),fun(fun(U_213,bool),fun(U_213,bool)),combc(U_213,fun(U_213,bool),bool),member(U_213)),U_211))),hAPP(U_214,fun(U_213,bool),hAPP(fun(U_213,fun(U_214,bool)),fun(U_214,fun(U_213,bool)),combc(U_213,U_214,bool),hAPP(fun(U_213,U_214),fun(U_213,fun(U_214,bool)),hAPP(fun(U_214,fun(U_214,bool)),fun(fun(U_213,U_214),fun(U_213,fun(U_214,bool))),combb(U_214,fun(U_214,bool),U_213),fequal(U_214)),U_212)),hAPP(U_213,U_214,U_212,U_210))))))
          & hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),U_210),U_211)) )
      | ~ hBOOL(hAPP(fun(U_214,bool),bool,finite_finite(U_214),hAPP(fun(U_213,bool),fun(U_214,bool),hAPP(fun(U_213,U_214),fun(fun(U_213,bool),fun(U_214,bool)),image(U_213,U_214),U_212),U_211)))
      | hBOOL(hAPP(fun(U_213,bool),bool,finite_finite(U_213),U_211)) ),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

fof(f_102_3,plain,
    ! [U_214,U_213,U_212,U_211] :
      ( ( ~ hBOOL(hAPP(fun(U_213,bool),bool,finite_finite(U_213),hAPP(fun(U_213,bool),fun(U_213,bool),collect(U_213),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(fun(U_213,fun(bool,bool)),fun(fun(U_213,bool),fun(U_213,bool)),combs(U_213,bool,bool),hAPP(fun(U_213,bool),fun(U_213,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_213,bool),fun(U_213,fun(bool,bool))),combb(bool,fun(bool,bool),U_213),fconj),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(fun(U_213,fun(fun(U_213,bool),bool)),fun(fun(U_213,bool),fun(U_213,bool)),combc(U_213,fun(U_213,bool),bool),member(U_213)),U_211))),hAPP(U_214,fun(U_213,bool),hAPP(fun(U_213,fun(U_214,bool)),fun(U_214,fun(U_213,bool)),combc(U_213,U_214,bool),hAPP(fun(U_213,U_214),fun(U_213,fun(U_214,bool)),hAPP(fun(U_214,fun(U_214,bool)),fun(fun(U_213,U_214),fun(U_213,fun(U_214,bool))),combb(U_214,fun(U_214,bool),U_213),fequal(U_214)),U_212)),hAPP(U_213,U_214,U_212,sK3(U_214,U_213,U_212,U_211)))))))
        & hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),sK3(U_214,U_213,U_212,U_211)),U_211)) )
      | ~ hBOOL(hAPP(fun(U_214,bool),bool,finite_finite(U_214),hAPP(fun(U_213,bool),fun(U_214,bool),hAPP(fun(U_213,U_214),fun(fun(U_213,bool),fun(U_214,bool)),image(U_213,U_214),U_212),U_211)))
      | hBOOL(hAPP(fun(U_213,bool),bool,finite_finite(U_213),U_211)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_210,sK3(U_214,U_213,U_212,U_211))],[f_102_2]) ).

fof(f_102_4,plain,
    ( ! [U_212,U_214,U_213,U_211] :
        ( ~ hBOOL(hAPP(fun(U_213,bool),bool,finite_finite(U_213),hAPP(fun(U_213,bool),fun(U_213,bool),collect(U_213),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(fun(U_213,fun(bool,bool)),fun(fun(U_213,bool),fun(U_213,bool)),combs(U_213,bool,bool),hAPP(fun(U_213,bool),fun(U_213,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_213,bool),fun(U_213,fun(bool,bool))),combb(bool,fun(bool,bool),U_213),fconj),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(fun(U_213,fun(fun(U_213,bool),bool)),fun(fun(U_213,bool),fun(U_213,bool)),combc(U_213,fun(U_213,bool),bool),member(U_213)),U_211))),hAPP(U_214,fun(U_213,bool),hAPP(fun(U_213,fun(U_214,bool)),fun(U_214,fun(U_213,bool)),combc(U_213,U_214,bool),hAPP(fun(U_213,U_214),fun(U_213,fun(U_214,bool)),hAPP(fun(U_214,fun(U_214,bool)),fun(fun(U_213,U_214),fun(U_213,fun(U_214,bool))),combb(U_214,fun(U_214,bool),U_213),fequal(U_214)),U_212)),hAPP(U_213,U_214,U_212,sK3(U_214,U_213,U_212,U_211)))))))
        | ~ sP7(U_212,U_214,U_213,U_211) )
    & ! [U_212,U_214,U_213,U_211] :
        ( hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),sK3(U_214,U_213,U_212,U_211)),U_211))
        | ~ sP7(U_212,U_214,U_213,U_211) )
    & ! [U_212,U_214,U_213,U_211] :
        ( sP7(U_212,U_214,U_213,U_211)
        | ~ hBOOL(hAPP(fun(U_214,bool),bool,finite_finite(U_214),hAPP(fun(U_213,bool),fun(U_214,bool),hAPP(fun(U_213,U_214),fun(fun(U_213,bool),fun(U_214,bool)),image(U_213,U_214),U_212),U_211)))
        | hBOOL(hAPP(fun(U_213,bool),bool,finite_finite(U_213),U_211)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_102_3]) ).

cnf(f_102_5,plain,
    ( sP7(U_212,U_214,U_213,U_211)
    | ~ hBOOL(hAPP(fun(U_214,bool),bool,finite_finite(U_214),hAPP(fun(U_213,bool),fun(U_214,bool),hAPP(fun(U_213,U_214),fun(fun(U_213,bool),fun(U_214,bool)),image(U_213,U_214),U_212),U_211)))
    | hBOOL(hAPP(fun(U_213,bool),bool,finite_finite(U_213),U_211)) ),
    inference(clausify,[status(thm)],[f_102_4]) ).

cnf(f_102_6,plain,
    ( hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),sK3(U_214,U_213,U_212,U_211)),U_211))
    | ~ sP7(U_212,U_214,U_213,U_211) ),
    inference(clausify,[status(thm)],[f_102_4]) ).

cnf(f_102_7,plain,
    ( ~ hBOOL(hAPP(fun(U_213,bool),bool,finite_finite(U_213),hAPP(fun(U_213,bool),fun(U_213,bool),collect(U_213),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(fun(U_213,fun(bool,bool)),fun(fun(U_213,bool),fun(U_213,bool)),combs(U_213,bool,bool),hAPP(fun(U_213,bool),fun(U_213,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_213,bool),fun(U_213,fun(bool,bool))),combb(bool,fun(bool,bool),U_213),fconj),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(fun(U_213,fun(fun(U_213,bool),bool)),fun(fun(U_213,bool),fun(U_213,bool)),combc(U_213,fun(U_213,bool),bool),member(U_213)),U_211))),hAPP(U_214,fun(U_213,bool),hAPP(fun(U_213,fun(U_214,bool)),fun(U_214,fun(U_213,bool)),combc(U_213,U_214,bool),hAPP(fun(U_213,U_214),fun(U_213,fun(U_214,bool)),hAPP(fun(U_214,fun(U_214,bool)),fun(fun(U_213,U_214),fun(U_213,fun(U_214,bool))),combb(U_214,fun(U_214,bool),U_213),fequal(U_214)),U_212)),hAPP(U_213,U_214,U_212,sK3(U_214,U_213,U_212,U_211)))))))
    | ~ sP7(U_212,U_214,U_213,U_211) ),
    inference(clausify,[status(thm)],[f_102_4]) ).

fof(f_103_1,plain,
    ! [X_b,X_c,A_3,B,F,X_1] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))
      | ti(X_b,B) != hAPP(X_c,X_b,F,X_1) ),
    inference(fof_nnf,[status(thm)],[fact_50_image__eqI]) ).

fof(f_103_2,plain,
    ! [U_220,U_219,U_218,U_217,U_216,U_215] :
      ( hBOOL(hAPP(fun(U_220,bool),bool,hAPP(U_220,fun(fun(U_220,bool),bool),member(U_220),U_217),hAPP(fun(U_219,bool),fun(U_220,bool),hAPP(fun(U_219,U_220),fun(fun(U_219,bool),fun(U_220,bool)),image(U_219,U_220),U_216),U_218)))
      | ~ hBOOL(hAPP(fun(U_219,bool),bool,hAPP(U_219,fun(fun(U_219,bool),bool),member(U_219),U_215),U_218))
      | ti(U_220,U_217) != hAPP(U_219,U_220,U_216,U_215) ),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

fof(f_103_3,plain,
    ! [U_216,U_217,U_215,U_220,U_219,U_218] :
      ( hBOOL(hAPP(fun(U_220,bool),bool,hAPP(U_220,fun(fun(U_220,bool),bool),member(U_220),U_217),hAPP(fun(U_219,bool),fun(U_220,bool),hAPP(fun(U_219,U_220),fun(fun(U_219,bool),fun(U_220,bool)),image(U_219,U_220),U_216),U_218)))
      | ~ hBOOL(hAPP(fun(U_219,bool),bool,hAPP(U_219,fun(fun(U_219,bool),bool),member(U_219),U_215),U_218))
      | ti(U_220,U_217) != hAPP(U_219,U_220,U_216,U_215) ),
    inference(definitional_conversion,[status(esa)],[f_103_2]) ).

cnf(f_103_4,plain,
    ( hBOOL(hAPP(fun(U_220,bool),bool,hAPP(U_220,fun(fun(U_220,bool),bool),member(U_220),U_217),hAPP(fun(U_219,bool),fun(U_220,bool),hAPP(fun(U_219,U_220),fun(fun(U_219,bool),fun(U_220,bool)),image(U_219,U_220),U_216),U_218)))
    | ~ hBOOL(hAPP(fun(U_219,bool),bool,hAPP(U_219,fun(fun(U_219,bool),bool),member(U_219),U_215),U_218))
    | ti(U_220,U_217) != hAPP(U_219,U_220,U_216,U_215) ),
    inference(clausify,[status(thm)],[f_103_3]) ).

fof(f_104_1,plain,
    ! [X_b,A_3,B_2] :
      ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_51_equalityI]) ).

fof(f_104_2,plain,
    ! [U_223,U_222,U_221] :
      ( ti(fun(U_223,bool),U_222) = ti(fun(U_223,bool),U_221)
      | ~ hBOOL(hAPP(fun(U_223,bool),bool,hAPP(fun(U_223,bool),fun(fun(U_223,bool),bool),ord_less_eq(fun(U_223,bool)),U_221),U_222))
      | ~ hBOOL(hAPP(fun(U_223,bool),bool,hAPP(fun(U_223,bool),fun(fun(U_223,bool),bool),ord_less_eq(fun(U_223,bool)),U_222),U_221)) ),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

fof(f_104_3,plain,
    ! [U_221,U_222,U_223] :
      ( ti(fun(U_223,bool),U_222) = ti(fun(U_223,bool),U_221)
      | ~ hBOOL(hAPP(fun(U_223,bool),bool,hAPP(fun(U_223,bool),fun(fun(U_223,bool),bool),ord_less_eq(fun(U_223,bool)),U_221),U_222))
      | ~ hBOOL(hAPP(fun(U_223,bool),bool,hAPP(fun(U_223,bool),fun(fun(U_223,bool),bool),ord_less_eq(fun(U_223,bool)),U_222),U_221)) ),
    inference(definitional_conversion,[status(esa)],[f_104_2]) ).

cnf(f_104_4,plain,
    ( ti(fun(U_223,bool),U_222) = ti(fun(U_223,bool),U_221)
    | ~ hBOOL(hAPP(fun(U_223,bool),bool,hAPP(fun(U_223,bool),fun(fun(U_223,bool),bool),ord_less_eq(fun(U_223,bool)),U_221),U_222))
    | ~ hBOOL(hAPP(fun(U_223,bool),bool,hAPP(fun(U_223,bool),fun(fun(U_223,bool),bool),ord_less_eq(fun(U_223,bool)),U_222),U_221)) ),
    inference(clausify,[status(thm)],[f_104_3]) ).

fof(f_105_1,plain,
    ! [X_b,C_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_52_subsetD]) ).

fof(f_105_2,plain,
    ! [U_227,U_226,U_225,U_224] :
      ( hBOOL(hAPP(fun(U_227,bool),bool,hAPP(U_227,fun(fun(U_227,bool),bool),member(U_227),U_226),U_224))
      | ~ hBOOL(hAPP(fun(U_227,bool),bool,hAPP(U_227,fun(fun(U_227,bool),bool),member(U_227),U_226),U_225))
      | ~ hBOOL(hAPP(fun(U_227,bool),bool,hAPP(fun(U_227,bool),fun(fun(U_227,bool),bool),ord_less_eq(fun(U_227,bool)),U_225),U_224)) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

fof(f_105_3,plain,
    ! [U_225,U_224,U_227,U_226] :
      ( hBOOL(hAPP(fun(U_227,bool),bool,hAPP(U_227,fun(fun(U_227,bool),bool),member(U_227),U_226),U_224))
      | ~ hBOOL(hAPP(fun(U_227,bool),bool,hAPP(U_227,fun(fun(U_227,bool),bool),member(U_227),U_226),U_225))
      | ~ hBOOL(hAPP(fun(U_227,bool),bool,hAPP(fun(U_227,bool),fun(fun(U_227,bool),bool),ord_less_eq(fun(U_227,bool)),U_225),U_224)) ),
    inference(definitional_conversion,[status(esa)],[f_105_2]) ).

cnf(f_105_4,plain,
    ( hBOOL(hAPP(fun(U_227,bool),bool,hAPP(U_227,fun(fun(U_227,bool),bool),member(U_227),U_226),U_224))
    | ~ hBOOL(hAPP(fun(U_227,bool),bool,hAPP(U_227,fun(fun(U_227,bool),bool),member(U_227),U_226),U_225))
    | ~ hBOOL(hAPP(fun(U_227,bool),bool,hAPP(fun(U_227,bool),fun(fun(U_227,bool),bool),ord_less_eq(fun(U_227,bool)),U_225),U_224)) ),
    inference(clausify,[status(thm)],[f_105_3]) ).

fof(f_106_1,plain,
    ! [X_b,B,A_2,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),B_2)))
      | ( ti(X_b,A_2) != ti(X_b,B)
        & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_53_insertCI]) ).

fof(f_106_2,plain,
    ! [U_231,U_230,U_229,U_228] :
      ( hBOOL(hAPP(fun(U_231,bool),bool,hAPP(U_231,fun(fun(U_231,bool),bool),member(U_231),U_229),hAPP(fun(U_231,bool),fun(U_231,bool),hAPP(U_231,fun(fun(U_231,bool),fun(U_231,bool)),insert(U_231),U_230),U_228)))
      | ( ti(U_231,U_229) != ti(U_231,U_230)
        & ~ hBOOL(hAPP(fun(U_231,bool),bool,hAPP(U_231,fun(fun(U_231,bool),bool),member(U_231),U_229),U_228)) ) ),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

fof(f_106_3,plain,
    ( ! [U_229,U_228,U_230,U_231] :
        ( ti(U_231,U_229) != ti(U_231,U_230)
        | ~ sP8(U_229,U_228,U_230,U_231) )
    & ! [U_229,U_228,U_230,U_231] :
        ( ~ hBOOL(hAPP(fun(U_231,bool),bool,hAPP(U_231,fun(fun(U_231,bool),bool),member(U_231),U_229),U_228))
        | ~ sP8(U_229,U_228,U_230,U_231) )
    & ! [U_229,U_228,U_230,U_231] :
        ( hBOOL(hAPP(fun(U_231,bool),bool,hAPP(U_231,fun(fun(U_231,bool),bool),member(U_231),U_229),hAPP(fun(U_231,bool),fun(U_231,bool),hAPP(U_231,fun(fun(U_231,bool),fun(U_231,bool)),insert(U_231),U_230),U_228)))
        | sP8(U_229,U_228,U_230,U_231) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_106_2]) ).

cnf(f_106_4,plain,
    ( hBOOL(hAPP(fun(U_231,bool),bool,hAPP(U_231,fun(fun(U_231,bool),bool),member(U_231),U_229),hAPP(fun(U_231,bool),fun(U_231,bool),hAPP(U_231,fun(fun(U_231,bool),fun(U_231,bool)),insert(U_231),U_230),U_228)))
    | sP8(U_229,U_228,U_230,U_231) ),
    inference(clausify,[status(thm)],[f_106_3]) ).

cnf(f_106_5,plain,
    ( ~ hBOOL(hAPP(fun(U_231,bool),bool,hAPP(U_231,fun(fun(U_231,bool),bool),member(U_231),U_229),U_228))
    | ~ sP8(U_229,U_228,U_230,U_231) ),
    inference(clausify,[status(thm)],[f_106_3]) ).

cnf(f_106_6,plain,
    ( ti(U_231,U_229) != ti(U_231,U_230)
    | ~ sP8(U_229,U_228,U_230,U_231) ),
    inference(clausify,[status(thm)],[f_106_3]) ).

fof(f_107_1,plain,
    ! [X_b,A_2,B,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))
      | ti(X_b,A_2) = ti(X_b,B)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),A_3))) ),
    inference(fof_nnf,[status(thm)],[fact_54_insertE]) ).

fof(f_107_2,plain,
    ! [U_235,U_234,U_233,U_232] :
      ( hBOOL(hAPP(fun(U_235,bool),bool,hAPP(U_235,fun(fun(U_235,bool),bool),member(U_235),U_234),U_232))
      | ti(U_235,U_234) = ti(U_235,U_233)
      | ~ hBOOL(hAPP(fun(U_235,bool),bool,hAPP(U_235,fun(fun(U_235,bool),bool),member(U_235),U_234),hAPP(fun(U_235,bool),fun(U_235,bool),hAPP(U_235,fun(fun(U_235,bool),fun(U_235,bool)),insert(U_235),U_233),U_232))) ),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

fof(f_107_3,plain,
    ! [U_234,U_233,U_235,U_232] :
      ( hBOOL(hAPP(fun(U_235,bool),bool,hAPP(U_235,fun(fun(U_235,bool),bool),member(U_235),U_234),U_232))
      | ti(U_235,U_234) = ti(U_235,U_233)
      | ~ hBOOL(hAPP(fun(U_235,bool),bool,hAPP(U_235,fun(fun(U_235,bool),bool),member(U_235),U_234),hAPP(fun(U_235,bool),fun(U_235,bool),hAPP(U_235,fun(fun(U_235,bool),fun(U_235,bool)),insert(U_235),U_233),U_232))) ),
    inference(definitional_conversion,[status(esa)],[f_107_2]) ).

cnf(f_107_4,plain,
    ( hBOOL(hAPP(fun(U_235,bool),bool,hAPP(U_235,fun(fun(U_235,bool),bool),member(U_235),U_234),U_232))
    | ti(U_235,U_234) = ti(U_235,U_233)
    | ~ hBOOL(hAPP(fun(U_235,bool),bool,hAPP(U_235,fun(fun(U_235,bool),bool),member(U_235),U_234),hAPP(fun(U_235,bool),fun(U_235,bool),hAPP(U_235,fun(fun(U_235,bool),fun(U_235,bool)),insert(U_235),U_233),U_232))) ),
    inference(clausify,[status(thm)],[f_107_3]) ).

fof(f_108_1,plain,
    ! [I_1,Pa,K_2] :
      ( hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K_2),I_1)))
      | ? [N_2] :
          ( ~ hBOOL(hAPP(nat,bool,Pa,N_2))
          & hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_2))) )
      | ~ hBOOL(hAPP(nat,bool,Pa,K_2)) ),
    inference(fof_nnf,[status(thm)],[fact_55_zero__induct__lemma]) ).

fof(f_108_2,plain,
    ! [U_239,U_238,U_237] :
      ( hBOOL(hAPP(nat,bool,U_238,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_237),U_239)))
      | ? [U_236] :
          ( ~ hBOOL(hAPP(nat,bool,U_238,U_236))
          & hBOOL(hAPP(nat,bool,U_238,hAPP(nat,nat,suc,U_236))) )
      | ~ hBOOL(hAPP(nat,bool,U_238,U_237)) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

fof(f_108_3,plain,
    ! [U_239,U_238,U_237] :
      ( hBOOL(hAPP(nat,bool,U_238,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_237),U_239)))
      | ( ~ hBOOL(hAPP(nat,bool,U_238,sK4(U_239,U_238,U_237)))
        & hBOOL(hAPP(nat,bool,U_238,hAPP(nat,nat,suc,sK4(U_239,U_238,U_237)))) )
      | ~ hBOOL(hAPP(nat,bool,U_238,U_237)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_236,sK4(U_239,U_238,U_237))],[f_108_2]) ).

fof(f_108_4,plain,
    ( ! [U_237,U_238,U_239] :
        ( ~ hBOOL(hAPP(nat,bool,U_238,sK4(U_239,U_238,U_237)))
        | ~ sP9(U_237,U_238,U_239) )
    & ! [U_237,U_238,U_239] :
        ( hBOOL(hAPP(nat,bool,U_238,hAPP(nat,nat,suc,sK4(U_239,U_238,U_237))))
        | ~ sP9(U_237,U_238,U_239) )
    & ! [U_237,U_238,U_239] :
        ( hBOOL(hAPP(nat,bool,U_238,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_237),U_239)))
        | sP9(U_237,U_238,U_239)
        | ~ hBOOL(hAPP(nat,bool,U_238,U_237)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_108_3]) ).

cnf(f_108_5,plain,
    ( hBOOL(hAPP(nat,bool,U_238,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_237),U_239)))
    | sP9(U_237,U_238,U_239)
    | ~ hBOOL(hAPP(nat,bool,U_238,U_237)) ),
    inference(clausify,[status(thm)],[f_108_4]) ).

cnf(f_108_6,plain,
    ( hBOOL(hAPP(nat,bool,U_238,hAPP(nat,nat,suc,sK4(U_239,U_238,U_237))))
    | ~ sP9(U_237,U_238,U_239) ),
    inference(clausify,[status(thm)],[f_108_4]) ).

cnf(f_108_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_238,sK4(U_239,U_238,U_237)))
    | ~ sP9(U_237,U_238,U_239) ),
    inference(clausify,[status(thm)],[f_108_4]) ).

fof(f_109_1,plain,
    ! [N,M_3] :
      ( ? [M_2] : M_3 = hAPP(nat,nat,suc,M_2)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_56_Suc__le__D]) ).

fof(f_109_2,plain,
    ! [U_242,U_241] :
      ( ? [U_240] : U_241 = hAPP(nat,nat,suc,U_240)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_242)),U_241)) ),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

fof(f_109_3,plain,
    ! [U_242,U_241] :
      ( U_241 = hAPP(nat,nat,suc,sK5(U_242,U_241))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_242)),U_241)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_240,sK5(U_242,U_241))],[f_109_2]) ).

fof(f_109_4,plain,
    ! [U_241,U_242] :
      ( U_241 = hAPP(nat,nat,suc,sK5(U_242,U_241))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_242)),U_241)) ),
    inference(definitional_conversion,[status(esa)],[f_109_3]) ).

cnf(f_109_5,plain,
    ( U_241 = hAPP(nat,nat,suc,sK5(U_242,U_241))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_242)),U_241)) ),
    inference(clausify,[status(thm)],[f_109_4]) ).

fof(f_110_1,plain,
    ! [X_b,A_2,B_2] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2))),
    inference(fof_nnf,[status(thm)],[fact_57_insertI1]) ).

fof(f_110_2,plain,
    ! [U_245,U_244,U_243] : hBOOL(hAPP(fun(U_245,bool),bool,hAPP(U_245,fun(fun(U_245,bool),bool),member(U_245),U_244),hAPP(fun(U_245,bool),fun(U_245,bool),hAPP(U_245,fun(fun(U_245,bool),fun(U_245,bool)),insert(U_245),U_244),U_243))),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

fof(f_110_3,plain,
    ! [U_244,U_245,U_243] : hBOOL(hAPP(fun(U_245,bool),bool,hAPP(U_245,fun(fun(U_245,bool),bool),member(U_245),U_244),hAPP(fun(U_245,bool),fun(U_245,bool),hAPP(U_245,fun(fun(U_245,bool),fun(U_245,bool)),insert(U_245),U_244),U_243))),
    inference(definitional_conversion,[status(esa)],[f_110_2]) ).

cnf(f_110_4,plain,
    hBOOL(hAPP(fun(U_245,bool),bool,hAPP(U_245,fun(fun(U_245,bool),bool),member(U_245),U_244),hAPP(fun(U_245,bool),fun(U_245,bool),hAPP(U_245,fun(fun(U_245,bool),fun(U_245,bool)),insert(U_245),U_244),U_243))),
    inference(clausify,[status(thm)],[f_110_3]) ).

fof(f_111_1,plain,
    ! [X_b,A_2,B_2] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2))),
    inference(fof_nnf,[status(thm)],[fact_58_insert__compr]) ).

fof(f_111_2,plain,
    ! [U_248,U_247,U_246] : hAPP(fun(U_248,bool),fun(U_248,bool),hAPP(U_248,fun(fun(U_248,bool),fun(U_248,bool)),insert(U_248),U_247),U_246) = hAPP(fun(U_248,bool),fun(U_248,bool),collect(U_248),hAPP(fun(U_248,bool),fun(U_248,bool),hAPP(fun(U_248,fun(bool,bool)),fun(fun(U_248,bool),fun(U_248,bool)),combs(U_248,bool,bool),hAPP(fun(U_248,bool),fun(U_248,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_248,bool),fun(U_248,fun(bool,bool))),combb(bool,fun(bool,bool),U_248),fdisj),hAPP(U_248,fun(U_248,bool),hAPP(fun(U_248,fun(U_248,bool)),fun(U_248,fun(U_248,bool)),combc(U_248,U_248,bool),fequal(U_248)),U_247))),hAPP(fun(U_248,bool),fun(U_248,bool),hAPP(fun(U_248,fun(fun(U_248,bool),bool)),fun(fun(U_248,bool),fun(U_248,bool)),combc(U_248,fun(U_248,bool),bool),member(U_248)),U_246))),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

fof(f_111_3,plain,
    ! [U_248,U_246,U_247] : hAPP(fun(U_248,bool),fun(U_248,bool),hAPP(U_248,fun(fun(U_248,bool),fun(U_248,bool)),insert(U_248),U_247),U_246) = hAPP(fun(U_248,bool),fun(U_248,bool),collect(U_248),hAPP(fun(U_248,bool),fun(U_248,bool),hAPP(fun(U_248,fun(bool,bool)),fun(fun(U_248,bool),fun(U_248,bool)),combs(U_248,bool,bool),hAPP(fun(U_248,bool),fun(U_248,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_248,bool),fun(U_248,fun(bool,bool))),combb(bool,fun(bool,bool),U_248),fdisj),hAPP(U_248,fun(U_248,bool),hAPP(fun(U_248,fun(U_248,bool)),fun(U_248,fun(U_248,bool)),combc(U_248,U_248,bool),fequal(U_248)),U_247))),hAPP(fun(U_248,bool),fun(U_248,bool),hAPP(fun(U_248,fun(fun(U_248,bool),bool)),fun(fun(U_248,bool),fun(U_248,bool)),combc(U_248,fun(U_248,bool),bool),member(U_248)),U_246))),
    inference(definitional_conversion,[status(esa)],[f_111_2]) ).

cnf(f_111_4,plain,
    hAPP(fun(U_248,bool),fun(U_248,bool),hAPP(U_248,fun(fun(U_248,bool),fun(U_248,bool)),insert(U_248),U_247),U_246) = hAPP(fun(U_248,bool),fun(U_248,bool),collect(U_248),hAPP(fun(U_248,bool),fun(U_248,bool),hAPP(fun(U_248,fun(bool,bool)),fun(fun(U_248,bool),fun(U_248,bool)),combs(U_248,bool,bool),hAPP(fun(U_248,bool),fun(U_248,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_248,bool),fun(U_248,fun(bool,bool))),combb(bool,fun(bool,bool),U_248),fdisj),hAPP(U_248,fun(U_248,bool),hAPP(fun(U_248,fun(U_248,bool)),fun(U_248,fun(U_248,bool)),combc(U_248,U_248,bool),fequal(U_248)),U_247))),hAPP(fun(U_248,bool),fun(U_248,bool),hAPP(fun(U_248,fun(fun(U_248,bool),bool)),fun(fun(U_248,bool),fun(U_248,bool)),combc(U_248,fun(U_248,bool),bool),member(U_248)),U_246))),
    inference(clausify,[status(thm)],[f_111_3]) ).

fof(f_112_1,plain,
    ! [X_b,A_2,Pa] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fimplies),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_59_insert__Collect]) ).

fof(f_112_2,plain,
    ! [U_251,U_250,U_249] : hAPP(fun(U_251,bool),fun(U_251,bool),hAPP(U_251,fun(fun(U_251,bool),fun(U_251,bool)),insert(U_251),U_250),hAPP(fun(U_251,bool),fun(U_251,bool),collect(U_251),U_249)) = hAPP(fun(U_251,bool),fun(U_251,bool),collect(U_251),hAPP(fun(U_251,bool),fun(U_251,bool),hAPP(fun(U_251,fun(bool,bool)),fun(fun(U_251,bool),fun(U_251,bool)),combs(U_251,bool,bool),hAPP(fun(U_251,bool),fun(U_251,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_251,bool),fun(U_251,fun(bool,bool))),combb(bool,fun(bool,bool),U_251),fimplies),hAPP(fun(U_251,bool),fun(U_251,bool),hAPP(fun(bool,bool),fun(fun(U_251,bool),fun(U_251,bool)),combb(bool,bool,U_251),fNot),hAPP(U_251,fun(U_251,bool),hAPP(fun(U_251,fun(U_251,bool)),fun(U_251,fun(U_251,bool)),combc(U_251,U_251,bool),fequal(U_251)),U_250)))),U_249)),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

fof(f_112_3,plain,
    ! [U_250,U_249,U_251] : hAPP(fun(U_251,bool),fun(U_251,bool),hAPP(U_251,fun(fun(U_251,bool),fun(U_251,bool)),insert(U_251),U_250),hAPP(fun(U_251,bool),fun(U_251,bool),collect(U_251),U_249)) = hAPP(fun(U_251,bool),fun(U_251,bool),collect(U_251),hAPP(fun(U_251,bool),fun(U_251,bool),hAPP(fun(U_251,fun(bool,bool)),fun(fun(U_251,bool),fun(U_251,bool)),combs(U_251,bool,bool),hAPP(fun(U_251,bool),fun(U_251,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_251,bool),fun(U_251,fun(bool,bool))),combb(bool,fun(bool,bool),U_251),fimplies),hAPP(fun(U_251,bool),fun(U_251,bool),hAPP(fun(bool,bool),fun(fun(U_251,bool),fun(U_251,bool)),combb(bool,bool,U_251),fNot),hAPP(U_251,fun(U_251,bool),hAPP(fun(U_251,fun(U_251,bool)),fun(U_251,fun(U_251,bool)),combc(U_251,U_251,bool),fequal(U_251)),U_250)))),U_249)),
    inference(definitional_conversion,[status(esa)],[f_112_2]) ).

cnf(f_112_4,plain,
    hAPP(fun(U_251,bool),fun(U_251,bool),hAPP(U_251,fun(fun(U_251,bool),fun(U_251,bool)),insert(U_251),U_250),hAPP(fun(U_251,bool),fun(U_251,bool),collect(U_251),U_249)) = hAPP(fun(U_251,bool),fun(U_251,bool),collect(U_251),hAPP(fun(U_251,bool),fun(U_251,bool),hAPP(fun(U_251,fun(bool,bool)),fun(fun(U_251,bool),fun(U_251,bool)),combs(U_251,bool,bool),hAPP(fun(U_251,bool),fun(U_251,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_251,bool),fun(U_251,fun(bool,bool))),combb(bool,fun(bool,bool),U_251),fimplies),hAPP(fun(U_251,bool),fun(U_251,bool),hAPP(fun(bool,bool),fun(fun(U_251,bool),fun(U_251,bool)),combb(bool,bool,U_251),fNot),hAPP(U_251,fun(U_251,bool),hAPP(fun(U_251,fun(U_251,bool)),fun(U_251,fun(U_251,bool)),combc(U_251,U_251,bool),fequal(U_251)),U_250)))),U_249)),
    inference(clausify,[status(thm)],[f_112_3]) ).

fof(f_113_1,plain,
    ! [X_b,X_1,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3),
    inference(fof_nnf,[status(thm)],[fact_60_insert__absorb2]) ).

fof(f_113_2,plain,
    ! [U_254,U_253,U_252] : hAPP(fun(U_254,bool),fun(U_254,bool),hAPP(U_254,fun(fun(U_254,bool),fun(U_254,bool)),insert(U_254),U_253),hAPP(fun(U_254,bool),fun(U_254,bool),hAPP(U_254,fun(fun(U_254,bool),fun(U_254,bool)),insert(U_254),U_253),U_252)) = hAPP(fun(U_254,bool),fun(U_254,bool),hAPP(U_254,fun(fun(U_254,bool),fun(U_254,bool)),insert(U_254),U_253),U_252),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

fof(f_113_3,plain,
    ! [U_253,U_254,U_252] : hAPP(fun(U_254,bool),fun(U_254,bool),hAPP(U_254,fun(fun(U_254,bool),fun(U_254,bool)),insert(U_254),U_253),hAPP(fun(U_254,bool),fun(U_254,bool),hAPP(U_254,fun(fun(U_254,bool),fun(U_254,bool)),insert(U_254),U_253),U_252)) = hAPP(fun(U_254,bool),fun(U_254,bool),hAPP(U_254,fun(fun(U_254,bool),fun(U_254,bool)),insert(U_254),U_253),U_252),
    inference(definitional_conversion,[status(esa)],[f_113_2]) ).

cnf(f_113_4,plain,
    hAPP(fun(U_254,bool),fun(U_254,bool),hAPP(U_254,fun(fun(U_254,bool),fun(U_254,bool)),insert(U_254),U_253),hAPP(fun(U_254,bool),fun(U_254,bool),hAPP(U_254,fun(fun(U_254,bool),fun(U_254,bool)),insert(U_254),U_253),U_252)) = hAPP(fun(U_254,bool),fun(U_254,bool),hAPP(U_254,fun(fun(U_254,bool),fun(U_254,bool)),insert(U_254),U_253),U_252),
    inference(clausify,[status(thm)],[f_113_3]) ).

fof(f_114_1,plain,
    ! [X_b,X_1,Y_1,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),A_3)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),
    inference(fof_nnf,[status(thm)],[fact_61_insert__commute]) ).

fof(f_114_2,plain,
    ! [U_258,U_257,U_256,U_255] : hAPP(fun(U_258,bool),fun(U_258,bool),hAPP(U_258,fun(fun(U_258,bool),fun(U_258,bool)),insert(U_258),U_257),hAPP(fun(U_258,bool),fun(U_258,bool),hAPP(U_258,fun(fun(U_258,bool),fun(U_258,bool)),insert(U_258),U_256),U_255)) = hAPP(fun(U_258,bool),fun(U_258,bool),hAPP(U_258,fun(fun(U_258,bool),fun(U_258,bool)),insert(U_258),U_256),hAPP(fun(U_258,bool),fun(U_258,bool),hAPP(U_258,fun(fun(U_258,bool),fun(U_258,bool)),insert(U_258),U_257),U_255)),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

fof(f_114_3,plain,
    ! [U_257,U_258,U_255,U_256] : hAPP(fun(U_258,bool),fun(U_258,bool),hAPP(U_258,fun(fun(U_258,bool),fun(U_258,bool)),insert(U_258),U_257),hAPP(fun(U_258,bool),fun(U_258,bool),hAPP(U_258,fun(fun(U_258,bool),fun(U_258,bool)),insert(U_258),U_256),U_255)) = hAPP(fun(U_258,bool),fun(U_258,bool),hAPP(U_258,fun(fun(U_258,bool),fun(U_258,bool)),insert(U_258),U_256),hAPP(fun(U_258,bool),fun(U_258,bool),hAPP(U_258,fun(fun(U_258,bool),fun(U_258,bool)),insert(U_258),U_257),U_255)),
    inference(definitional_conversion,[status(esa)],[f_114_2]) ).

cnf(f_114_4,plain,
    hAPP(fun(U_258,bool),fun(U_258,bool),hAPP(U_258,fun(fun(U_258,bool),fun(U_258,bool)),insert(U_258),U_257),hAPP(fun(U_258,bool),fun(U_258,bool),hAPP(U_258,fun(fun(U_258,bool),fun(U_258,bool)),insert(U_258),U_256),U_255)) = hAPP(fun(U_258,bool),fun(U_258,bool),hAPP(U_258,fun(fun(U_258,bool),fun(U_258,bool)),insert(U_258),U_256),hAPP(fun(U_258,bool),fun(U_258,bool),hAPP(U_258,fun(fun(U_258,bool),fun(U_258,bool)),insert(U_258),U_257),U_255)),
    inference(clausify,[status(thm)],[f_114_3]) ).

fof(f_115_1,plain,
    ! [X_b,A_2,B,A_3] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),A_3)))
        | ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))
          & ti(X_b,A_2) != ti(X_b,B) ) )
      & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))
        | ti(X_b,A_2) = ti(X_b,B)
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),A_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_62_insert__iff]) ).

fof(f_115_2,plain,
    ! [U_262,U_261,U_260,U_259] :
      ( ( hBOOL(hAPP(fun(U_262,bool),bool,hAPP(U_262,fun(fun(U_262,bool),bool),member(U_262),U_261),hAPP(fun(U_262,bool),fun(U_262,bool),hAPP(U_262,fun(fun(U_262,bool),fun(U_262,bool)),insert(U_262),U_260),U_259)))
        | ( ~ hBOOL(hAPP(fun(U_262,bool),bool,hAPP(U_262,fun(fun(U_262,bool),bool),member(U_262),U_261),U_259))
          & ti(U_262,U_261) != ti(U_262,U_260) ) )
      & ( hBOOL(hAPP(fun(U_262,bool),bool,hAPP(U_262,fun(fun(U_262,bool),bool),member(U_262),U_261),U_259))
        | ti(U_262,U_261) = ti(U_262,U_260)
        | ~ hBOOL(hAPP(fun(U_262,bool),bool,hAPP(U_262,fun(fun(U_262,bool),bool),member(U_262),U_261),hAPP(fun(U_262,bool),fun(U_262,bool),hAPP(U_262,fun(fun(U_262,bool),fun(U_262,bool)),insert(U_262),U_260),U_259))) ) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

fof(f_115_3,plain,
    ( ! [U_270,U_268,U_266,U_264] :
        ( hBOOL(hAPP(fun(U_270,bool),bool,hAPP(U_270,fun(fun(U_270,bool),bool),member(U_270),U_268),hAPP(fun(U_270,bool),fun(U_270,bool),hAPP(U_270,fun(fun(U_270,bool),fun(U_270,bool)),insert(U_270),U_266),U_264)))
        | ( ~ hBOOL(hAPP(fun(U_270,bool),bool,hAPP(U_270,fun(fun(U_270,bool),bool),member(U_270),U_268),U_264))
          & ti(U_270,U_268) != ti(U_270,U_266) ) )
    & ! [U_269,U_267,U_265,U_263] :
        ( hBOOL(hAPP(fun(U_269,bool),bool,hAPP(U_269,fun(fun(U_269,bool),bool),member(U_269),U_267),U_263))
        | ti(U_269,U_267) = ti(U_269,U_265)
        | ~ hBOOL(hAPP(fun(U_269,bool),bool,hAPP(U_269,fun(fun(U_269,bool),bool),member(U_269),U_267),hAPP(fun(U_269,bool),fun(U_269,bool),hAPP(U_269,fun(fun(U_269,bool),fun(U_269,bool)),insert(U_269),U_265),U_263))) ) ),
    inference(miniscope,[status(thm)],[f_115_2]) ).

fof(f_115_4,plain,
    ( ! [U_264,U_268,U_266,U_270] :
        ( ~ hBOOL(hAPP(fun(U_270,bool),bool,hAPP(U_270,fun(fun(U_270,bool),bool),member(U_270),U_268),U_264))
        | ~ sP10(U_264,U_268,U_266,U_270) )
    & ! [U_264,U_268,U_266,U_270] :
        ( ti(U_270,U_268) != ti(U_270,U_266)
        | ~ sP10(U_264,U_268,U_266,U_270) )
    & ! [U_264,U_268,U_266,U_270] :
        ( hBOOL(hAPP(fun(U_270,bool),bool,hAPP(U_270,fun(fun(U_270,bool),bool),member(U_270),U_268),hAPP(fun(U_270,bool),fun(U_270,bool),hAPP(U_270,fun(fun(U_270,bool),fun(U_270,bool)),insert(U_270),U_266),U_264)))
        | sP10(U_264,U_268,U_266,U_270) )
    & ! [U_265,U_263,U_267,U_269] :
        ( hBOOL(hAPP(fun(U_269,bool),bool,hAPP(U_269,fun(fun(U_269,bool),bool),member(U_269),U_267),U_263))
        | ti(U_269,U_267) = ti(U_269,U_265)
        | ~ hBOOL(hAPP(fun(U_269,bool),bool,hAPP(U_269,fun(fun(U_269,bool),bool),member(U_269),U_267),hAPP(fun(U_269,bool),fun(U_269,bool),hAPP(U_269,fun(fun(U_269,bool),fun(U_269,bool)),insert(U_269),U_265),U_263))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_115_3]) ).

cnf(f_115_5,plain,
    ( hBOOL(hAPP(fun(U_269,bool),bool,hAPP(U_269,fun(fun(U_269,bool),bool),member(U_269),U_267),U_263))
    | ti(U_269,U_267) = ti(U_269,U_265)
    | ~ hBOOL(hAPP(fun(U_269,bool),bool,hAPP(U_269,fun(fun(U_269,bool),bool),member(U_269),U_267),hAPP(fun(U_269,bool),fun(U_269,bool),hAPP(U_269,fun(fun(U_269,bool),fun(U_269,bool)),insert(U_269),U_265),U_263))) ),
    inference(clausify,[status(thm)],[f_115_4]) ).

cnf(f_115_6,plain,
    ( hBOOL(hAPP(fun(U_270,bool),bool,hAPP(U_270,fun(fun(U_270,bool),bool),member(U_270),U_268),hAPP(fun(U_270,bool),fun(U_270,bool),hAPP(U_270,fun(fun(U_270,bool),fun(U_270,bool)),insert(U_270),U_266),U_264)))
    | sP10(U_264,U_268,U_266,U_270) ),
    inference(clausify,[status(thm)],[f_115_4]) ).

cnf(f_115_7,plain,
    ( ti(U_270,U_268) != ti(U_270,U_266)
    | ~ sP10(U_264,U_268,U_266,U_270) ),
    inference(clausify,[status(thm)],[f_115_4]) ).

cnf(f_115_8,plain,
    ( ~ hBOOL(hAPP(fun(U_270,bool),bool,hAPP(U_270,fun(fun(U_270,bool),bool),member(U_270),U_268),U_264))
    | ~ sP10(U_264,U_268,U_266,U_270) ),
    inference(clausify,[status(thm)],[f_115_4]) ).

fof(f_116_1,plain,
    ! [X_b,Y_1,A_3,X_1] :
      ( ( hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),A_3),X_1))
        | ( ~ hBOOL(hAPP(X_b,bool,A_3,X_1))
          & ti(X_b,Y_1) != ti(X_b,X_1) ) )
      & ( hBOOL(hAPP(X_b,bool,A_3,X_1))
        | ti(X_b,Y_1) = ti(X_b,X_1)
        | ~ hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),A_3),X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_63_insert__code]) ).

fof(f_116_2,plain,
    ! [U_274,U_273,U_272,U_271] :
      ( ( hBOOL(hAPP(U_274,bool,hAPP(fun(U_274,bool),fun(U_274,bool),hAPP(U_274,fun(fun(U_274,bool),fun(U_274,bool)),insert(U_274),U_273),U_272),U_271))
        | ( ~ hBOOL(hAPP(U_274,bool,U_272,U_271))
          & ti(U_274,U_273) != ti(U_274,U_271) ) )
      & ( hBOOL(hAPP(U_274,bool,U_272,U_271))
        | ti(U_274,U_273) = ti(U_274,U_271)
        | ~ hBOOL(hAPP(U_274,bool,hAPP(fun(U_274,bool),fun(U_274,bool),hAPP(U_274,fun(fun(U_274,bool),fun(U_274,bool)),insert(U_274),U_273),U_272),U_271)) ) ),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

fof(f_116_3,plain,
    ( ! [U_282,U_280,U_278,U_276] :
        ( hBOOL(hAPP(U_282,bool,hAPP(fun(U_282,bool),fun(U_282,bool),hAPP(U_282,fun(fun(U_282,bool),fun(U_282,bool)),insert(U_282),U_280),U_278),U_276))
        | ( ~ hBOOL(hAPP(U_282,bool,U_278,U_276))
          & ti(U_282,U_280) != ti(U_282,U_276) ) )
    & ! [U_281,U_279,U_277,U_275] :
        ( hBOOL(hAPP(U_281,bool,U_277,U_275))
        | ti(U_281,U_279) = ti(U_281,U_275)
        | ~ hBOOL(hAPP(U_281,bool,hAPP(fun(U_281,bool),fun(U_281,bool),hAPP(U_281,fun(fun(U_281,bool),fun(U_281,bool)),insert(U_281),U_279),U_277),U_275)) ) ),
    inference(miniscope,[status(thm)],[f_116_2]) ).

fof(f_116_4,plain,
    ( ! [U_276,U_280,U_278,U_282] :
        ( ~ hBOOL(hAPP(U_282,bool,U_278,U_276))
        | ~ sP11(U_276,U_280,U_278,U_282) )
    & ! [U_276,U_280,U_278,U_282] :
        ( ti(U_282,U_280) != ti(U_282,U_276)
        | ~ sP11(U_276,U_280,U_278,U_282) )
    & ! [U_276,U_280,U_278,U_282] :
        ( hBOOL(hAPP(U_282,bool,hAPP(fun(U_282,bool),fun(U_282,bool),hAPP(U_282,fun(fun(U_282,bool),fun(U_282,bool)),insert(U_282),U_280),U_278),U_276))
        | sP11(U_276,U_280,U_278,U_282) )
    & ! [U_275,U_277,U_279,U_281] :
        ( hBOOL(hAPP(U_281,bool,U_277,U_275))
        | ti(U_281,U_279) = ti(U_281,U_275)
        | ~ hBOOL(hAPP(U_281,bool,hAPP(fun(U_281,bool),fun(U_281,bool),hAPP(U_281,fun(fun(U_281,bool),fun(U_281,bool)),insert(U_281),U_279),U_277),U_275)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_116_3]) ).

cnf(f_116_5,plain,
    ( hBOOL(hAPP(U_281,bool,U_277,U_275))
    | ti(U_281,U_279) = ti(U_281,U_275)
    | ~ hBOOL(hAPP(U_281,bool,hAPP(fun(U_281,bool),fun(U_281,bool),hAPP(U_281,fun(fun(U_281,bool),fun(U_281,bool)),insert(U_281),U_279),U_277),U_275)) ),
    inference(clausify,[status(thm)],[f_116_4]) ).

cnf(f_116_6,plain,
    ( hBOOL(hAPP(U_282,bool,hAPP(fun(U_282,bool),fun(U_282,bool),hAPP(U_282,fun(fun(U_282,bool),fun(U_282,bool)),insert(U_282),U_280),U_278),U_276))
    | sP11(U_276,U_280,U_278,U_282) ),
    inference(clausify,[status(thm)],[f_116_4]) ).

cnf(f_116_7,plain,
    ( ti(U_282,U_280) != ti(U_282,U_276)
    | ~ sP11(U_276,U_280,U_278,U_282) ),
    inference(clausify,[status(thm)],[f_116_4]) ).

cnf(f_116_8,plain,
    ( ~ hBOOL(hAPP(U_282,bool,U_278,U_276))
    | ~ sP11(U_276,U_280,U_278,U_282) ),
    inference(clausify,[status(thm)],[f_116_4]) ).

fof(f_117_1,plain,
    ! [X_b,B_2,X_1,A_3] :
      ( ( ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2)
          | ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_2) )
        & ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)
          | hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2) ) )
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_64_insert__ident]) ).

fof(f_117_2,plain,
    ! [U_286,U_285,U_284,U_283] :
      ( ( ( hAPP(fun(U_286,bool),fun(U_286,bool),hAPP(U_286,fun(fun(U_286,bool),fun(U_286,bool)),insert(U_286),U_284),U_283) = hAPP(fun(U_286,bool),fun(U_286,bool),hAPP(U_286,fun(fun(U_286,bool),fun(U_286,bool)),insert(U_286),U_284),U_285)
          | ti(fun(U_286,bool),U_283) != ti(fun(U_286,bool),U_285) )
        & ( ti(fun(U_286,bool),U_283) = ti(fun(U_286,bool),U_285)
          | hAPP(fun(U_286,bool),fun(U_286,bool),hAPP(U_286,fun(fun(U_286,bool),fun(U_286,bool)),insert(U_286),U_284),U_283) != hAPP(fun(U_286,bool),fun(U_286,bool),hAPP(U_286,fun(fun(U_286,bool),fun(U_286,bool)),insert(U_286),U_284),U_285) ) )
      | hBOOL(hAPP(fun(U_286,bool),bool,hAPP(U_286,fun(fun(U_286,bool),bool),member(U_286),U_284),U_285))
      | hBOOL(hAPP(fun(U_286,bool),bool,hAPP(U_286,fun(fun(U_286,bool),bool),member(U_286),U_284),U_283)) ),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

fof(f_117_3,plain,
    ( ! [U_284,U_285,U_286,U_283] :
        ( hAPP(fun(U_286,bool),fun(U_286,bool),hAPP(U_286,fun(fun(U_286,bool),fun(U_286,bool)),insert(U_286),U_284),U_283) = hAPP(fun(U_286,bool),fun(U_286,bool),hAPP(U_286,fun(fun(U_286,bool),fun(U_286,bool)),insert(U_286),U_284),U_285)
        | ti(fun(U_286,bool),U_283) != ti(fun(U_286,bool),U_285)
        | ~ sP12(U_284,U_285,U_286,U_283) )
    & ! [U_284,U_285,U_286,U_283] :
        ( ti(fun(U_286,bool),U_283) = ti(fun(U_286,bool),U_285)
        | hAPP(fun(U_286,bool),fun(U_286,bool),hAPP(U_286,fun(fun(U_286,bool),fun(U_286,bool)),insert(U_286),U_284),U_283) != hAPP(fun(U_286,bool),fun(U_286,bool),hAPP(U_286,fun(fun(U_286,bool),fun(U_286,bool)),insert(U_286),U_284),U_285)
        | ~ sP12(U_284,U_285,U_286,U_283) )
    & ! [U_284,U_285,U_286,U_283] :
        ( sP12(U_284,U_285,U_286,U_283)
        | hBOOL(hAPP(fun(U_286,bool),bool,hAPP(U_286,fun(fun(U_286,bool),bool),member(U_286),U_284),U_285))
        | hBOOL(hAPP(fun(U_286,bool),bool,hAPP(U_286,fun(fun(U_286,bool),bool),member(U_286),U_284),U_283)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_117_2]) ).

cnf(f_117_4,plain,
    ( sP12(U_284,U_285,U_286,U_283)
    | hBOOL(hAPP(fun(U_286,bool),bool,hAPP(U_286,fun(fun(U_286,bool),bool),member(U_286),U_284),U_285))
    | hBOOL(hAPP(fun(U_286,bool),bool,hAPP(U_286,fun(fun(U_286,bool),bool),member(U_286),U_284),U_283)) ),
    inference(clausify,[status(thm)],[f_117_3]) ).

cnf(f_117_5,plain,
    ( ti(fun(U_286,bool),U_283) = ti(fun(U_286,bool),U_285)
    | hAPP(fun(U_286,bool),fun(U_286,bool),hAPP(U_286,fun(fun(U_286,bool),fun(U_286,bool)),insert(U_286),U_284),U_283) != hAPP(fun(U_286,bool),fun(U_286,bool),hAPP(U_286,fun(fun(U_286,bool),fun(U_286,bool)),insert(U_286),U_284),U_285)
    | ~ sP12(U_284,U_285,U_286,U_283) ),
    inference(clausify,[status(thm)],[f_117_3]) ).

cnf(f_117_6,plain,
    ( hAPP(fun(U_286,bool),fun(U_286,bool),hAPP(U_286,fun(fun(U_286,bool),fun(U_286,bool)),insert(U_286),U_284),U_283) = hAPP(fun(U_286,bool),fun(U_286,bool),hAPP(U_286,fun(fun(U_286,bool),fun(U_286,bool)),insert(U_286),U_284),U_285)
    | ti(fun(U_286,bool),U_283) != ti(fun(U_286,bool),U_285)
    | ~ sP12(U_284,U_285,U_286,U_283) ),
    inference(clausify,[status(thm)],[f_117_3]) ).

fof(f_118_1,plain,
    ! [X_b,B,A_2,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),B_2)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_65_insertI2]) ).

fof(f_118_2,plain,
    ! [U_290,U_289,U_288,U_287] :
      ( hBOOL(hAPP(fun(U_290,bool),bool,hAPP(U_290,fun(fun(U_290,bool),bool),member(U_290),U_288),hAPP(fun(U_290,bool),fun(U_290,bool),hAPP(U_290,fun(fun(U_290,bool),fun(U_290,bool)),insert(U_290),U_289),U_287)))
      | ~ hBOOL(hAPP(fun(U_290,bool),bool,hAPP(U_290,fun(fun(U_290,bool),bool),member(U_290),U_288),U_287)) ),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

fof(f_118_3,plain,
    ! [U_287,U_290,U_289,U_288] :
      ( hBOOL(hAPP(fun(U_290,bool),bool,hAPP(U_290,fun(fun(U_290,bool),bool),member(U_290),U_288),hAPP(fun(U_290,bool),fun(U_290,bool),hAPP(U_290,fun(fun(U_290,bool),fun(U_290,bool)),insert(U_290),U_289),U_287)))
      | ~ hBOOL(hAPP(fun(U_290,bool),bool,hAPP(U_290,fun(fun(U_290,bool),bool),member(U_290),U_288),U_287)) ),
    inference(definitional_conversion,[status(esa)],[f_118_2]) ).

cnf(f_118_4,plain,
    ( hBOOL(hAPP(fun(U_290,bool),bool,hAPP(U_290,fun(fun(U_290,bool),bool),member(U_290),U_288),hAPP(fun(U_290,bool),fun(U_290,bool),hAPP(U_290,fun(fun(U_290,bool),fun(U_290,bool)),insert(U_290),U_289),U_287)))
    | ~ hBOOL(hAPP(fun(U_290,bool),bool,hAPP(U_290,fun(fun(U_290,bool),bool),member(U_290),U_288),U_287)) ),
    inference(clausify,[status(thm)],[f_118_3]) ).

fof(f_119_1,plain,
    ! [X_b,A_2,A_3] :
      ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) = ti(fun(X_b,bool),A_3)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_66_insert__absorb]) ).

fof(f_119_2,plain,
    ! [U_293,U_292,U_291] :
      ( hAPP(fun(U_293,bool),fun(U_293,bool),hAPP(U_293,fun(fun(U_293,bool),fun(U_293,bool)),insert(U_293),U_292),U_291) = ti(fun(U_293,bool),U_291)
      | ~ hBOOL(hAPP(fun(U_293,bool),bool,hAPP(U_293,fun(fun(U_293,bool),bool),member(U_293),U_292),U_291)) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

fof(f_119_3,plain,
    ! [U_293,U_291,U_292] :
      ( hAPP(fun(U_293,bool),fun(U_293,bool),hAPP(U_293,fun(fun(U_293,bool),fun(U_293,bool)),insert(U_293),U_292),U_291) = ti(fun(U_293,bool),U_291)
      | ~ hBOOL(hAPP(fun(U_293,bool),bool,hAPP(U_293,fun(fun(U_293,bool),bool),member(U_293),U_292),U_291)) ),
    inference(definitional_conversion,[status(esa)],[f_119_2]) ).

cnf(f_119_4,plain,
    ( hAPP(fun(U_293,bool),fun(U_293,bool),hAPP(U_293,fun(fun(U_293,bool),fun(U_293,bool)),insert(U_293),U_292),U_291) = ti(fun(U_293,bool),U_291)
    | ~ hBOOL(hAPP(fun(U_293,bool),bool,hAPP(U_293,fun(fun(U_293,bool),bool),member(U_293),U_292),U_291)) ),
    inference(clausify,[status(thm)],[f_119_3]) ).

fof(f_120_1,plain,
    ! [X_b,A_3] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),A_3)),
    inference(fof_nnf,[status(thm)],[fact_67_subset__refl]) ).

fof(f_120_2,plain,
    ! [U_295,U_294] : hBOOL(hAPP(fun(U_295,bool),bool,hAPP(fun(U_295,bool),fun(fun(U_295,bool),bool),ord_less_eq(fun(U_295,bool)),U_294),U_294)),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

fof(f_120_3,plain,
    ! [U_294,U_295] : hBOOL(hAPP(fun(U_295,bool),bool,hAPP(fun(U_295,bool),fun(fun(U_295,bool),bool),ord_less_eq(fun(U_295,bool)),U_294),U_294)),
    inference(definitional_conversion,[status(esa)],[f_120_2]) ).

cnf(f_120_4,plain,
    hBOOL(hAPP(fun(U_295,bool),bool,hAPP(fun(U_295,bool),fun(fun(U_295,bool),bool),ord_less_eq(fun(U_295,bool)),U_294),U_294)),
    inference(clausify,[status(thm)],[f_120_3]) ).

fof(f_121_1,plain,
    ! [X_b,A_3,B_2] :
      ( ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) )
      & ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) )
        | ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_68_set__eq__subset]) ).

fof(f_121_2,plain,
    ! [U_298,U_297,U_296] :
      ( ( ti(fun(U_298,bool),U_297) = ti(fun(U_298,bool),U_296)
        | ~ hBOOL(hAPP(fun(U_298,bool),bool,hAPP(fun(U_298,bool),fun(fun(U_298,bool),bool),ord_less_eq(fun(U_298,bool)),U_296),U_297))
        | ~ hBOOL(hAPP(fun(U_298,bool),bool,hAPP(fun(U_298,bool),fun(fun(U_298,bool),bool),ord_less_eq(fun(U_298,bool)),U_297),U_296)) )
      & ( ( hBOOL(hAPP(fun(U_298,bool),bool,hAPP(fun(U_298,bool),fun(fun(U_298,bool),bool),ord_less_eq(fun(U_298,bool)),U_296),U_297))
          & hBOOL(hAPP(fun(U_298,bool),bool,hAPP(fun(U_298,bool),fun(fun(U_298,bool),bool),ord_less_eq(fun(U_298,bool)),U_297),U_296)) )
        | ti(fun(U_298,bool),U_297) != ti(fun(U_298,bool),U_296) ) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

fof(f_121_3,plain,
    ( ! [U_304,U_302,U_300] :
        ( ti(fun(U_304,bool),U_302) = ti(fun(U_304,bool),U_300)
        | ~ hBOOL(hAPP(fun(U_304,bool),bool,hAPP(fun(U_304,bool),fun(fun(U_304,bool),bool),ord_less_eq(fun(U_304,bool)),U_300),U_302))
        | ~ hBOOL(hAPP(fun(U_304,bool),bool,hAPP(fun(U_304,bool),fun(fun(U_304,bool),bool),ord_less_eq(fun(U_304,bool)),U_302),U_300)) )
    & ! [U_303,U_301,U_299] :
        ( ( hBOOL(hAPP(fun(U_303,bool),bool,hAPP(fun(U_303,bool),fun(fun(U_303,bool),bool),ord_less_eq(fun(U_303,bool)),U_299),U_301))
          & hBOOL(hAPP(fun(U_303,bool),bool,hAPP(fun(U_303,bool),fun(fun(U_303,bool),bool),ord_less_eq(fun(U_303,bool)),U_301),U_299)) )
        | ti(fun(U_303,bool),U_301) != ti(fun(U_303,bool),U_299) ) ),
    inference(miniscope,[status(thm)],[f_121_2]) ).

fof(f_121_4,plain,
    ( ! [U_299,U_303,U_301] :
        ( hBOOL(hAPP(fun(U_303,bool),bool,hAPP(fun(U_303,bool),fun(fun(U_303,bool),bool),ord_less_eq(fun(U_303,bool)),U_299),U_301))
        | ~ sP13(U_299,U_303,U_301) )
    & ! [U_299,U_303,U_301] :
        ( hBOOL(hAPP(fun(U_303,bool),bool,hAPP(fun(U_303,bool),fun(fun(U_303,bool),bool),ord_less_eq(fun(U_303,bool)),U_301),U_299))
        | ~ sP13(U_299,U_303,U_301) )
    & ! [U_304,U_302,U_300] :
        ( ti(fun(U_304,bool),U_302) = ti(fun(U_304,bool),U_300)
        | ~ hBOOL(hAPP(fun(U_304,bool),bool,hAPP(fun(U_304,bool),fun(fun(U_304,bool),bool),ord_less_eq(fun(U_304,bool)),U_300),U_302))
        | ~ hBOOL(hAPP(fun(U_304,bool),bool,hAPP(fun(U_304,bool),fun(fun(U_304,bool),bool),ord_less_eq(fun(U_304,bool)),U_302),U_300)) )
    & ! [U_299,U_303,U_301] :
        ( sP13(U_299,U_303,U_301)
        | ti(fun(U_303,bool),U_301) != ti(fun(U_303,bool),U_299) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_121_3]) ).

cnf(f_121_5,plain,
    ( sP13(U_299,U_303,U_301)
    | ti(fun(U_303,bool),U_301) != ti(fun(U_303,bool),U_299) ),
    inference(clausify,[status(thm)],[f_121_4]) ).

cnf(f_121_6,plain,
    ( ti(fun(U_304,bool),U_302) = ti(fun(U_304,bool),U_300)
    | ~ hBOOL(hAPP(fun(U_304,bool),bool,hAPP(fun(U_304,bool),fun(fun(U_304,bool),bool),ord_less_eq(fun(U_304,bool)),U_300),U_302))
    | ~ hBOOL(hAPP(fun(U_304,bool),bool,hAPP(fun(U_304,bool),fun(fun(U_304,bool),bool),ord_less_eq(fun(U_304,bool)),U_302),U_300)) ),
    inference(clausify,[status(thm)],[f_121_4]) ).

cnf(f_121_7,plain,
    ( hBOOL(hAPP(fun(U_303,bool),bool,hAPP(fun(U_303,bool),fun(fun(U_303,bool),bool),ord_less_eq(fun(U_303,bool)),U_301),U_299))
    | ~ sP13(U_299,U_303,U_301) ),
    inference(clausify,[status(thm)],[f_121_4]) ).

cnf(f_121_8,plain,
    ( hBOOL(hAPP(fun(U_303,bool),bool,hAPP(fun(U_303,bool),fun(fun(U_303,bool),bool),ord_less_eq(fun(U_303,bool)),U_299),U_301))
    | ~ sP13(U_299,U_303,U_301) ),
    inference(clausify,[status(thm)],[f_121_4]) ).

fof(f_122_1,plain,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
      | ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_2) ),
    inference(fof_nnf,[status(thm)],[fact_69_equalityD1]) ).

fof(f_122_2,plain,
    ! [U_307,U_306,U_305] :
      ( hBOOL(hAPP(fun(U_307,bool),bool,hAPP(fun(U_307,bool),fun(fun(U_307,bool),bool),ord_less_eq(fun(U_307,bool)),U_306),U_305))
      | ti(fun(U_307,bool),U_306) != ti(fun(U_307,bool),U_305) ),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

fof(f_122_3,plain,
    ! [U_305,U_307,U_306] :
      ( hBOOL(hAPP(fun(U_307,bool),bool,hAPP(fun(U_307,bool),fun(fun(U_307,bool),bool),ord_less_eq(fun(U_307,bool)),U_306),U_305))
      | ti(fun(U_307,bool),U_306) != ti(fun(U_307,bool),U_305) ),
    inference(definitional_conversion,[status(esa)],[f_122_2]) ).

cnf(f_122_4,plain,
    ( hBOOL(hAPP(fun(U_307,bool),bool,hAPP(fun(U_307,bool),fun(fun(U_307,bool),bool),ord_less_eq(fun(U_307,bool)),U_306),U_305))
    | ti(fun(U_307,bool),U_306) != ti(fun(U_307,bool),U_305) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

fof(f_123_1,plain,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))
      | ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_2) ),
    inference(fof_nnf,[status(thm)],[fact_70_equalityD2]) ).

fof(f_123_2,plain,
    ! [U_310,U_309,U_308] :
      ( hBOOL(hAPP(fun(U_310,bool),bool,hAPP(fun(U_310,bool),fun(fun(U_310,bool),bool),ord_less_eq(fun(U_310,bool)),U_308),U_309))
      | ti(fun(U_310,bool),U_309) != ti(fun(U_310,bool),U_308) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

fof(f_123_3,plain,
    ! [U_308,U_309,U_310] :
      ( hBOOL(hAPP(fun(U_310,bool),bool,hAPP(fun(U_310,bool),fun(fun(U_310,bool),bool),ord_less_eq(fun(U_310,bool)),U_308),U_309))
      | ti(fun(U_310,bool),U_309) != ti(fun(U_310,bool),U_308) ),
    inference(definitional_conversion,[status(esa)],[f_123_2]) ).

cnf(f_123_4,plain,
    ( hBOOL(hAPP(fun(U_310,bool),bool,hAPP(fun(U_310,bool),fun(fun(U_310,bool),bool),ord_less_eq(fun(U_310,bool)),U_308),U_309))
    | ti(fun(U_310,bool),U_309) != ti(fun(U_310,bool),U_308) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

fof(f_124_1,plain,
    ! [X_b,X_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_71_in__mono]) ).

fof(f_124_2,plain,
    ! [U_314,U_313,U_312,U_311] :
      ( hBOOL(hAPP(fun(U_314,bool),bool,hAPP(U_314,fun(fun(U_314,bool),bool),member(U_314),U_313),U_311))
      | ~ hBOOL(hAPP(fun(U_314,bool),bool,hAPP(U_314,fun(fun(U_314,bool),bool),member(U_314),U_313),U_312))
      | ~ hBOOL(hAPP(fun(U_314,bool),bool,hAPP(fun(U_314,bool),fun(fun(U_314,bool),bool),ord_less_eq(fun(U_314,bool)),U_312),U_311)) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ! [U_311,U_314,U_312,U_313] :
      ( hBOOL(hAPP(fun(U_314,bool),bool,hAPP(U_314,fun(fun(U_314,bool),bool),member(U_314),U_313),U_311))
      | ~ hBOOL(hAPP(fun(U_314,bool),bool,hAPP(U_314,fun(fun(U_314,bool),bool),member(U_314),U_313),U_312))
      | ~ hBOOL(hAPP(fun(U_314,bool),bool,hAPP(fun(U_314,bool),fun(fun(U_314,bool),bool),ord_less_eq(fun(U_314,bool)),U_312),U_311)) ),
    inference(definitional_conversion,[status(esa)],[f_124_2]) ).

cnf(f_124_4,plain,
    ( hBOOL(hAPP(fun(U_314,bool),bool,hAPP(U_314,fun(fun(U_314,bool),bool),member(U_314),U_313),U_311))
    | ~ hBOOL(hAPP(fun(U_314,bool),bool,hAPP(U_314,fun(fun(U_314,bool),bool),member(U_314),U_313),U_312))
    | ~ hBOOL(hAPP(fun(U_314,bool),bool,hAPP(fun(U_314,bool),fun(fun(U_314,bool),bool),ord_less_eq(fun(U_314,bool)),U_312),U_311)) ),
    inference(clausify,[status(thm)],[f_124_3]) ).

fof(f_125_1,plain,
    ! [X_b,B_2,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_72_set__rev__mp]) ).

fof(f_125_2,plain,
    ! [U_318,U_317,U_316,U_315] :
      ( hBOOL(hAPP(fun(U_318,bool),bool,hAPP(U_318,fun(fun(U_318,bool),bool),member(U_318),U_316),U_317))
      | ~ hBOOL(hAPP(fun(U_318,bool),bool,hAPP(fun(U_318,bool),fun(fun(U_318,bool),bool),ord_less_eq(fun(U_318,bool)),U_315),U_317))
      | ~ hBOOL(hAPP(fun(U_318,bool),bool,hAPP(U_318,fun(fun(U_318,bool),bool),member(U_318),U_316),U_315)) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ! [U_316,U_315,U_318,U_317] :
      ( hBOOL(hAPP(fun(U_318,bool),bool,hAPP(U_318,fun(fun(U_318,bool),bool),member(U_318),U_316),U_317))
      | ~ hBOOL(hAPP(fun(U_318,bool),bool,hAPP(fun(U_318,bool),fun(fun(U_318,bool),bool),ord_less_eq(fun(U_318,bool)),U_315),U_317))
      | ~ hBOOL(hAPP(fun(U_318,bool),bool,hAPP(U_318,fun(fun(U_318,bool),bool),member(U_318),U_316),U_315)) ),
    inference(definitional_conversion,[status(esa)],[f_125_2]) ).

cnf(f_125_4,plain,
    ( hBOOL(hAPP(fun(U_318,bool),bool,hAPP(U_318,fun(fun(U_318,bool),bool),member(U_318),U_316),U_317))
    | ~ hBOOL(hAPP(fun(U_318,bool),bool,hAPP(fun(U_318,bool),fun(fun(U_318,bool),bool),ord_less_eq(fun(U_318,bool)),U_315),U_317))
    | ~ hBOOL(hAPP(fun(U_318,bool),bool,hAPP(U_318,fun(fun(U_318,bool),bool),member(U_318),U_316),U_315)) ),
    inference(clausify,[status(thm)],[f_125_3]) ).

fof(f_126_1,plain,
    ! [X_b,X_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_73_set__mp]) ).

fof(f_126_2,plain,
    ! [U_322,U_321,U_320,U_319] :
      ( hBOOL(hAPP(fun(U_322,bool),bool,hAPP(U_322,fun(fun(U_322,bool),bool),member(U_322),U_321),U_319))
      | ~ hBOOL(hAPP(fun(U_322,bool),bool,hAPP(U_322,fun(fun(U_322,bool),bool),member(U_322),U_321),U_320))
      | ~ hBOOL(hAPP(fun(U_322,bool),bool,hAPP(fun(U_322,bool),fun(fun(U_322,bool),bool),ord_less_eq(fun(U_322,bool)),U_320),U_319)) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ! [U_320,U_322,U_319,U_321] :
      ( hBOOL(hAPP(fun(U_322,bool),bool,hAPP(U_322,fun(fun(U_322,bool),bool),member(U_322),U_321),U_319))
      | ~ hBOOL(hAPP(fun(U_322,bool),bool,hAPP(U_322,fun(fun(U_322,bool),bool),member(U_322),U_321),U_320))
      | ~ hBOOL(hAPP(fun(U_322,bool),bool,hAPP(fun(U_322,bool),fun(fun(U_322,bool),bool),ord_less_eq(fun(U_322,bool)),U_320),U_319)) ),
    inference(definitional_conversion,[status(esa)],[f_126_2]) ).

cnf(f_126_4,plain,
    ( hBOOL(hAPP(fun(U_322,bool),bool,hAPP(U_322,fun(fun(U_322,bool),bool),member(U_322),U_321),U_319))
    | ~ hBOOL(hAPP(fun(U_322,bool),bool,hAPP(U_322,fun(fun(U_322,bool),bool),member(U_322),U_321),U_320))
    | ~ hBOOL(hAPP(fun(U_322,bool),bool,hAPP(fun(U_322,bool),fun(fun(U_322,bool),bool),ord_less_eq(fun(U_322,bool)),U_320),U_319)) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

fof(f_127_1,plain,
    ! [X_b,X_c,F,G] :
      ( ti(fun(X_b,X_c),F) = ti(fun(X_b,X_c),G)
      | ? [X_2] : hAPP(X_b,X_c,F,X_2) != hAPP(X_b,X_c,G,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_74_ext]) ).

fof(f_127_2,plain,
    ! [U_327,U_326,U_325,U_324] :
      ( ti(fun(U_327,U_326),U_325) = ti(fun(U_327,U_326),U_324)
      | ? [U_323] : hAPP(U_327,U_326,U_325,U_323) != hAPP(U_327,U_326,U_324,U_323) ),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

fof(f_127_3,plain,
    ! [U_327,U_326,U_325,U_324] :
      ( ti(fun(U_327,U_326),U_325) = ti(fun(U_327,U_326),U_324)
      | hAPP(U_327,U_326,U_325,sK6(U_327,U_326,U_325,U_324)) != hAPP(U_327,U_326,U_324,sK6(U_327,U_326,U_325,U_324)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_323,sK6(U_327,U_326,U_325,U_324))],[f_127_2]) ).

fof(f_127_4,plain,
    ! [U_324,U_325,U_326,U_327] :
      ( ti(fun(U_327,U_326),U_325) = ti(fun(U_327,U_326),U_324)
      | hAPP(U_327,U_326,U_325,sK6(U_327,U_326,U_325,U_324)) != hAPP(U_327,U_326,U_324,sK6(U_327,U_326,U_325,U_324)) ),
    inference(definitional_conversion,[status(esa)],[f_127_3]) ).

cnf(f_127_5,plain,
    ( ti(fun(U_327,U_326),U_325) = ti(fun(U_327,U_326),U_324)
    | hAPP(U_327,U_326,U_325,sK6(U_327,U_326,U_325,U_324)) != hAPP(U_327,U_326,U_324,sK6(U_327,U_326,U_325,U_324)) ),
    inference(clausify,[status(thm)],[f_127_4]) ).

fof(f_128_1,plain,
    ! [X_b,X_1,A_3] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
        | ~ hBOOL(hAPP(X_b,bool,A_3,X_1)) )
      & ( hBOOL(hAPP(X_b,bool,A_3,X_1))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_75_mem__def]) ).

fof(f_128_2,plain,
    ! [U_330,U_329,U_328] :
      ( ( hBOOL(hAPP(fun(U_330,bool),bool,hAPP(U_330,fun(fun(U_330,bool),bool),member(U_330),U_329),U_328))
        | ~ hBOOL(hAPP(U_330,bool,U_328,U_329)) )
      & ( hBOOL(hAPP(U_330,bool,U_328,U_329))
        | ~ hBOOL(hAPP(fun(U_330,bool),bool,hAPP(U_330,fun(fun(U_330,bool),bool),member(U_330),U_329),U_328)) ) ),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

fof(f_128_3,plain,
    ( ! [U_336,U_334,U_332] :
        ( hBOOL(hAPP(fun(U_336,bool),bool,hAPP(U_336,fun(fun(U_336,bool),bool),member(U_336),U_334),U_332))
        | ~ hBOOL(hAPP(U_336,bool,U_332,U_334)) )
    & ! [U_335,U_333,U_331] :
        ( hBOOL(hAPP(U_335,bool,U_331,U_333))
        | ~ hBOOL(hAPP(fun(U_335,bool),bool,hAPP(U_335,fun(fun(U_335,bool),bool),member(U_335),U_333),U_331)) ) ),
    inference(miniscope,[status(thm)],[f_128_2]) ).

fof(f_128_4,plain,
    ( ! [U_334,U_332,U_336] :
        ( hBOOL(hAPP(fun(U_336,bool),bool,hAPP(U_336,fun(fun(U_336,bool),bool),member(U_336),U_334),U_332))
        | ~ hBOOL(hAPP(U_336,bool,U_332,U_334)) )
    & ! [U_335,U_331,U_333] :
        ( hBOOL(hAPP(U_335,bool,U_331,U_333))
        | ~ hBOOL(hAPP(fun(U_335,bool),bool,hAPP(U_335,fun(fun(U_335,bool),bool),member(U_335),U_333),U_331)) ) ),
    inference(definitional_conversion,[status(esa)],[f_128_3]) ).

cnf(f_128_5,plain,
    ( hBOOL(hAPP(U_335,bool,U_331,U_333))
    | ~ hBOOL(hAPP(fun(U_335,bool),bool,hAPP(U_335,fun(fun(U_335,bool),bool),member(U_335),U_333),U_331)) ),
    inference(clausify,[status(thm)],[f_128_4]) ).

cnf(f_128_6,plain,
    ( hBOOL(hAPP(fun(U_336,bool),bool,hAPP(U_336,fun(fun(U_336,bool),bool),member(U_336),U_334),U_332))
    | ~ hBOOL(hAPP(U_336,bool,U_332,U_334)) ),
    inference(clausify,[status(thm)],[f_128_4]) ).

fof(f_129_1,plain,
    ! [X_b,Pa] : hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa),
    inference(fof_nnf,[status(thm)],[fact_76_Collect__def]) ).

fof(f_129_2,plain,
    ! [U_338,U_337] : hAPP(fun(U_338,bool),fun(U_338,bool),collect(U_338),U_337) = ti(fun(U_338,bool),U_337),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

fof(f_129_3,plain,
    ! [U_337,U_338] : hAPP(fun(U_338,bool),fun(U_338,bool),collect(U_338),U_337) = ti(fun(U_338,bool),U_337),
    inference(definitional_conversion,[status(esa)],[f_129_2]) ).

cnf(f_129_4,plain,
    hAPP(fun(U_338,bool),fun(U_338,bool),collect(U_338),U_337) = ti(fun(U_338,bool),U_337),
    inference(clausify,[status(thm)],[f_129_3]) ).

fof(f_130_1,plain,
    ! [X_b,C_2,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),C_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_77_subset__trans]) ).

fof(f_130_2,plain,
    ! [U_342,U_341,U_340,U_339] :
      ( hBOOL(hAPP(fun(U_342,bool),bool,hAPP(fun(U_342,bool),fun(fun(U_342,bool),bool),ord_less_eq(fun(U_342,bool)),U_340),U_341))
      | ~ hBOOL(hAPP(fun(U_342,bool),bool,hAPP(fun(U_342,bool),fun(fun(U_342,bool),bool),ord_less_eq(fun(U_342,bool)),U_339),U_341))
      | ~ hBOOL(hAPP(fun(U_342,bool),bool,hAPP(fun(U_342,bool),fun(fun(U_342,bool),bool),ord_less_eq(fun(U_342,bool)),U_340),U_339)) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

fof(f_130_3,plain,
    ! [U_342,U_340,U_341,U_339] :
      ( hBOOL(hAPP(fun(U_342,bool),bool,hAPP(fun(U_342,bool),fun(fun(U_342,bool),bool),ord_less_eq(fun(U_342,bool)),U_340),U_341))
      | ~ hBOOL(hAPP(fun(U_342,bool),bool,hAPP(fun(U_342,bool),fun(fun(U_342,bool),bool),ord_less_eq(fun(U_342,bool)),U_339),U_341))
      | ~ hBOOL(hAPP(fun(U_342,bool),bool,hAPP(fun(U_342,bool),fun(fun(U_342,bool),bool),ord_less_eq(fun(U_342,bool)),U_340),U_339)) ),
    inference(definitional_conversion,[status(esa)],[f_130_2]) ).

cnf(f_130_4,plain,
    ( hBOOL(hAPP(fun(U_342,bool),bool,hAPP(fun(U_342,bool),fun(fun(U_342,bool),bool),ord_less_eq(fun(U_342,bool)),U_340),U_341))
    | ~ hBOOL(hAPP(fun(U_342,bool),bool,hAPP(fun(U_342,bool),fun(fun(U_342,bool),bool),ord_less_eq(fun(U_342,bool)),U_339),U_341))
    | ~ hBOOL(hAPP(fun(U_342,bool),bool,hAPP(fun(U_342,bool),fun(fun(U_342,bool),bool),ord_less_eq(fun(U_342,bool)),U_340),U_339)) ),
    inference(clausify,[status(thm)],[f_130_3]) ).

fof(f_131_1,plain,
    ! [X_b,A_3,B_2] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))
        & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) )
      | ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_2) ),
    inference(fof_nnf,[status(thm)],[fact_78_equalityE]) ).

fof(f_131_2,plain,
    ! [U_345,U_344,U_343] :
      ( ( hBOOL(hAPP(fun(U_345,bool),bool,hAPP(fun(U_345,bool),fun(fun(U_345,bool),bool),ord_less_eq(fun(U_345,bool)),U_343),U_344))
        & hBOOL(hAPP(fun(U_345,bool),bool,hAPP(fun(U_345,bool),fun(fun(U_345,bool),bool),ord_less_eq(fun(U_345,bool)),U_344),U_343)) )
      | ti(fun(U_345,bool),U_344) != ti(fun(U_345,bool),U_343) ),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

fof(f_131_3,plain,
    ( ! [U_344,U_343,U_345] :
        ( hBOOL(hAPP(fun(U_345,bool),bool,hAPP(fun(U_345,bool),fun(fun(U_345,bool),bool),ord_less_eq(fun(U_345,bool)),U_343),U_344))
        | ~ sP14(U_344,U_343,U_345) )
    & ! [U_344,U_343,U_345] :
        ( hBOOL(hAPP(fun(U_345,bool),bool,hAPP(fun(U_345,bool),fun(fun(U_345,bool),bool),ord_less_eq(fun(U_345,bool)),U_344),U_343))
        | ~ sP14(U_344,U_343,U_345) )
    & ! [U_344,U_343,U_345] :
        ( sP14(U_344,U_343,U_345)
        | ti(fun(U_345,bool),U_344) != ti(fun(U_345,bool),U_343) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_131_2]) ).

cnf(f_131_4,plain,
    ( sP14(U_344,U_343,U_345)
    | ti(fun(U_345,bool),U_344) != ti(fun(U_345,bool),U_343) ),
    inference(clausify,[status(thm)],[f_131_3]) ).

cnf(f_131_5,plain,
    ( hBOOL(hAPP(fun(U_345,bool),bool,hAPP(fun(U_345,bool),fun(fun(U_345,bool),bool),ord_less_eq(fun(U_345,bool)),U_344),U_343))
    | ~ sP14(U_344,U_343,U_345) ),
    inference(clausify,[status(thm)],[f_131_3]) ).

cnf(f_131_6,plain,
    ( hBOOL(hAPP(fun(U_345,bool),bool,hAPP(fun(U_345,bool),fun(fun(U_345,bool),bool),ord_less_eq(fun(U_345,bool)),U_343),U_344))
    | ~ sP14(U_344,U_343,U_345) ),
    inference(clausify,[status(thm)],[f_131_3]) ).

fof(f_132_1,plain,
    ! [X_b,X_c,Z_1,F,A_3] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))
        | ! [X_2] :
            ( ti(X_b,Z_1) != hAPP(X_c,X_b,F,X_2)
            | ~ hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) ) )
      & ( ? [X_2] :
            ( ti(X_b,Z_1) = hAPP(X_c,X_b,F,X_2)
            & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) )
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_1),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_79_image__iff]) ).

fof(f_132_2,plain,
    ! [U_352,U_351,U_350,U_349,U_348] :
      ( ( hBOOL(hAPP(fun(U_352,bool),bool,hAPP(U_352,fun(fun(U_352,bool),bool),member(U_352),U_350),hAPP(fun(U_351,bool),fun(U_352,bool),hAPP(fun(U_351,U_352),fun(fun(U_351,bool),fun(U_352,bool)),image(U_351,U_352),U_349),U_348)))
        | ! [U_347] :
            ( ti(U_352,U_350) != hAPP(U_351,U_352,U_349,U_347)
            | ~ hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),U_347),U_348)) ) )
      & ( ? [U_346] :
            ( ti(U_352,U_350) = hAPP(U_351,U_352,U_349,U_346)
            & hBOOL(hAPP(fun(U_351,bool),bool,hAPP(U_351,fun(fun(U_351,bool),bool),member(U_351),U_346),U_348)) )
        | ~ hBOOL(hAPP(fun(U_352,bool),bool,hAPP(U_352,fun(fun(U_352,bool),bool),member(U_352),U_350),hAPP(fun(U_351,bool),fun(U_352,bool),hAPP(fun(U_351,U_352),fun(fun(U_351,bool),fun(U_352,bool)),image(U_351,U_352),U_349),U_348))) ) ),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

fof(f_132_3,plain,
    ( ! [U_362,U_360,U_358,U_356,U_354] :
        ( hBOOL(hAPP(fun(U_362,bool),bool,hAPP(U_362,fun(fun(U_362,bool),bool),member(U_362),U_358),hAPP(fun(U_360,bool),fun(U_362,bool),hAPP(fun(U_360,U_362),fun(fun(U_360,bool),fun(U_362,bool)),image(U_360,U_362),U_356),U_354)))
        | ! [U_347] :
            ( ti(U_362,U_358) != hAPP(U_360,U_362,U_356,U_347)
            | ~ hBOOL(hAPP(fun(U_360,bool),bool,hAPP(U_360,fun(fun(U_360,bool),bool),member(U_360),U_347),U_354)) ) )
    & ! [U_361,U_359,U_357,U_355,U_353] :
        ( ? [U_346] :
            ( ti(U_361,U_357) = hAPP(U_359,U_361,U_355,U_346)
            & hBOOL(hAPP(fun(U_359,bool),bool,hAPP(U_359,fun(fun(U_359,bool),bool),member(U_359),U_346),U_353)) )
        | ~ hBOOL(hAPP(fun(U_361,bool),bool,hAPP(U_361,fun(fun(U_361,bool),bool),member(U_361),U_357),hAPP(fun(U_359,bool),fun(U_361,bool),hAPP(fun(U_359,U_361),fun(fun(U_359,bool),fun(U_361,bool)),image(U_359,U_361),U_355),U_353))) ) ),
    inference(miniscope,[status(thm)],[f_132_2]) ).

fof(f_132_4,plain,
    ( ! [U_362,U_360,U_358,U_356,U_354] :
        ( hBOOL(hAPP(fun(U_362,bool),bool,hAPP(U_362,fun(fun(U_362,bool),bool),member(U_362),U_358),hAPP(fun(U_360,bool),fun(U_362,bool),hAPP(fun(U_360,U_362),fun(fun(U_360,bool),fun(U_362,bool)),image(U_360,U_362),U_356),U_354)))
        | ! [U_347] :
            ( ti(U_362,U_358) != hAPP(U_360,U_362,U_356,U_347)
            | ~ hBOOL(hAPP(fun(U_360,bool),bool,hAPP(U_360,fun(fun(U_360,bool),bool),member(U_360),U_347),U_354)) ) )
    & ! [U_361,U_359,U_357,U_355,U_353] :
        ( ( ti(U_361,U_357) = hAPP(U_359,U_361,U_355,sK7(U_361,U_359,U_357,U_355,U_353))
          & hBOOL(hAPP(fun(U_359,bool),bool,hAPP(U_359,fun(fun(U_359,bool),bool),member(U_359),sK7(U_361,U_359,U_357,U_355,U_353)),U_353)) )
        | ~ hBOOL(hAPP(fun(U_361,bool),bool,hAPP(U_361,fun(fun(U_361,bool),bool),member(U_361),U_357),hAPP(fun(U_359,bool),fun(U_361,bool),hAPP(fun(U_359,U_361),fun(fun(U_359,bool),fun(U_361,bool)),image(U_359,U_361),U_355),U_353))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_346,sK7(U_361,U_359,U_357,U_355,U_353))],[f_132_3]) ).

fof(f_132_5,plain,
    ( ! [U_355,U_357,U_359,U_353,U_361] :
        ( ti(U_361,U_357) = hAPP(U_359,U_361,U_355,sK7(U_361,U_359,U_357,U_355,U_353))
        | ~ sP15(U_355,U_357,U_359,U_353,U_361) )
    & ! [U_355,U_357,U_359,U_353,U_361] :
        ( hBOOL(hAPP(fun(U_359,bool),bool,hAPP(U_359,fun(fun(U_359,bool),bool),member(U_359),sK7(U_361,U_359,U_357,U_355,U_353)),U_353))
        | ~ sP15(U_355,U_357,U_359,U_353,U_361) )
    & ! [U_347,U_356,U_354,U_358,U_360,U_362] :
        ( hBOOL(hAPP(fun(U_362,bool),bool,hAPP(U_362,fun(fun(U_362,bool),bool),member(U_362),U_358),hAPP(fun(U_360,bool),fun(U_362,bool),hAPP(fun(U_360,U_362),fun(fun(U_360,bool),fun(U_362,bool)),image(U_360,U_362),U_356),U_354)))
        | ti(U_362,U_358) != hAPP(U_360,U_362,U_356,U_347)
        | ~ hBOOL(hAPP(fun(U_360,bool),bool,hAPP(U_360,fun(fun(U_360,bool),bool),member(U_360),U_347),U_354)) )
    & ! [U_355,U_357,U_359,U_353,U_361] :
        ( sP15(U_355,U_357,U_359,U_353,U_361)
        | ~ hBOOL(hAPP(fun(U_361,bool),bool,hAPP(U_361,fun(fun(U_361,bool),bool),member(U_361),U_357),hAPP(fun(U_359,bool),fun(U_361,bool),hAPP(fun(U_359,U_361),fun(fun(U_359,bool),fun(U_361,bool)),image(U_359,U_361),U_355),U_353))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_132_4]) ).

cnf(f_132_6,plain,
    ( sP15(U_355,U_357,U_359,U_353,U_361)
    | ~ hBOOL(hAPP(fun(U_361,bool),bool,hAPP(U_361,fun(fun(U_361,bool),bool),member(U_361),U_357),hAPP(fun(U_359,bool),fun(U_361,bool),hAPP(fun(U_359,U_361),fun(fun(U_359,bool),fun(U_361,bool)),image(U_359,U_361),U_355),U_353))) ),
    inference(clausify,[status(thm)],[f_132_5]) ).

cnf(f_132_7,plain,
    ( hBOOL(hAPP(fun(U_362,bool),bool,hAPP(U_362,fun(fun(U_362,bool),bool),member(U_362),U_358),hAPP(fun(U_360,bool),fun(U_362,bool),hAPP(fun(U_360,U_362),fun(fun(U_360,bool),fun(U_362,bool)),image(U_360,U_362),U_356),U_354)))
    | ti(U_362,U_358) != hAPP(U_360,U_362,U_356,U_347)
    | ~ hBOOL(hAPP(fun(U_360,bool),bool,hAPP(U_360,fun(fun(U_360,bool),bool),member(U_360),U_347),U_354)) ),
    inference(clausify,[status(thm)],[f_132_5]) ).

cnf(f_132_8,plain,
    ( hBOOL(hAPP(fun(U_359,bool),bool,hAPP(U_359,fun(fun(U_359,bool),bool),member(U_359),sK7(U_361,U_359,U_357,U_355,U_353)),U_353))
    | ~ sP15(U_355,U_357,U_359,U_353,U_361) ),
    inference(clausify,[status(thm)],[f_132_5]) ).

cnf(f_132_9,plain,
    ( ti(U_361,U_357) = hAPP(U_359,U_361,U_355,sK7(U_361,U_359,U_357,U_355,U_353))
    | ~ sP15(U_355,U_357,U_359,U_353,U_361) ),
    inference(clausify,[status(thm)],[f_132_5]) ).

fof(f_133_1,plain,
    ! [X_c,X_b,F,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_80_imageI]) ).

fof(f_133_2,plain,
    ! [U_367,U_366,U_365,U_364,U_363] :
      ( hBOOL(hAPP(fun(U_367,bool),bool,hAPP(U_367,fun(fun(U_367,bool),bool),member(U_367),hAPP(U_366,U_367,U_365,U_364)),hAPP(fun(U_366,bool),fun(U_367,bool),hAPP(fun(U_366,U_367),fun(fun(U_366,bool),fun(U_367,bool)),image(U_366,U_367),U_365),U_363)))
      | ~ hBOOL(hAPP(fun(U_366,bool),bool,hAPP(U_366,fun(fun(U_366,bool),bool),member(U_366),U_364),U_363)) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

fof(f_133_3,plain,
    ! [U_364,U_363,U_366,U_365,U_367] :
      ( hBOOL(hAPP(fun(U_367,bool),bool,hAPP(U_367,fun(fun(U_367,bool),bool),member(U_367),hAPP(U_366,U_367,U_365,U_364)),hAPP(fun(U_366,bool),fun(U_367,bool),hAPP(fun(U_366,U_367),fun(fun(U_366,bool),fun(U_367,bool)),image(U_366,U_367),U_365),U_363)))
      | ~ hBOOL(hAPP(fun(U_366,bool),bool,hAPP(U_366,fun(fun(U_366,bool),bool),member(U_366),U_364),U_363)) ),
    inference(definitional_conversion,[status(esa)],[f_133_2]) ).

cnf(f_133_4,plain,
    ( hBOOL(hAPP(fun(U_367,bool),bool,hAPP(U_367,fun(fun(U_367,bool),bool),member(U_367),hAPP(U_366,U_367,U_365,U_364)),hAPP(fun(U_366,bool),fun(U_367,bool),hAPP(fun(U_366,U_367),fun(fun(U_366,bool),fun(U_367,bool)),image(U_366,U_367),U_365),U_363)))
    | ~ hBOOL(hAPP(fun(U_366,bool),bool,hAPP(U_366,fun(fun(U_366,bool),bool),member(U_366),U_364),U_363)) ),
    inference(clausify,[status(thm)],[f_133_3]) ).

fof(f_134_1,plain,
    ! [X_c,X_b,B,F,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)))
      | ti(X_c,B) != hAPP(X_b,X_c,F,X_1)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_81_rev__image__eqI]) ).

fof(f_134_2,plain,
    ! [U_373,U_372,U_371,U_370,U_369,U_368] :
      ( hBOOL(hAPP(fun(U_373,bool),bool,hAPP(U_373,fun(fun(U_373,bool),bool),member(U_373),U_371),hAPP(fun(U_372,bool),fun(U_373,bool),hAPP(fun(U_372,U_373),fun(fun(U_372,bool),fun(U_373,bool)),image(U_372,U_373),U_370),U_368)))
      | ti(U_373,U_371) != hAPP(U_372,U_373,U_370,U_369)
      | ~ hBOOL(hAPP(fun(U_372,bool),bool,hAPP(U_372,fun(fun(U_372,bool),bool),member(U_372),U_369),U_368)) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

fof(f_134_3,plain,
    ! [U_369,U_368,U_370,U_371,U_372,U_373] :
      ( hBOOL(hAPP(fun(U_373,bool),bool,hAPP(U_373,fun(fun(U_373,bool),bool),member(U_373),U_371),hAPP(fun(U_372,bool),fun(U_373,bool),hAPP(fun(U_372,U_373),fun(fun(U_372,bool),fun(U_373,bool)),image(U_372,U_373),U_370),U_368)))
      | ti(U_373,U_371) != hAPP(U_372,U_373,U_370,U_369)
      | ~ hBOOL(hAPP(fun(U_372,bool),bool,hAPP(U_372,fun(fun(U_372,bool),bool),member(U_372),U_369),U_368)) ),
    inference(definitional_conversion,[status(esa)],[f_134_2]) ).

cnf(f_134_4,plain,
    ( hBOOL(hAPP(fun(U_373,bool),bool,hAPP(U_373,fun(fun(U_373,bool),bool),member(U_373),U_371),hAPP(fun(U_372,bool),fun(U_373,bool),hAPP(fun(U_372,U_373),fun(fun(U_372,bool),fun(U_373,bool)),image(U_372,U_373),U_370),U_368)))
    | ti(U_373,U_371) != hAPP(U_372,U_373,U_370,U_369)
    | ~ hBOOL(hAPP(fun(U_372,bool),bool,hAPP(U_372,fun(fun(U_372,bool),bool),member(U_372),U_369),U_368)) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

fof(f_135_1,plain,
    ! [X_b,X_2,Xa] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),Xa) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Xa))),
    inference(fof_nnf,[status(thm)],[fact_82_insert__compr__raw]) ).

fof(f_135_2,plain,
    ! [U_376,U_375,U_374] : hAPP(fun(U_376,bool),fun(U_376,bool),hAPP(U_376,fun(fun(U_376,bool),fun(U_376,bool)),insert(U_376),U_375),U_374) = hAPP(fun(U_376,bool),fun(U_376,bool),collect(U_376),hAPP(fun(U_376,bool),fun(U_376,bool),hAPP(fun(U_376,fun(bool,bool)),fun(fun(U_376,bool),fun(U_376,bool)),combs(U_376,bool,bool),hAPP(fun(U_376,bool),fun(U_376,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_376,bool),fun(U_376,fun(bool,bool))),combb(bool,fun(bool,bool),U_376),fdisj),hAPP(U_376,fun(U_376,bool),hAPP(fun(U_376,fun(U_376,bool)),fun(U_376,fun(U_376,bool)),combc(U_376,U_376,bool),fequal(U_376)),U_375))),hAPP(fun(U_376,bool),fun(U_376,bool),hAPP(fun(U_376,fun(fun(U_376,bool),bool)),fun(fun(U_376,bool),fun(U_376,bool)),combc(U_376,fun(U_376,bool),bool),member(U_376)),U_374))),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

fof(f_135_3,plain,
    ! [U_375,U_374,U_376] : hAPP(fun(U_376,bool),fun(U_376,bool),hAPP(U_376,fun(fun(U_376,bool),fun(U_376,bool)),insert(U_376),U_375),U_374) = hAPP(fun(U_376,bool),fun(U_376,bool),collect(U_376),hAPP(fun(U_376,bool),fun(U_376,bool),hAPP(fun(U_376,fun(bool,bool)),fun(fun(U_376,bool),fun(U_376,bool)),combs(U_376,bool,bool),hAPP(fun(U_376,bool),fun(U_376,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_376,bool),fun(U_376,fun(bool,bool))),combb(bool,fun(bool,bool),U_376),fdisj),hAPP(U_376,fun(U_376,bool),hAPP(fun(U_376,fun(U_376,bool)),fun(U_376,fun(U_376,bool)),combc(U_376,U_376,bool),fequal(U_376)),U_375))),hAPP(fun(U_376,bool),fun(U_376,bool),hAPP(fun(U_376,fun(fun(U_376,bool),bool)),fun(fun(U_376,bool),fun(U_376,bool)),combc(U_376,fun(U_376,bool),bool),member(U_376)),U_374))),
    inference(definitional_conversion,[status(esa)],[f_135_2]) ).

cnf(f_135_4,plain,
    hAPP(fun(U_376,bool),fun(U_376,bool),hAPP(U_376,fun(fun(U_376,bool),fun(U_376,bool)),insert(U_376),U_375),U_374) = hAPP(fun(U_376,bool),fun(U_376,bool),collect(U_376),hAPP(fun(U_376,bool),fun(U_376,bool),hAPP(fun(U_376,fun(bool,bool)),fun(fun(U_376,bool),fun(U_376,bool)),combs(U_376,bool,bool),hAPP(fun(U_376,bool),fun(U_376,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_376,bool),fun(U_376,fun(bool,bool))),combb(bool,fun(bool,bool),U_376),fdisj),hAPP(U_376,fun(U_376,bool),hAPP(fun(U_376,fun(U_376,bool)),fun(U_376,fun(U_376,bool)),combc(U_376,U_376,bool),fequal(U_376)),U_375))),hAPP(fun(U_376,bool),fun(U_376,bool),hAPP(fun(U_376,fun(fun(U_376,bool),bool)),fun(fun(U_376,bool),fun(U_376,bool)),combc(U_376,fun(U_376,bool),bool),member(U_376)),U_374))),
    inference(clausify,[status(thm)],[f_135_3]) ).

fof(f_136_1,plain,
    ! [X_c,X_b,X_d,F,G,A_3] : hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_d,bool),fun(X_c,bool),hAPP(fun(X_d,X_c),fun(fun(X_d,bool),fun(X_c,bool)),image(X_d,X_c),G),A_3)) = hAPP(fun(X_d,bool),fun(X_b,bool),hAPP(fun(X_d,X_b),fun(fun(X_d,bool),fun(X_b,bool)),image(X_d,X_b),hAPP(fun(X_d,X_c),fun(X_d,X_b),hAPP(fun(X_c,X_b),fun(fun(X_d,X_c),fun(X_d,X_b)),combb(X_c,X_b,X_d),F),G)),A_3),
    inference(fof_nnf,[status(thm)],[fact_83_image__image]) ).

fof(f_136_2,plain,
    ! [U_382,U_381,U_380,U_379,U_378,U_377] : hAPP(fun(U_382,bool),fun(U_381,bool),hAPP(fun(U_382,U_381),fun(fun(U_382,bool),fun(U_381,bool)),image(U_382,U_381),U_379),hAPP(fun(U_380,bool),fun(U_382,bool),hAPP(fun(U_380,U_382),fun(fun(U_380,bool),fun(U_382,bool)),image(U_380,U_382),U_378),U_377)) = hAPP(fun(U_380,bool),fun(U_381,bool),hAPP(fun(U_380,U_381),fun(fun(U_380,bool),fun(U_381,bool)),image(U_380,U_381),hAPP(fun(U_380,U_382),fun(U_380,U_381),hAPP(fun(U_382,U_381),fun(fun(U_380,U_382),fun(U_380,U_381)),combb(U_382,U_381,U_380),U_379),U_378)),U_377),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

fof(f_136_3,plain,
    ! [U_379,U_377,U_378,U_380,U_381,U_382] : hAPP(fun(U_382,bool),fun(U_381,bool),hAPP(fun(U_382,U_381),fun(fun(U_382,bool),fun(U_381,bool)),image(U_382,U_381),U_379),hAPP(fun(U_380,bool),fun(U_382,bool),hAPP(fun(U_380,U_382),fun(fun(U_380,bool),fun(U_382,bool)),image(U_380,U_382),U_378),U_377)) = hAPP(fun(U_380,bool),fun(U_381,bool),hAPP(fun(U_380,U_381),fun(fun(U_380,bool),fun(U_381,bool)),image(U_380,U_381),hAPP(fun(U_380,U_382),fun(U_380,U_381),hAPP(fun(U_382,U_381),fun(fun(U_380,U_382),fun(U_380,U_381)),combb(U_382,U_381,U_380),U_379),U_378)),U_377),
    inference(definitional_conversion,[status(esa)],[f_136_2]) ).

cnf(f_136_4,plain,
    hAPP(fun(U_382,bool),fun(U_381,bool),hAPP(fun(U_382,U_381),fun(fun(U_382,bool),fun(U_381,bool)),image(U_382,U_381),U_379),hAPP(fun(U_380,bool),fun(U_382,bool),hAPP(fun(U_380,U_382),fun(fun(U_380,bool),fun(U_382,bool)),image(U_380,U_382),U_378),U_377)) = hAPP(fun(U_380,bool),fun(U_381,bool),hAPP(fun(U_380,U_381),fun(fun(U_380,bool),fun(U_381,bool)),image(U_380,U_381),hAPP(fun(U_380,U_382),fun(U_380,U_381),hAPP(fun(U_382,U_381),fun(fun(U_380,U_382),fun(U_380,U_381)),combb(U_382,U_381,U_380),U_379),U_378)),U_377),
    inference(clausify,[status(thm)],[f_136_3]) ).

fof(f_137_1,plain,
    ! [X_b,Y_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),combi(X_b)),Y_3) = ti(fun(X_b,bool),Y_3),
    inference(fof_nnf,[status(thm)],[fact_84_image__ident]) ).

fof(f_137_2,plain,
    ! [U_384,U_383] : hAPP(fun(U_384,bool),fun(U_384,bool),hAPP(fun(U_384,U_384),fun(fun(U_384,bool),fun(U_384,bool)),image(U_384,U_384),combi(U_384)),U_383) = ti(fun(U_384,bool),U_383),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

fof(f_137_3,plain,
    ! [U_383,U_384] : hAPP(fun(U_384,bool),fun(U_384,bool),hAPP(fun(U_384,U_384),fun(fun(U_384,bool),fun(U_384,bool)),image(U_384,U_384),combi(U_384)),U_383) = ti(fun(U_384,bool),U_383),
    inference(definitional_conversion,[status(esa)],[f_137_2]) ).

cnf(f_137_4,plain,
    hAPP(fun(U_384,bool),fun(U_384,bool),hAPP(fun(U_384,U_384),fun(fun(U_384,bool),fun(U_384,bool)),image(U_384,U_384),combi(U_384)),U_383) = ti(fun(U_384,bool),U_383),
    inference(clausify,[status(thm)],[f_137_3]) ).

fof(f_138_1,plain,
    ! [X_b,B_2,A_2] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2))),
    inference(fof_nnf,[status(thm)],[fact_85_subset__insertI]) ).

fof(f_138_2,plain,
    ! [U_387,U_386,U_385] : hBOOL(hAPP(fun(U_387,bool),bool,hAPP(fun(U_387,bool),fun(fun(U_387,bool),bool),ord_less_eq(fun(U_387,bool)),U_386),hAPP(fun(U_387,bool),fun(U_387,bool),hAPP(U_387,fun(fun(U_387,bool),fun(U_387,bool)),insert(U_387),U_385),U_386))),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

fof(f_138_3,plain,
    ! [U_386,U_387,U_385] : hBOOL(hAPP(fun(U_387,bool),bool,hAPP(fun(U_387,bool),fun(fun(U_387,bool),bool),ord_less_eq(fun(U_387,bool)),U_386),hAPP(fun(U_387,bool),fun(U_387,bool),hAPP(U_387,fun(fun(U_387,bool),fun(U_387,bool)),insert(U_387),U_385),U_386))),
    inference(definitional_conversion,[status(esa)],[f_138_2]) ).

cnf(f_138_4,plain,
    hBOOL(hAPP(fun(U_387,bool),bool,hAPP(fun(U_387,bool),fun(fun(U_387,bool),bool),ord_less_eq(fun(U_387,bool)),U_386),hAPP(fun(U_387,bool),fun(U_387,bool),hAPP(U_387,fun(fun(U_387,bool),fun(U_387,bool)),insert(U_387),U_385),U_386))),
    inference(clausify,[status(thm)],[f_138_3]) ).

fof(f_139_1,plain,
    ! [X_b,X_1,A_3,B_2] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) )
      & ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) )
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_86_insert__subset]) ).

fof(f_139_2,plain,
    ! [U_391,U_390,U_389,U_388] :
      ( ( hBOOL(hAPP(fun(U_391,bool),bool,hAPP(fun(U_391,bool),fun(fun(U_391,bool),bool),ord_less_eq(fun(U_391,bool)),hAPP(fun(U_391,bool),fun(U_391,bool),hAPP(U_391,fun(fun(U_391,bool),fun(U_391,bool)),insert(U_391),U_390),U_389)),U_388))
        | ~ hBOOL(hAPP(fun(U_391,bool),bool,hAPP(fun(U_391,bool),fun(fun(U_391,bool),bool),ord_less_eq(fun(U_391,bool)),U_389),U_388))
        | ~ hBOOL(hAPP(fun(U_391,bool),bool,hAPP(U_391,fun(fun(U_391,bool),bool),member(U_391),U_390),U_388)) )
      & ( ( hBOOL(hAPP(fun(U_391,bool),bool,hAPP(fun(U_391,bool),fun(fun(U_391,bool),bool),ord_less_eq(fun(U_391,bool)),U_389),U_388))
          & hBOOL(hAPP(fun(U_391,bool),bool,hAPP(U_391,fun(fun(U_391,bool),bool),member(U_391),U_390),U_388)) )
        | ~ hBOOL(hAPP(fun(U_391,bool),bool,hAPP(fun(U_391,bool),fun(fun(U_391,bool),bool),ord_less_eq(fun(U_391,bool)),hAPP(fun(U_391,bool),fun(U_391,bool),hAPP(U_391,fun(fun(U_391,bool),fun(U_391,bool)),insert(U_391),U_390),U_389)),U_388)) ) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

fof(f_139_3,plain,
    ( ! [U_399,U_397,U_395,U_393] :
        ( hBOOL(hAPP(fun(U_399,bool),bool,hAPP(fun(U_399,bool),fun(fun(U_399,bool),bool),ord_less_eq(fun(U_399,bool)),hAPP(fun(U_399,bool),fun(U_399,bool),hAPP(U_399,fun(fun(U_399,bool),fun(U_399,bool)),insert(U_399),U_397),U_395)),U_393))
        | ~ hBOOL(hAPP(fun(U_399,bool),bool,hAPP(fun(U_399,bool),fun(fun(U_399,bool),bool),ord_less_eq(fun(U_399,bool)),U_395),U_393))
        | ~ hBOOL(hAPP(fun(U_399,bool),bool,hAPP(U_399,fun(fun(U_399,bool),bool),member(U_399),U_397),U_393)) )
    & ! [U_398,U_396,U_394,U_392] :
        ( ( hBOOL(hAPP(fun(U_398,bool),bool,hAPP(fun(U_398,bool),fun(fun(U_398,bool),bool),ord_less_eq(fun(U_398,bool)),U_394),U_392))
          & hBOOL(hAPP(fun(U_398,bool),bool,hAPP(U_398,fun(fun(U_398,bool),bool),member(U_398),U_396),U_392)) )
        | ~ hBOOL(hAPP(fun(U_398,bool),bool,hAPP(fun(U_398,bool),fun(fun(U_398,bool),bool),ord_less_eq(fun(U_398,bool)),hAPP(fun(U_398,bool),fun(U_398,bool),hAPP(U_398,fun(fun(U_398,bool),fun(U_398,bool)),insert(U_398),U_396),U_394)),U_392)) ) ),
    inference(miniscope,[status(thm)],[f_139_2]) ).

fof(f_139_4,plain,
    ( ! [U_398,U_392,U_396,U_394] :
        ( hBOOL(hAPP(fun(U_398,bool),bool,hAPP(fun(U_398,bool),fun(fun(U_398,bool),bool),ord_less_eq(fun(U_398,bool)),U_394),U_392))
        | ~ sP16(U_398,U_392,U_396,U_394) )
    & ! [U_398,U_392,U_396,U_394] :
        ( hBOOL(hAPP(fun(U_398,bool),bool,hAPP(U_398,fun(fun(U_398,bool),bool),member(U_398),U_396),U_392))
        | ~ sP16(U_398,U_392,U_396,U_394) )
    & ! [U_393,U_395,U_397,U_399] :
        ( hBOOL(hAPP(fun(U_399,bool),bool,hAPP(fun(U_399,bool),fun(fun(U_399,bool),bool),ord_less_eq(fun(U_399,bool)),hAPP(fun(U_399,bool),fun(U_399,bool),hAPP(U_399,fun(fun(U_399,bool),fun(U_399,bool)),insert(U_399),U_397),U_395)),U_393))
        | ~ hBOOL(hAPP(fun(U_399,bool),bool,hAPP(fun(U_399,bool),fun(fun(U_399,bool),bool),ord_less_eq(fun(U_399,bool)),U_395),U_393))
        | ~ hBOOL(hAPP(fun(U_399,bool),bool,hAPP(U_399,fun(fun(U_399,bool),bool),member(U_399),U_397),U_393)) )
    & ! [U_398,U_392,U_396,U_394] :
        ( sP16(U_398,U_392,U_396,U_394)
        | ~ hBOOL(hAPP(fun(U_398,bool),bool,hAPP(fun(U_398,bool),fun(fun(U_398,bool),bool),ord_less_eq(fun(U_398,bool)),hAPP(fun(U_398,bool),fun(U_398,bool),hAPP(U_398,fun(fun(U_398,bool),fun(U_398,bool)),insert(U_398),U_396),U_394)),U_392)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_139_3]) ).

cnf(f_139_5,plain,
    ( sP16(U_398,U_392,U_396,U_394)
    | ~ hBOOL(hAPP(fun(U_398,bool),bool,hAPP(fun(U_398,bool),fun(fun(U_398,bool),bool),ord_less_eq(fun(U_398,bool)),hAPP(fun(U_398,bool),fun(U_398,bool),hAPP(U_398,fun(fun(U_398,bool),fun(U_398,bool)),insert(U_398),U_396),U_394)),U_392)) ),
    inference(clausify,[status(thm)],[f_139_4]) ).

cnf(f_139_6,plain,
    ( hBOOL(hAPP(fun(U_399,bool),bool,hAPP(fun(U_399,bool),fun(fun(U_399,bool),bool),ord_less_eq(fun(U_399,bool)),hAPP(fun(U_399,bool),fun(U_399,bool),hAPP(U_399,fun(fun(U_399,bool),fun(U_399,bool)),insert(U_399),U_397),U_395)),U_393))
    | ~ hBOOL(hAPP(fun(U_399,bool),bool,hAPP(fun(U_399,bool),fun(fun(U_399,bool),bool),ord_less_eq(fun(U_399,bool)),U_395),U_393))
    | ~ hBOOL(hAPP(fun(U_399,bool),bool,hAPP(U_399,fun(fun(U_399,bool),bool),member(U_399),U_397),U_393)) ),
    inference(clausify,[status(thm)],[f_139_4]) ).

cnf(f_139_7,plain,
    ( hBOOL(hAPP(fun(U_398,bool),bool,hAPP(U_398,fun(fun(U_398,bool),bool),member(U_398),U_396),U_392))
    | ~ sP16(U_398,U_392,U_396,U_394) ),
    inference(clausify,[status(thm)],[f_139_4]) ).

cnf(f_139_8,plain,
    ( hBOOL(hAPP(fun(U_398,bool),bool,hAPP(fun(U_398,bool),fun(fun(U_398,bool),bool),ord_less_eq(fun(U_398,bool)),U_394),U_392))
    | ~ sP16(U_398,U_392,U_396,U_394) ),
    inference(clausify,[status(thm)],[f_139_4]) ).

fof(f_140_1,plain,
    ! [X_b,B_2,X_1,A_3] :
      ( ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2)))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) )
        & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2))) ) )
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_87_subset__insert]) ).

fof(f_140_2,plain,
    ! [U_403,U_402,U_401,U_400] :
      ( ( ( hBOOL(hAPP(fun(U_403,bool),bool,hAPP(fun(U_403,bool),fun(fun(U_403,bool),bool),ord_less_eq(fun(U_403,bool)),U_400),hAPP(fun(U_403,bool),fun(U_403,bool),hAPP(U_403,fun(fun(U_403,bool),fun(U_403,bool)),insert(U_403),U_401),U_402)))
          | ~ hBOOL(hAPP(fun(U_403,bool),bool,hAPP(fun(U_403,bool),fun(fun(U_403,bool),bool),ord_less_eq(fun(U_403,bool)),U_400),U_402)) )
        & ( hBOOL(hAPP(fun(U_403,bool),bool,hAPP(fun(U_403,bool),fun(fun(U_403,bool),bool),ord_less_eq(fun(U_403,bool)),U_400),U_402))
          | ~ hBOOL(hAPP(fun(U_403,bool),bool,hAPP(fun(U_403,bool),fun(fun(U_403,bool),bool),ord_less_eq(fun(U_403,bool)),U_400),hAPP(fun(U_403,bool),fun(U_403,bool),hAPP(U_403,fun(fun(U_403,bool),fun(U_403,bool)),insert(U_403),U_401),U_402))) ) )
      | hBOOL(hAPP(fun(U_403,bool),bool,hAPP(U_403,fun(fun(U_403,bool),bool),member(U_403),U_401),U_400)) ),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

fof(f_140_3,plain,
    ( ! [U_400,U_402,U_401,U_403] :
        ( hBOOL(hAPP(fun(U_403,bool),bool,hAPP(fun(U_403,bool),fun(fun(U_403,bool),bool),ord_less_eq(fun(U_403,bool)),U_400),hAPP(fun(U_403,bool),fun(U_403,bool),hAPP(U_403,fun(fun(U_403,bool),fun(U_403,bool)),insert(U_403),U_401),U_402)))
        | ~ hBOOL(hAPP(fun(U_403,bool),bool,hAPP(fun(U_403,bool),fun(fun(U_403,bool),bool),ord_less_eq(fun(U_403,bool)),U_400),U_402))
        | ~ sP17(U_400,U_402,U_401,U_403) )
    & ! [U_400,U_402,U_401,U_403] :
        ( hBOOL(hAPP(fun(U_403,bool),bool,hAPP(fun(U_403,bool),fun(fun(U_403,bool),bool),ord_less_eq(fun(U_403,bool)),U_400),U_402))
        | ~ hBOOL(hAPP(fun(U_403,bool),bool,hAPP(fun(U_403,bool),fun(fun(U_403,bool),bool),ord_less_eq(fun(U_403,bool)),U_400),hAPP(fun(U_403,bool),fun(U_403,bool),hAPP(U_403,fun(fun(U_403,bool),fun(U_403,bool)),insert(U_403),U_401),U_402)))
        | ~ sP17(U_400,U_402,U_401,U_403) )
    & ! [U_400,U_402,U_401,U_403] :
        ( sP17(U_400,U_402,U_401,U_403)
        | hBOOL(hAPP(fun(U_403,bool),bool,hAPP(U_403,fun(fun(U_403,bool),bool),member(U_403),U_401),U_400)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_140_2]) ).

cnf(f_140_4,plain,
    ( sP17(U_400,U_402,U_401,U_403)
    | hBOOL(hAPP(fun(U_403,bool),bool,hAPP(U_403,fun(fun(U_403,bool),bool),member(U_403),U_401),U_400)) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

cnf(f_140_5,plain,
    ( hBOOL(hAPP(fun(U_403,bool),bool,hAPP(fun(U_403,bool),fun(fun(U_403,bool),bool),ord_less_eq(fun(U_403,bool)),U_400),U_402))
    | ~ hBOOL(hAPP(fun(U_403,bool),bool,hAPP(fun(U_403,bool),fun(fun(U_403,bool),bool),ord_less_eq(fun(U_403,bool)),U_400),hAPP(fun(U_403,bool),fun(U_403,bool),hAPP(U_403,fun(fun(U_403,bool),fun(U_403,bool)),insert(U_403),U_401),U_402)))
    | ~ sP17(U_400,U_402,U_401,U_403) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

cnf(f_140_6,plain,
    ( hBOOL(hAPP(fun(U_403,bool),bool,hAPP(fun(U_403,bool),fun(fun(U_403,bool),bool),ord_less_eq(fun(U_403,bool)),U_400),hAPP(fun(U_403,bool),fun(U_403,bool),hAPP(U_403,fun(fun(U_403,bool),fun(U_403,bool)),insert(U_403),U_401),U_402)))
    | ~ hBOOL(hAPP(fun(U_403,bool),bool,hAPP(fun(U_403,bool),fun(fun(U_403,bool),bool),ord_less_eq(fun(U_403,bool)),U_400),U_402))
    | ~ sP17(U_400,U_402,U_401,U_403) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

fof(f_141_1,plain,
    ! [X_b,B,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),B_2)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_88_subset__insertI2]) ).

fof(f_141_2,plain,
    ! [U_407,U_406,U_405,U_404] :
      ( hBOOL(hAPP(fun(U_407,bool),bool,hAPP(fun(U_407,bool),fun(fun(U_407,bool),bool),ord_less_eq(fun(U_407,bool)),U_405),hAPP(fun(U_407,bool),fun(U_407,bool),hAPP(U_407,fun(fun(U_407,bool),fun(U_407,bool)),insert(U_407),U_406),U_404)))
      | ~ hBOOL(hAPP(fun(U_407,bool),bool,hAPP(fun(U_407,bool),fun(fun(U_407,bool),bool),ord_less_eq(fun(U_407,bool)),U_405),U_404)) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

fof(f_141_3,plain,
    ! [U_406,U_407,U_405,U_404] :
      ( hBOOL(hAPP(fun(U_407,bool),bool,hAPP(fun(U_407,bool),fun(fun(U_407,bool),bool),ord_less_eq(fun(U_407,bool)),U_405),hAPP(fun(U_407,bool),fun(U_407,bool),hAPP(U_407,fun(fun(U_407,bool),fun(U_407,bool)),insert(U_407),U_406),U_404)))
      | ~ hBOOL(hAPP(fun(U_407,bool),bool,hAPP(fun(U_407,bool),fun(fun(U_407,bool),bool),ord_less_eq(fun(U_407,bool)),U_405),U_404)) ),
    inference(definitional_conversion,[status(esa)],[f_141_2]) ).

cnf(f_141_4,plain,
    ( hBOOL(hAPP(fun(U_407,bool),bool,hAPP(fun(U_407,bool),fun(fun(U_407,bool),bool),ord_less_eq(fun(U_407,bool)),U_405),hAPP(fun(U_407,bool),fun(U_407,bool),hAPP(U_407,fun(fun(U_407,bool),fun(U_407,bool)),insert(U_407),U_406),U_404)))
    | ~ hBOOL(hAPP(fun(U_407,bool),bool,hAPP(fun(U_407,bool),fun(fun(U_407,bool),bool),ord_less_eq(fun(U_407,bool)),U_405),U_404)) ),
    inference(clausify,[status(thm)],[f_141_3]) ).

fof(f_142_1,plain,
    ! [X_b,A_2,C_2,D_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),C_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),D_2)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_2),D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_89_insert__mono]) ).

fof(f_142_2,plain,
    ! [U_411,U_410,U_409,U_408] :
      ( hBOOL(hAPP(fun(U_411,bool),bool,hAPP(fun(U_411,bool),fun(fun(U_411,bool),bool),ord_less_eq(fun(U_411,bool)),hAPP(fun(U_411,bool),fun(U_411,bool),hAPP(U_411,fun(fun(U_411,bool),fun(U_411,bool)),insert(U_411),U_410),U_409)),hAPP(fun(U_411,bool),fun(U_411,bool),hAPP(U_411,fun(fun(U_411,bool),fun(U_411,bool)),insert(U_411),U_410),U_408)))
      | ~ hBOOL(hAPP(fun(U_411,bool),bool,hAPP(fun(U_411,bool),fun(fun(U_411,bool),bool),ord_less_eq(fun(U_411,bool)),U_409),U_408)) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

fof(f_142_3,plain,
    ! [U_411,U_408,U_409,U_410] :
      ( hBOOL(hAPP(fun(U_411,bool),bool,hAPP(fun(U_411,bool),fun(fun(U_411,bool),bool),ord_less_eq(fun(U_411,bool)),hAPP(fun(U_411,bool),fun(U_411,bool),hAPP(U_411,fun(fun(U_411,bool),fun(U_411,bool)),insert(U_411),U_410),U_409)),hAPP(fun(U_411,bool),fun(U_411,bool),hAPP(U_411,fun(fun(U_411,bool),fun(U_411,bool)),insert(U_411),U_410),U_408)))
      | ~ hBOOL(hAPP(fun(U_411,bool),bool,hAPP(fun(U_411,bool),fun(fun(U_411,bool),bool),ord_less_eq(fun(U_411,bool)),U_409),U_408)) ),
    inference(definitional_conversion,[status(esa)],[f_142_2]) ).

cnf(f_142_4,plain,
    ( hBOOL(hAPP(fun(U_411,bool),bool,hAPP(fun(U_411,bool),fun(fun(U_411,bool),bool),ord_less_eq(fun(U_411,bool)),hAPP(fun(U_411,bool),fun(U_411,bool),hAPP(U_411,fun(fun(U_411,bool),fun(U_411,bool)),insert(U_411),U_410),U_409)),hAPP(fun(U_411,bool),fun(U_411,bool),hAPP(U_411,fun(fun(U_411,bool),fun(U_411,bool)),insert(U_411),U_410),U_408)))
    | ~ hBOOL(hAPP(fun(U_411,bool),bool,hAPP(fun(U_411,bool),fun(fun(U_411,bool),bool),ord_less_eq(fun(U_411,bool)),U_409),U_408)) ),
    inference(clausify,[status(thm)],[f_142_3]) ).

fof(f_143_1,plain,
    ! [X_c,X_b,F,A_2,B_2] : hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),hAPP(X_c,X_b,F,A_2)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_2)),
    inference(fof_nnf,[status(thm)],[fact_90_image__insert]) ).

fof(f_143_2,plain,
    ! [U_416,U_415,U_414,U_413,U_412] : hAPP(fun(U_416,bool),fun(U_415,bool),hAPP(fun(U_416,U_415),fun(fun(U_416,bool),fun(U_415,bool)),image(U_416,U_415),U_414),hAPP(fun(U_416,bool),fun(U_416,bool),hAPP(U_416,fun(fun(U_416,bool),fun(U_416,bool)),insert(U_416),U_413),U_412)) = hAPP(fun(U_415,bool),fun(U_415,bool),hAPP(U_415,fun(fun(U_415,bool),fun(U_415,bool)),insert(U_415),hAPP(U_416,U_415,U_414,U_413)),hAPP(fun(U_416,bool),fun(U_415,bool),hAPP(fun(U_416,U_415),fun(fun(U_416,bool),fun(U_415,bool)),image(U_416,U_415),U_414),U_412)),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

fof(f_143_3,plain,
    ! [U_413,U_412,U_415,U_414,U_416] : hAPP(fun(U_416,bool),fun(U_415,bool),hAPP(fun(U_416,U_415),fun(fun(U_416,bool),fun(U_415,bool)),image(U_416,U_415),U_414),hAPP(fun(U_416,bool),fun(U_416,bool),hAPP(U_416,fun(fun(U_416,bool),fun(U_416,bool)),insert(U_416),U_413),U_412)) = hAPP(fun(U_415,bool),fun(U_415,bool),hAPP(U_415,fun(fun(U_415,bool),fun(U_415,bool)),insert(U_415),hAPP(U_416,U_415,U_414,U_413)),hAPP(fun(U_416,bool),fun(U_415,bool),hAPP(fun(U_416,U_415),fun(fun(U_416,bool),fun(U_415,bool)),image(U_416,U_415),U_414),U_412)),
    inference(definitional_conversion,[status(esa)],[f_143_2]) ).

cnf(f_143_4,plain,
    hAPP(fun(U_416,bool),fun(U_415,bool),hAPP(fun(U_416,U_415),fun(fun(U_416,bool),fun(U_415,bool)),image(U_416,U_415),U_414),hAPP(fun(U_416,bool),fun(U_416,bool),hAPP(U_416,fun(fun(U_416,bool),fun(U_416,bool)),insert(U_416),U_413),U_412)) = hAPP(fun(U_415,bool),fun(U_415,bool),hAPP(U_415,fun(fun(U_415,bool),fun(U_415,bool)),insert(U_415),hAPP(U_416,U_415,U_414,U_413)),hAPP(fun(U_416,bool),fun(U_415,bool),hAPP(fun(U_416,U_415),fun(fun(U_416,bool),fun(U_415,bool)),image(U_416,U_415),U_414),U_412)),
    inference(clausify,[status(thm)],[f_143_3]) ).

fof(f_144_1,plain,
    ! [X_c,X_b,F,X_1,A_3] :
      ( hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_91_insert__image]) ).

fof(f_144_2,plain,
    ! [U_421,U_420,U_419,U_418,U_417] :
      ( hAPP(fun(U_421,bool),fun(U_421,bool),hAPP(U_421,fun(fun(U_421,bool),fun(U_421,bool)),insert(U_421),hAPP(U_420,U_421,U_419,U_418)),hAPP(fun(U_420,bool),fun(U_421,bool),hAPP(fun(U_420,U_421),fun(fun(U_420,bool),fun(U_421,bool)),image(U_420,U_421),U_419),U_417)) = hAPP(fun(U_420,bool),fun(U_421,bool),hAPP(fun(U_420,U_421),fun(fun(U_420,bool),fun(U_421,bool)),image(U_420,U_421),U_419),U_417)
      | ~ hBOOL(hAPP(fun(U_420,bool),bool,hAPP(U_420,fun(fun(U_420,bool),bool),member(U_420),U_418),U_417)) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ! [U_418,U_417,U_420,U_419,U_421] :
      ( hAPP(fun(U_421,bool),fun(U_421,bool),hAPP(U_421,fun(fun(U_421,bool),fun(U_421,bool)),insert(U_421),hAPP(U_420,U_421,U_419,U_418)),hAPP(fun(U_420,bool),fun(U_421,bool),hAPP(fun(U_420,U_421),fun(fun(U_420,bool),fun(U_421,bool)),image(U_420,U_421),U_419),U_417)) = hAPP(fun(U_420,bool),fun(U_421,bool),hAPP(fun(U_420,U_421),fun(fun(U_420,bool),fun(U_421,bool)),image(U_420,U_421),U_419),U_417)
      | ~ hBOOL(hAPP(fun(U_420,bool),bool,hAPP(U_420,fun(fun(U_420,bool),bool),member(U_420),U_418),U_417)) ),
    inference(definitional_conversion,[status(esa)],[f_144_2]) ).

cnf(f_144_4,plain,
    ( hAPP(fun(U_421,bool),fun(U_421,bool),hAPP(U_421,fun(fun(U_421,bool),fun(U_421,bool)),insert(U_421),hAPP(U_420,U_421,U_419,U_418)),hAPP(fun(U_420,bool),fun(U_421,bool),hAPP(fun(U_420,U_421),fun(fun(U_420,bool),fun(U_421,bool)),image(U_420,U_421),U_419),U_417)) = hAPP(fun(U_420,bool),fun(U_421,bool),hAPP(fun(U_420,U_421),fun(fun(U_420,bool),fun(U_421,bool)),image(U_420,U_421),U_419),U_417)
    | ~ hBOOL(hAPP(fun(U_420,bool),bool,hAPP(U_420,fun(fun(U_420,bool),bool),member(U_420),U_418),U_417)) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_1,plain,
    ! [X_b,X_c,B_2,F,A_3] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)))
        | ! [AA] :
            ( ti(fun(X_b,bool),B_2) != hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),AA)
            | ~ hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),AA),A_3)) ) )
      & ( ? [AA] :
            ( ti(fun(X_b,bool),B_2) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),AA)
            & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),AA),A_3)) )
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_92_subset__image__iff]) ).

fof(f_145_2,plain,
    ! [U_428,U_427,U_426,U_425,U_424] :
      ( ( hBOOL(hAPP(fun(U_428,bool),bool,hAPP(fun(U_428,bool),fun(fun(U_428,bool),bool),ord_less_eq(fun(U_428,bool)),U_426),hAPP(fun(U_427,bool),fun(U_428,bool),hAPP(fun(U_427,U_428),fun(fun(U_427,bool),fun(U_428,bool)),image(U_427,U_428),U_425),U_424)))
        | ! [U_423] :
            ( ti(fun(U_428,bool),U_426) != hAPP(fun(U_427,bool),fun(U_428,bool),hAPP(fun(U_427,U_428),fun(fun(U_427,bool),fun(U_428,bool)),image(U_427,U_428),U_425),U_423)
            | ~ hBOOL(hAPP(fun(U_427,bool),bool,hAPP(fun(U_427,bool),fun(fun(U_427,bool),bool),ord_less_eq(fun(U_427,bool)),U_423),U_424)) ) )
      & ( ? [U_422] :
            ( ti(fun(U_428,bool),U_426) = hAPP(fun(U_427,bool),fun(U_428,bool),hAPP(fun(U_427,U_428),fun(fun(U_427,bool),fun(U_428,bool)),image(U_427,U_428),U_425),U_422)
            & hBOOL(hAPP(fun(U_427,bool),bool,hAPP(fun(U_427,bool),fun(fun(U_427,bool),bool),ord_less_eq(fun(U_427,bool)),U_422),U_424)) )
        | ~ hBOOL(hAPP(fun(U_428,bool),bool,hAPP(fun(U_428,bool),fun(fun(U_428,bool),bool),ord_less_eq(fun(U_428,bool)),U_426),hAPP(fun(U_427,bool),fun(U_428,bool),hAPP(fun(U_427,U_428),fun(fun(U_427,bool),fun(U_428,bool)),image(U_427,U_428),U_425),U_424))) ) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

fof(f_145_3,plain,
    ( ! [U_438,U_436,U_434,U_432,U_430] :
        ( hBOOL(hAPP(fun(U_438,bool),bool,hAPP(fun(U_438,bool),fun(fun(U_438,bool),bool),ord_less_eq(fun(U_438,bool)),U_434),hAPP(fun(U_436,bool),fun(U_438,bool),hAPP(fun(U_436,U_438),fun(fun(U_436,bool),fun(U_438,bool)),image(U_436,U_438),U_432),U_430)))
        | ! [U_423] :
            ( ti(fun(U_438,bool),U_434) != hAPP(fun(U_436,bool),fun(U_438,bool),hAPP(fun(U_436,U_438),fun(fun(U_436,bool),fun(U_438,bool)),image(U_436,U_438),U_432),U_423)
            | ~ hBOOL(hAPP(fun(U_436,bool),bool,hAPP(fun(U_436,bool),fun(fun(U_436,bool),bool),ord_less_eq(fun(U_436,bool)),U_423),U_430)) ) )
    & ! [U_437,U_435,U_433,U_431,U_429] :
        ( ? [U_422] :
            ( ti(fun(U_437,bool),U_433) = hAPP(fun(U_435,bool),fun(U_437,bool),hAPP(fun(U_435,U_437),fun(fun(U_435,bool),fun(U_437,bool)),image(U_435,U_437),U_431),U_422)
            & hBOOL(hAPP(fun(U_435,bool),bool,hAPP(fun(U_435,bool),fun(fun(U_435,bool),bool),ord_less_eq(fun(U_435,bool)),U_422),U_429)) )
        | ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),U_433),hAPP(fun(U_435,bool),fun(U_437,bool),hAPP(fun(U_435,U_437),fun(fun(U_435,bool),fun(U_437,bool)),image(U_435,U_437),U_431),U_429))) ) ),
    inference(miniscope,[status(thm)],[f_145_2]) ).

fof(f_145_4,plain,
    ( ! [U_438,U_436,U_434,U_432,U_430] :
        ( hBOOL(hAPP(fun(U_438,bool),bool,hAPP(fun(U_438,bool),fun(fun(U_438,bool),bool),ord_less_eq(fun(U_438,bool)),U_434),hAPP(fun(U_436,bool),fun(U_438,bool),hAPP(fun(U_436,U_438),fun(fun(U_436,bool),fun(U_438,bool)),image(U_436,U_438),U_432),U_430)))
        | ! [U_423] :
            ( ti(fun(U_438,bool),U_434) != hAPP(fun(U_436,bool),fun(U_438,bool),hAPP(fun(U_436,U_438),fun(fun(U_436,bool),fun(U_438,bool)),image(U_436,U_438),U_432),U_423)
            | ~ hBOOL(hAPP(fun(U_436,bool),bool,hAPP(fun(U_436,bool),fun(fun(U_436,bool),bool),ord_less_eq(fun(U_436,bool)),U_423),U_430)) ) )
    & ! [U_437,U_435,U_433,U_431,U_429] :
        ( ( ti(fun(U_437,bool),U_433) = hAPP(fun(U_435,bool),fun(U_437,bool),hAPP(fun(U_435,U_437),fun(fun(U_435,bool),fun(U_437,bool)),image(U_435,U_437),U_431),sK8(U_437,U_435,U_433,U_431,U_429))
          & hBOOL(hAPP(fun(U_435,bool),bool,hAPP(fun(U_435,bool),fun(fun(U_435,bool),bool),ord_less_eq(fun(U_435,bool)),sK8(U_437,U_435,U_433,U_431,U_429)),U_429)) )
        | ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),U_433),hAPP(fun(U_435,bool),fun(U_437,bool),hAPP(fun(U_435,U_437),fun(fun(U_435,bool),fun(U_437,bool)),image(U_435,U_437),U_431),U_429))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_422,sK8(U_437,U_435,U_433,U_431,U_429))],[f_145_3]) ).

fof(f_145_5,plain,
    ( ! [U_433,U_431,U_429,U_435,U_437] :
        ( ti(fun(U_437,bool),U_433) = hAPP(fun(U_435,bool),fun(U_437,bool),hAPP(fun(U_435,U_437),fun(fun(U_435,bool),fun(U_437,bool)),image(U_435,U_437),U_431),sK8(U_437,U_435,U_433,U_431,U_429))
        | ~ sP18(U_433,U_431,U_429,U_435,U_437) )
    & ! [U_433,U_431,U_429,U_435,U_437] :
        ( hBOOL(hAPP(fun(U_435,bool),bool,hAPP(fun(U_435,bool),fun(fun(U_435,bool),bool),ord_less_eq(fun(U_435,bool)),sK8(U_437,U_435,U_433,U_431,U_429)),U_429))
        | ~ sP18(U_433,U_431,U_429,U_435,U_437) )
    & ! [U_423,U_430,U_434,U_432,U_436,U_438] :
        ( hBOOL(hAPP(fun(U_438,bool),bool,hAPP(fun(U_438,bool),fun(fun(U_438,bool),bool),ord_less_eq(fun(U_438,bool)),U_434),hAPP(fun(U_436,bool),fun(U_438,bool),hAPP(fun(U_436,U_438),fun(fun(U_436,bool),fun(U_438,bool)),image(U_436,U_438),U_432),U_430)))
        | ti(fun(U_438,bool),U_434) != hAPP(fun(U_436,bool),fun(U_438,bool),hAPP(fun(U_436,U_438),fun(fun(U_436,bool),fun(U_438,bool)),image(U_436,U_438),U_432),U_423)
        | ~ hBOOL(hAPP(fun(U_436,bool),bool,hAPP(fun(U_436,bool),fun(fun(U_436,bool),bool),ord_less_eq(fun(U_436,bool)),U_423),U_430)) )
    & ! [U_433,U_431,U_429,U_435,U_437] :
        ( sP18(U_433,U_431,U_429,U_435,U_437)
        | ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),U_433),hAPP(fun(U_435,bool),fun(U_437,bool),hAPP(fun(U_435,U_437),fun(fun(U_435,bool),fun(U_437,bool)),image(U_435,U_437),U_431),U_429))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_145_4]) ).

cnf(f_145_6,plain,
    ( sP18(U_433,U_431,U_429,U_435,U_437)
    | ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),U_433),hAPP(fun(U_435,bool),fun(U_437,bool),hAPP(fun(U_435,U_437),fun(fun(U_435,bool),fun(U_437,bool)),image(U_435,U_437),U_431),U_429))) ),
    inference(clausify,[status(thm)],[f_145_5]) ).

cnf(f_145_7,plain,
    ( hBOOL(hAPP(fun(U_438,bool),bool,hAPP(fun(U_438,bool),fun(fun(U_438,bool),bool),ord_less_eq(fun(U_438,bool)),U_434),hAPP(fun(U_436,bool),fun(U_438,bool),hAPP(fun(U_436,U_438),fun(fun(U_436,bool),fun(U_438,bool)),image(U_436,U_438),U_432),U_430)))
    | ti(fun(U_438,bool),U_434) != hAPP(fun(U_436,bool),fun(U_438,bool),hAPP(fun(U_436,U_438),fun(fun(U_436,bool),fun(U_438,bool)),image(U_436,U_438),U_432),U_423)
    | ~ hBOOL(hAPP(fun(U_436,bool),bool,hAPP(fun(U_436,bool),fun(fun(U_436,bool),bool),ord_less_eq(fun(U_436,bool)),U_423),U_430)) ),
    inference(clausify,[status(thm)],[f_145_5]) ).

cnf(f_145_8,plain,
    ( hBOOL(hAPP(fun(U_435,bool),bool,hAPP(fun(U_435,bool),fun(fun(U_435,bool),bool),ord_less_eq(fun(U_435,bool)),sK8(U_437,U_435,U_433,U_431,U_429)),U_429))
    | ~ sP18(U_433,U_431,U_429,U_435,U_437) ),
    inference(clausify,[status(thm)],[f_145_5]) ).

cnf(f_145_9,plain,
    ( ti(fun(U_437,bool),U_433) = hAPP(fun(U_435,bool),fun(U_437,bool),hAPP(fun(U_435,U_437),fun(fun(U_435,bool),fun(U_437,bool)),image(U_435,U_437),U_431),sK8(U_437,U_435,U_433,U_431,U_429))
    | ~ sP18(U_433,U_431,U_429,U_435,U_437) ),
    inference(clausify,[status(thm)],[f_145_5]) ).

fof(f_146_1,plain,
    ! [X_c,X_b,F,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),B_2)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_93_image__mono]) ).

fof(f_146_2,plain,
    ! [U_443,U_442,U_441,U_440,U_439] :
      ( hBOOL(hAPP(fun(U_443,bool),bool,hAPP(fun(U_443,bool),fun(fun(U_443,bool),bool),ord_less_eq(fun(U_443,bool)),hAPP(fun(U_442,bool),fun(U_443,bool),hAPP(fun(U_442,U_443),fun(fun(U_442,bool),fun(U_443,bool)),image(U_442,U_443),U_441),U_440)),hAPP(fun(U_442,bool),fun(U_443,bool),hAPP(fun(U_442,U_443),fun(fun(U_442,bool),fun(U_443,bool)),image(U_442,U_443),U_441),U_439)))
      | ~ hBOOL(hAPP(fun(U_442,bool),bool,hAPP(fun(U_442,bool),fun(fun(U_442,bool),bool),ord_less_eq(fun(U_442,bool)),U_440),U_439)) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

fof(f_146_3,plain,
    ! [U_442,U_440,U_441,U_439,U_443] :
      ( hBOOL(hAPP(fun(U_443,bool),bool,hAPP(fun(U_443,bool),fun(fun(U_443,bool),bool),ord_less_eq(fun(U_443,bool)),hAPP(fun(U_442,bool),fun(U_443,bool),hAPP(fun(U_442,U_443),fun(fun(U_442,bool),fun(U_443,bool)),image(U_442,U_443),U_441),U_440)),hAPP(fun(U_442,bool),fun(U_443,bool),hAPP(fun(U_442,U_443),fun(fun(U_442,bool),fun(U_443,bool)),image(U_442,U_443),U_441),U_439)))
      | ~ hBOOL(hAPP(fun(U_442,bool),bool,hAPP(fun(U_442,bool),fun(fun(U_442,bool),bool),ord_less_eq(fun(U_442,bool)),U_440),U_439)) ),
    inference(definitional_conversion,[status(esa)],[f_146_2]) ).

cnf(f_146_4,plain,
    ( hBOOL(hAPP(fun(U_443,bool),bool,hAPP(fun(U_443,bool),fun(fun(U_443,bool),bool),ord_less_eq(fun(U_443,bool)),hAPP(fun(U_442,bool),fun(U_443,bool),hAPP(fun(U_442,U_443),fun(fun(U_442,bool),fun(U_443,bool)),image(U_442,U_443),U_441),U_440)),hAPP(fun(U_442,bool),fun(U_443,bool),hAPP(fun(U_442,U_443),fun(fun(U_442,bool),fun(U_443,bool)),image(U_442,U_443),U_441),U_439)))
    | ~ hBOOL(hAPP(fun(U_442,bool),bool,hAPP(fun(U_442,bool),fun(fun(U_442,bool),bool),ord_less_eq(fun(U_442,bool)),U_440),U_439)) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

fof(f_147_1,plain,
    ! [X_b,X_c,B,F,A_3] :
      ( ? [X_2] :
          ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3))
          & ti(X_b,B) = hAPP(X_c,X_b,F,X_2) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) ),
    inference(fof_nnf,[status(thm)],[fact_94_imageE]) ).

fof(f_147_2,plain,
    ! [U_449,U_448,U_447,U_446,U_445] :
      ( ? [U_444] :
          ( hBOOL(hAPP(fun(U_448,bool),bool,hAPP(U_448,fun(fun(U_448,bool),bool),member(U_448),U_444),U_445))
          & ti(U_449,U_447) = hAPP(U_448,U_449,U_446,U_444) )
      | ~ hBOOL(hAPP(fun(U_449,bool),bool,hAPP(U_449,fun(fun(U_449,bool),bool),member(U_449),U_447),hAPP(fun(U_448,bool),fun(U_449,bool),hAPP(fun(U_448,U_449),fun(fun(U_448,bool),fun(U_449,bool)),image(U_448,U_449),U_446),U_445))) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

fof(f_147_3,plain,
    ! [U_449,U_448,U_447,U_446,U_445] :
      ( ( hBOOL(hAPP(fun(U_448,bool),bool,hAPP(U_448,fun(fun(U_448,bool),bool),member(U_448),sK9(U_449,U_448,U_447,U_446,U_445)),U_445))
        & ti(U_449,U_447) = hAPP(U_448,U_449,U_446,sK9(U_449,U_448,U_447,U_446,U_445)) )
      | ~ hBOOL(hAPP(fun(U_449,bool),bool,hAPP(U_449,fun(fun(U_449,bool),bool),member(U_449),U_447),hAPP(fun(U_448,bool),fun(U_449,bool),hAPP(fun(U_448,U_449),fun(fun(U_448,bool),fun(U_449,bool)),image(U_448,U_449),U_446),U_445))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_444,sK9(U_449,U_448,U_447,U_446,U_445))],[f_147_2]) ).

fof(f_147_4,plain,
    ( ! [U_447,U_445,U_446,U_448,U_449] :
        ( hBOOL(hAPP(fun(U_448,bool),bool,hAPP(U_448,fun(fun(U_448,bool),bool),member(U_448),sK9(U_449,U_448,U_447,U_446,U_445)),U_445))
        | ~ sP19(U_447,U_445,U_446,U_448,U_449) )
    & ! [U_447,U_445,U_446,U_448,U_449] :
        ( ti(U_449,U_447) = hAPP(U_448,U_449,U_446,sK9(U_449,U_448,U_447,U_446,U_445))
        | ~ sP19(U_447,U_445,U_446,U_448,U_449) )
    & ! [U_447,U_445,U_446,U_448,U_449] :
        ( sP19(U_447,U_445,U_446,U_448,U_449)
        | ~ hBOOL(hAPP(fun(U_449,bool),bool,hAPP(U_449,fun(fun(U_449,bool),bool),member(U_449),U_447),hAPP(fun(U_448,bool),fun(U_449,bool),hAPP(fun(U_448,U_449),fun(fun(U_448,bool),fun(U_449,bool)),image(U_448,U_449),U_446),U_445))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_147_3]) ).

cnf(f_147_5,plain,
    ( sP19(U_447,U_445,U_446,U_448,U_449)
    | ~ hBOOL(hAPP(fun(U_449,bool),bool,hAPP(U_449,fun(fun(U_449,bool),bool),member(U_449),U_447),hAPP(fun(U_448,bool),fun(U_449,bool),hAPP(fun(U_448,U_449),fun(fun(U_448,bool),fun(U_449,bool)),image(U_448,U_449),U_446),U_445))) ),
    inference(clausify,[status(thm)],[f_147_4]) ).

cnf(f_147_6,plain,
    ( ti(U_449,U_447) = hAPP(U_448,U_449,U_446,sK9(U_449,U_448,U_447,U_446,U_445))
    | ~ sP19(U_447,U_445,U_446,U_448,U_449) ),
    inference(clausify,[status(thm)],[f_147_4]) ).

cnf(f_147_7,plain,
    ( hBOOL(hAPP(fun(U_448,bool),bool,hAPP(U_448,fun(fun(U_448,bool),bool),member(U_448),sK9(U_449,U_448,U_447,U_446,U_445)),U_445))
    | ~ sP19(U_447,U_445,U_446,U_448,U_449) ),
    inference(clausify,[status(thm)],[f_147_4]) ).

fof(f_148_1,plain,
    ! [X_b,B_2,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
      | ? [X_2] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_95_subsetI]) ).

fof(f_148_2,plain,
    ! [U_453,U_452,U_451] :
      ( hBOOL(hAPP(fun(U_453,bool),bool,hAPP(fun(U_453,bool),fun(fun(U_453,bool),bool),ord_less_eq(fun(U_453,bool)),U_451),U_452))
      | ? [U_450] :
          ( ~ hBOOL(hAPP(fun(U_453,bool),bool,hAPP(U_453,fun(fun(U_453,bool),bool),member(U_453),U_450),U_452))
          & hBOOL(hAPP(fun(U_453,bool),bool,hAPP(U_453,fun(fun(U_453,bool),bool),member(U_453),U_450),U_451)) ) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

fof(f_148_3,plain,
    ! [U_453,U_452,U_451] :
      ( hBOOL(hAPP(fun(U_453,bool),bool,hAPP(fun(U_453,bool),fun(fun(U_453,bool),bool),ord_less_eq(fun(U_453,bool)),U_451),U_452))
      | ( ~ hBOOL(hAPP(fun(U_453,bool),bool,hAPP(U_453,fun(fun(U_453,bool),bool),member(U_453),sK10(U_453,U_452,U_451)),U_452))
        & hBOOL(hAPP(fun(U_453,bool),bool,hAPP(U_453,fun(fun(U_453,bool),bool),member(U_453),sK10(U_453,U_452,U_451)),U_451)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_450,sK10(U_453,U_452,U_451))],[f_148_2]) ).

fof(f_148_4,plain,
    ( ! [U_451,U_453,U_452] :
        ( ~ hBOOL(hAPP(fun(U_453,bool),bool,hAPP(U_453,fun(fun(U_453,bool),bool),member(U_453),sK10(U_453,U_452,U_451)),U_452))
        | ~ sP20(U_451,U_453,U_452) )
    & ! [U_451,U_453,U_452] :
        ( hBOOL(hAPP(fun(U_453,bool),bool,hAPP(U_453,fun(fun(U_453,bool),bool),member(U_453),sK10(U_453,U_452,U_451)),U_451))
        | ~ sP20(U_451,U_453,U_452) )
    & ! [U_451,U_453,U_452] :
        ( hBOOL(hAPP(fun(U_453,bool),bool,hAPP(fun(U_453,bool),fun(fun(U_453,bool),bool),ord_less_eq(fun(U_453,bool)),U_451),U_452))
        | sP20(U_451,U_453,U_452) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_148_3]) ).

cnf(f_148_5,plain,
    ( hBOOL(hAPP(fun(U_453,bool),bool,hAPP(fun(U_453,bool),fun(fun(U_453,bool),bool),ord_less_eq(fun(U_453,bool)),U_451),U_452))
    | sP20(U_451,U_453,U_452) ),
    inference(clausify,[status(thm)],[f_148_4]) ).

cnf(f_148_6,plain,
    ( hBOOL(hAPP(fun(U_453,bool),bool,hAPP(U_453,fun(fun(U_453,bool),bool),member(U_453),sK10(U_453,U_452,U_451)),U_451))
    | ~ sP20(U_451,U_453,U_452) ),
    inference(clausify,[status(thm)],[f_148_4]) ).

cnf(f_148_7,plain,
    ( ~ hBOOL(hAPP(fun(U_453,bool),bool,hAPP(U_453,fun(fun(U_453,bool),bool),member(U_453),sK10(U_453,U_452,U_451)),U_452))
    | ~ sP20(U_451,U_453,U_452) ),
    inference(clausify,[status(thm)],[f_148_4]) ).

fof(f_149_1,plain,
    ! [X_c,X_b,F,B_2,A_3] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3)),B_2))
      | ? [X_2] :
          ( ~ hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_2)),B_2))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_96_image__subsetI]) ).

fof(f_149_2,plain,
    ! [U_459,U_458,U_457,U_456,U_455] :
      ( hBOOL(hAPP(fun(U_459,bool),bool,hAPP(fun(U_459,bool),fun(fun(U_459,bool),bool),ord_less_eq(fun(U_459,bool)),hAPP(fun(U_458,bool),fun(U_459,bool),hAPP(fun(U_458,U_459),fun(fun(U_458,bool),fun(U_459,bool)),image(U_458,U_459),U_457),U_455)),U_456))
      | ? [U_454] :
          ( ~ hBOOL(hAPP(fun(U_459,bool),bool,hAPP(U_459,fun(fun(U_459,bool),bool),member(U_459),hAPP(U_458,U_459,U_457,U_454)),U_456))
          & hBOOL(hAPP(fun(U_458,bool),bool,hAPP(U_458,fun(fun(U_458,bool),bool),member(U_458),U_454),U_455)) ) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

fof(f_149_3,plain,
    ! [U_459,U_458,U_457,U_456,U_455] :
      ( hBOOL(hAPP(fun(U_459,bool),bool,hAPP(fun(U_459,bool),fun(fun(U_459,bool),bool),ord_less_eq(fun(U_459,bool)),hAPP(fun(U_458,bool),fun(U_459,bool),hAPP(fun(U_458,U_459),fun(fun(U_458,bool),fun(U_459,bool)),image(U_458,U_459),U_457),U_455)),U_456))
      | ( ~ hBOOL(hAPP(fun(U_459,bool),bool,hAPP(U_459,fun(fun(U_459,bool),bool),member(U_459),hAPP(U_458,U_459,U_457,sK11(U_459,U_458,U_457,U_456,U_455))),U_456))
        & hBOOL(hAPP(fun(U_458,bool),bool,hAPP(U_458,fun(fun(U_458,bool),bool),member(U_458),sK11(U_459,U_458,U_457,U_456,U_455)),U_455)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_454,sK11(U_459,U_458,U_457,U_456,U_455))],[f_149_2]) ).

fof(f_149_4,plain,
    ( ! [U_455,U_458,U_456,U_457,U_459] :
        ( ~ hBOOL(hAPP(fun(U_459,bool),bool,hAPP(U_459,fun(fun(U_459,bool),bool),member(U_459),hAPP(U_458,U_459,U_457,sK11(U_459,U_458,U_457,U_456,U_455))),U_456))
        | ~ sP21(U_455,U_458,U_456,U_457,U_459) )
    & ! [U_455,U_458,U_456,U_457,U_459] :
        ( hBOOL(hAPP(fun(U_458,bool),bool,hAPP(U_458,fun(fun(U_458,bool),bool),member(U_458),sK11(U_459,U_458,U_457,U_456,U_455)),U_455))
        | ~ sP21(U_455,U_458,U_456,U_457,U_459) )
    & ! [U_455,U_458,U_456,U_457,U_459] :
        ( hBOOL(hAPP(fun(U_459,bool),bool,hAPP(fun(U_459,bool),fun(fun(U_459,bool),bool),ord_less_eq(fun(U_459,bool)),hAPP(fun(U_458,bool),fun(U_459,bool),hAPP(fun(U_458,U_459),fun(fun(U_458,bool),fun(U_459,bool)),image(U_458,U_459),U_457),U_455)),U_456))
        | sP21(U_455,U_458,U_456,U_457,U_459) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_149_3]) ).

cnf(f_149_5,plain,
    ( hBOOL(hAPP(fun(U_459,bool),bool,hAPP(fun(U_459,bool),fun(fun(U_459,bool),bool),ord_less_eq(fun(U_459,bool)),hAPP(fun(U_458,bool),fun(U_459,bool),hAPP(fun(U_458,U_459),fun(fun(U_458,bool),fun(U_459,bool)),image(U_458,U_459),U_457),U_455)),U_456))
    | sP21(U_455,U_458,U_456,U_457,U_459) ),
    inference(clausify,[status(thm)],[f_149_4]) ).

cnf(f_149_6,plain,
    ( hBOOL(hAPP(fun(U_458,bool),bool,hAPP(U_458,fun(fun(U_458,bool),bool),member(U_458),sK11(U_459,U_458,U_457,U_456,U_455)),U_455))
    | ~ sP21(U_455,U_458,U_456,U_457,U_459) ),
    inference(clausify,[status(thm)],[f_149_4]) ).

cnf(f_149_7,plain,
    ( ~ hBOOL(hAPP(fun(U_459,bool),bool,hAPP(U_459,fun(fun(U_459,bool),bool),member(U_459),hAPP(U_458,U_459,U_457,sK11(U_459,U_458,U_457,U_456,U_455))),U_456))
    | ~ sP21(U_455,U_458,U_456,U_457,U_459) ),
    inference(clausify,[status(thm)],[f_149_4]) ).

fof(f_150_1,plain,
    ! [X_a] :
      ( ! [X] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X))
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_97_order__refl]) ).

fof(f_150_2,plain,
    ! [U_461] :
      ( ! [U_460] : hBOOL(hAPP(U_461,bool,hAPP(U_461,fun(U_461,bool),ord_less_eq(U_461),U_460),U_460))
      | ~ preorder(U_461) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

fof(f_150_3,plain,
    ! [U_461,U_460] :
      ( hBOOL(hAPP(U_461,bool,hAPP(U_461,fun(U_461,bool),ord_less_eq(U_461),U_460),U_460))
      | ~ preorder(U_461) ),
    inference(definitional_conversion,[status(esa)],[f_150_2]) ).

cnf(f_150_4,plain,
    ( hBOOL(hAPP(U_461,bool,hAPP(U_461,fun(U_461,bool),ord_less_eq(U_461),U_460),U_460))
    | ~ preorder(U_461) ),
    inference(clausify,[status(thm)],[f_150_3]) ).

fof(f_151_1,plain,
    ! [N_1] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_1))
        | ! [M_2] :
          ? [X_2] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M_2))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_1)) ) )
      & ( ? [M_2] :
          ! [X_2] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M_2))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_1)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_98_finite__nat__set__iff__bounded__le]) ).

fof(f_151_2,plain,
    ! [U_466] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_466))
        | ! [U_465] :
          ? [U_464] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_464),U_465))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_464),U_466)) ) )
      & ( ? [U_463] :
          ! [U_462] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_462),U_463))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_462),U_466)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_466)) ) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

fof(f_151_3,plain,
    ( ! [U_468] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_468))
        | ! [U_465] :
          ? [U_464] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_464),U_465))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_464),U_468)) ) )
    & ! [U_467] :
        ( ? [U_463] :
          ! [U_462] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_462),U_463))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_462),U_467)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_467)) ) ),
    inference(miniscope,[status(thm)],[f_151_2]) ).

fof(f_151_4,plain,
    ( ! [U_468] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_468))
        | ! [U_465] :
          ? [U_464] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_464),U_465))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_464),U_468)) ) )
    & ! [U_467] :
        ( ! [U_462] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_462),sK12(U_467)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_462),U_467)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_467)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_463,sK12(U_467))],[f_151_3]) ).

fof(f_151_5,plain,
    ( ! [U_468] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_468))
        | ! [U_465] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK13(U_468,U_465)),U_465))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK13(U_468,U_465)),U_468)) ) )
    & ! [U_467] :
        ( ! [U_462] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_462),sK12(U_467)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_462),U_467)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_467)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_464,sK13(U_468,U_465))],[f_151_4]) ).

fof(f_151_6,plain,
    ( ! [U_465,U_468] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK13(U_468,U_465)),U_465))
        | ~ sP22(U_465,U_468) )
    & ! [U_465,U_468] :
        ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK13(U_468,U_465)),U_468))
        | ~ sP22(U_465,U_468) )
    & ! [U_465,U_468] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_468))
        | sP22(U_465,U_468) )
    & ! [U_462,U_467] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_462),sK12(U_467)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_462),U_467))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_467)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_151_5]) ).

cnf(f_151_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_462),sK12(U_467)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_462),U_467))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_467)) ),
    inference(clausify,[status(thm)],[f_151_6]) ).

cnf(f_151_8,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_468))
    | sP22(U_465,U_468) ),
    inference(clausify,[status(thm)],[f_151_6]) ).

cnf(f_151_9,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK13(U_468,U_465)),U_468))
    | ~ sP22(U_465,U_468) ),
    inference(clausify,[status(thm)],[f_151_6]) ).

cnf(f_151_10,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK13(U_468,U_465)),U_465))
    | ~ sP22(U_465,U_468) ),
    inference(clausify,[status(thm)],[f_151_6]) ).

fof(f_152_1,plain,
    ! [G_1,C_1] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,C_1)),bot_bot(fun(x_a,bool)))))
      | ? [X_2] :
          ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X_2)),bot_bot(fun(x_a,bool)))))
          & hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X_2),u)) )
      | ~ hBOOL(hAPP(com,bool,wt,C_1)) ),
    inference(fof_nnf,[status(thm)],[fact_99_assms_I3_J]) ).

fof(f_152_2,plain,
    ! [U_471,U_470] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_471),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,U_470)),bot_bot(fun(x_a,bool)))))
      | ? [U_469] :
          ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_471),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,U_469)),bot_bot(fun(x_a,bool)))))
          & hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),U_469),u)) )
      | ~ hBOOL(hAPP(com,bool,wt,U_470)) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ! [U_471,U_470] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_471),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,U_470)),bot_bot(fun(x_a,bool)))))
      | ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_471),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,sK14(U_471,U_470))),bot_bot(fun(x_a,bool)))))
        & hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK14(U_471,U_470)),u)) )
      | ~ hBOOL(hAPP(com,bool,wt,U_470)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_469,sK14(U_471,U_470))],[f_152_2]) ).

fof(f_152_4,plain,
    ( ! [U_471,U_470] :
        ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_471),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,sK14(U_471,U_470))),bot_bot(fun(x_a,bool)))))
        | ~ sP23(U_471,U_470) )
    & ! [U_471,U_470] :
        ( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK14(U_471,U_470)),u))
        | ~ sP23(U_471,U_470) )
    & ! [U_471,U_470] :
        ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_471),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,U_470)),bot_bot(fun(x_a,bool)))))
        | sP23(U_471,U_470)
        | ~ hBOOL(hAPP(com,bool,wt,U_470)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_152_3]) ).

cnf(f_152_5,plain,
    ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_471),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,U_470)),bot_bot(fun(x_a,bool)))))
    | sP23(U_471,U_470)
    | ~ hBOOL(hAPP(com,bool,wt,U_470)) ),
    inference(clausify,[status(thm)],[f_152_4]) ).

cnf(f_152_6,plain,
    ( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK14(U_471,U_470)),u))
    | ~ sP23(U_471,U_470) ),
    inference(clausify,[status(thm)],[f_152_4]) ).

cnf(f_152_7,plain,
    ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_471),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,sK14(U_471,U_470))),bot_bot(fun(x_a,bool)))))
    | ~ sP23(U_471,U_470) ),
    inference(clausify,[status(thm)],[f_152_4]) ).

fof(f_153_1,plain,
    ! [X_b,X_c] :
      ( ! [F,G] :
          ( ( hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G))
            | ? [X_2] : ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))) )
          & ( ! [X_2] : hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2)))
            | ~ hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) ) )
      | ~ ord(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_100_le__fun__def]) ).

fof(f_153_2,plain,
    ! [U_477,U_476] :
      ( ! [U_475,U_474] :
          ( ( hBOOL(hAPP(fun(U_477,U_476),bool,hAPP(fun(U_477,U_476),fun(fun(U_477,U_476),bool),ord_less_eq(fun(U_477,U_476)),U_475),U_474))
            | ? [U_473] : ~ hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),hAPP(U_477,U_476,U_475,U_473)),hAPP(U_477,U_476,U_474,U_473))) )
          & ( ! [U_472] : hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),hAPP(U_477,U_476,U_475,U_472)),hAPP(U_477,U_476,U_474,U_472)))
            | ~ hBOOL(hAPP(fun(U_477,U_476),bool,hAPP(fun(U_477,U_476),fun(fun(U_477,U_476),bool),ord_less_eq(fun(U_477,U_476)),U_475),U_474)) ) )
      | ~ ord(U_476) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

fof(f_153_3,plain,
    ! [U_477,U_476] :
      ( ( ! [U_481,U_479] :
            ( hBOOL(hAPP(fun(U_477,U_476),bool,hAPP(fun(U_477,U_476),fun(fun(U_477,U_476),bool),ord_less_eq(fun(U_477,U_476)),U_481),U_479))
            | ? [U_473] : ~ hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),hAPP(U_477,U_476,U_481,U_473)),hAPP(U_477,U_476,U_479,U_473))) )
        & ! [U_480,U_478] :
            ( ! [U_472] : hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),hAPP(U_477,U_476,U_480,U_472)),hAPP(U_477,U_476,U_478,U_472)))
            | ~ hBOOL(hAPP(fun(U_477,U_476),bool,hAPP(fun(U_477,U_476),fun(fun(U_477,U_476),bool),ord_less_eq(fun(U_477,U_476)),U_480),U_478)) ) )
      | ~ ord(U_476) ),
    inference(miniscope,[status(thm)],[f_153_2]) ).

fof(f_153_4,plain,
    ! [U_477,U_476] :
      ( ( ! [U_481,U_479] :
            ( hBOOL(hAPP(fun(U_477,U_476),bool,hAPP(fun(U_477,U_476),fun(fun(U_477,U_476),bool),ord_less_eq(fun(U_477,U_476)),U_481),U_479))
            | ~ hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),hAPP(U_477,U_476,U_481,sK15(U_477,U_476,U_481,U_479))),hAPP(U_477,U_476,U_479,sK15(U_477,U_476,U_481,U_479)))) )
        & ! [U_480,U_478] :
            ( ! [U_472] : hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),hAPP(U_477,U_476,U_480,U_472)),hAPP(U_477,U_476,U_478,U_472)))
            | ~ hBOOL(hAPP(fun(U_477,U_476),bool,hAPP(fun(U_477,U_476),fun(fun(U_477,U_476),bool),ord_less_eq(fun(U_477,U_476)),U_480),U_478)) ) )
      | ~ ord(U_476) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_473,sK15(U_477,U_476,U_481,U_479))],[f_153_3]) ).

fof(f_153_5,plain,
    ( ! [U_472,U_476,U_481,U_477,U_479,U_478,U_480] :
        ( hBOOL(hAPP(fun(U_477,U_476),bool,hAPP(fun(U_477,U_476),fun(fun(U_477,U_476),bool),ord_less_eq(fun(U_477,U_476)),U_481),U_479))
        | ~ hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),hAPP(U_477,U_476,U_481,sK15(U_477,U_476,U_481,U_479))),hAPP(U_477,U_476,U_479,sK15(U_477,U_476,U_481,U_479))))
        | ~ sP24(U_472,U_476,U_481,U_477,U_479,U_478,U_480) )
    & ! [U_472,U_476,U_481,U_477,U_479,U_478,U_480] :
        ( hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),hAPP(U_477,U_476,U_480,U_472)),hAPP(U_477,U_476,U_478,U_472)))
        | ~ hBOOL(hAPP(fun(U_477,U_476),bool,hAPP(fun(U_477,U_476),fun(fun(U_477,U_476),bool),ord_less_eq(fun(U_477,U_476)),U_480),U_478))
        | ~ sP24(U_472,U_476,U_481,U_477,U_479,U_478,U_480) )
    & ! [U_472,U_476,U_481,U_477,U_479,U_478,U_480] :
        ( sP24(U_472,U_476,U_481,U_477,U_479,U_478,U_480)
        | ~ ord(U_476) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_153_4]) ).

cnf(f_153_6,plain,
    ( sP24(U_472,U_476,U_481,U_477,U_479,U_478,U_480)
    | ~ ord(U_476) ),
    inference(clausify,[status(thm)],[f_153_5]) ).

cnf(f_153_7,plain,
    ( hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),hAPP(U_477,U_476,U_480,U_472)),hAPP(U_477,U_476,U_478,U_472)))
    | ~ hBOOL(hAPP(fun(U_477,U_476),bool,hAPP(fun(U_477,U_476),fun(fun(U_477,U_476),bool),ord_less_eq(fun(U_477,U_476)),U_480),U_478))
    | ~ sP24(U_472,U_476,U_481,U_477,U_479,U_478,U_480) ),
    inference(clausify,[status(thm)],[f_153_5]) ).

cnf(f_153_8,plain,
    ( hBOOL(hAPP(fun(U_477,U_476),bool,hAPP(fun(U_477,U_476),fun(fun(U_477,U_476),bool),ord_less_eq(fun(U_477,U_476)),U_481),U_479))
    | ~ hBOOL(hAPP(U_476,bool,hAPP(U_476,fun(U_476,bool),ord_less_eq(U_476),hAPP(U_477,U_476,U_481,sK15(U_477,U_476,U_481,U_479))),hAPP(U_477,U_476,U_479,sK15(U_477,U_476,U_481,U_479))))
    | ~ sP24(U_472,U_476,U_481,U_477,U_479,U_478,U_480) ),
    inference(clausify,[status(thm)],[f_153_5]) ).

fof(f_154_1,plain,
    ! [X_b,X_c] :
      ( ! [X_1,F,G] :
          ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1)))
          | ~ hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) )
      | ~ ord(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_101_le__funD]) ).

fof(f_154_2,plain,
    ! [U_486,U_485] :
      ( ! [U_484,U_483,U_482] :
          ( hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less_eq(U_485),hAPP(U_486,U_485,U_483,U_484)),hAPP(U_486,U_485,U_482,U_484)))
          | ~ hBOOL(hAPP(fun(U_486,U_485),bool,hAPP(fun(U_486,U_485),fun(fun(U_486,U_485),bool),ord_less_eq(fun(U_486,U_485)),U_483),U_482)) )
      | ~ ord(U_485) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

fof(f_154_3,plain,
    ! [U_482,U_484,U_485,U_483,U_486] :
      ( hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less_eq(U_485),hAPP(U_486,U_485,U_483,U_484)),hAPP(U_486,U_485,U_482,U_484)))
      | ~ hBOOL(hAPP(fun(U_486,U_485),bool,hAPP(fun(U_486,U_485),fun(fun(U_486,U_485),bool),ord_less_eq(fun(U_486,U_485)),U_483),U_482))
      | ~ ord(U_485) ),
    inference(definitional_conversion,[status(esa)],[f_154_2]) ).

cnf(f_154_4,plain,
    ( hBOOL(hAPP(U_485,bool,hAPP(U_485,fun(U_485,bool),ord_less_eq(U_485),hAPP(U_486,U_485,U_483,U_484)),hAPP(U_486,U_485,U_482,U_484)))
    | ~ hBOOL(hAPP(fun(U_486,U_485),bool,hAPP(fun(U_486,U_485),fun(fun(U_486,U_485),bool),ord_less_eq(fun(U_486,U_485)),U_483),U_482))
    | ~ ord(U_485) ),
    inference(clausify,[status(thm)],[f_154_3]) ).

fof(f_155_1,plain,
    ! [X_b,X_c] :
      ( ! [X_1,F,G] :
          ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1)))
          | ~ hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) )
      | ~ ord(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_102_le__funE]) ).

fof(f_155_2,plain,
    ! [U_491,U_490] :
      ( ! [U_489,U_488,U_487] :
          ( hBOOL(hAPP(U_490,bool,hAPP(U_490,fun(U_490,bool),ord_less_eq(U_490),hAPP(U_491,U_490,U_488,U_489)),hAPP(U_491,U_490,U_487,U_489)))
          | ~ hBOOL(hAPP(fun(U_491,U_490),bool,hAPP(fun(U_491,U_490),fun(fun(U_491,U_490),bool),ord_less_eq(fun(U_491,U_490)),U_488),U_487)) )
      | ~ ord(U_490) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

fof(f_155_3,plain,
    ! [U_490,U_487,U_488,U_489,U_491] :
      ( hBOOL(hAPP(U_490,bool,hAPP(U_490,fun(U_490,bool),ord_less_eq(U_490),hAPP(U_491,U_490,U_488,U_489)),hAPP(U_491,U_490,U_487,U_489)))
      | ~ hBOOL(hAPP(fun(U_491,U_490),bool,hAPP(fun(U_491,U_490),fun(fun(U_491,U_490),bool),ord_less_eq(fun(U_491,U_490)),U_488),U_487))
      | ~ ord(U_490) ),
    inference(definitional_conversion,[status(esa)],[f_155_2]) ).

cnf(f_155_4,plain,
    ( hBOOL(hAPP(U_490,bool,hAPP(U_490,fun(U_490,bool),ord_less_eq(U_490),hAPP(U_491,U_490,U_488,U_489)),hAPP(U_491,U_490,U_487,U_489)))
    | ~ hBOOL(hAPP(fun(U_491,U_490),bool,hAPP(fun(U_491,U_490),fun(fun(U_491,U_490),bool),ord_less_eq(fun(U_491,U_490)),U_488),U_487))
    | ~ ord(U_490) ),
    inference(clausify,[status(thm)],[f_155_3]) ).

fof(f_156_1,plain,
    ! [X_b,A_2] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),bot_bot(fun(X_b,bool)))),
    inference(fof_nnf,[status(thm)],[fact_103_emptyE]) ).

fof(f_156_2,plain,
    ! [U_493,U_492] : ~ hBOOL(hAPP(fun(U_493,bool),bool,hAPP(U_493,fun(fun(U_493,bool),bool),member(U_493),U_492),bot_bot(fun(U_493,bool)))),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

fof(f_156_3,plain,
    ! [U_492,U_493] : ~ hBOOL(hAPP(fun(U_493,bool),bool,hAPP(U_493,fun(fun(U_493,bool),bool),member(U_493),U_492),bot_bot(fun(U_493,bool)))),
    inference(definitional_conversion,[status(esa)],[f_156_2]) ).

cnf(f_156_4,plain,
    ~ hBOOL(hAPP(fun(U_493,bool),bool,hAPP(U_493,fun(fun(U_493,bool),bool),member(U_493),U_492),bot_bot(fun(U_493,bool)))),
    inference(clausify,[status(thm)],[f_156_3]) ).

fof(f_157_1,plain,
    ! [X_b] : hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),bot_bot(fun(X_b,bool)))),
    inference(fof_nnf,[status(thm)],[fact_104_finite_OemptyI]) ).

fof(f_157_2,plain,
    ! [U_494] : hBOOL(hAPP(fun(U_494,bool),bool,finite_finite(U_494),bot_bot(fun(U_494,bool)))),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

fof(f_157_3,plain,
    ! [U_494] : hBOOL(hAPP(fun(U_494,bool),bool,finite_finite(U_494),bot_bot(fun(U_494,bool)))),
    inference(definitional_conversion,[status(esa)],[f_157_2]) ).

cnf(f_157_4,plain,
    hBOOL(hAPP(fun(U_494,bool),bool,finite_finite(U_494),bot_bot(fun(U_494,bool)))),
    inference(clausify,[status(thm)],[f_157_3]) ).

fof(f_158_1,plain,
    ! [X_b,A_3] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3)),
    inference(fof_nnf,[status(thm)],[fact_105_empty__subsetI]) ).

fof(f_158_2,plain,
    ! [U_496,U_495] : hBOOL(hAPP(fun(U_496,bool),bool,hAPP(fun(U_496,bool),fun(fun(U_496,bool),bool),ord_less_eq(fun(U_496,bool)),bot_bot(fun(U_496,bool))),U_495)),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

fof(f_158_3,plain,
    ! [U_495,U_496] : hBOOL(hAPP(fun(U_496,bool),bool,hAPP(fun(U_496,bool),fun(fun(U_496,bool),bool),ord_less_eq(fun(U_496,bool)),bot_bot(fun(U_496,bool))),U_495)),
    inference(definitional_conversion,[status(esa)],[f_158_2]) ).

cnf(f_158_4,plain,
    hBOOL(hAPP(fun(U_496,bool),bool,hAPP(fun(U_496,bool),fun(fun(U_496,bool),bool),ord_less_eq(fun(U_496,bool)),bot_bot(fun(U_496,bool))),U_495)),
    inference(clausify,[status(thm)],[f_158_3]) ).

fof(f_159_1,plain,
    ! [X_b,A_2,A_3] :
      ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))
      | ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) ),
    inference(fof_nnf,[status(thm)],[fact_106_equals0D]) ).

fof(f_159_2,plain,
    ! [U_499,U_498,U_497] :
      ( ~ hBOOL(hAPP(fun(U_499,bool),bool,hAPP(U_499,fun(fun(U_499,bool),bool),member(U_499),U_498),U_497))
      | ti(fun(U_499,bool),U_497) != bot_bot(fun(U_499,bool)) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

fof(f_159_3,plain,
    ! [U_497,U_499,U_498] :
      ( ~ hBOOL(hAPP(fun(U_499,bool),bool,hAPP(U_499,fun(fun(U_499,bool),bool),member(U_499),U_498),U_497))
      | ti(fun(U_499,bool),U_497) != bot_bot(fun(U_499,bool)) ),
    inference(definitional_conversion,[status(esa)],[f_159_2]) ).

cnf(f_159_4,plain,
    ( ~ hBOOL(hAPP(fun(U_499,bool),bool,hAPP(U_499,fun(fun(U_499,bool),bool),member(U_499),U_498),U_497))
    | ti(fun(U_499,bool),U_497) != bot_bot(fun(U_499,bool)) ),
    inference(clausify,[status(thm)],[f_159_3]) ).

fof(f_160_1,plain,
    ! [X_b,Pa] :
      ( ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = bot_bot(fun(X_b,bool))
        | ? [X_2] : hBOOL(hAPP(X_b,bool,Pa,X_2)) )
      & ( ! [X_2] : ~ hBOOL(hAPP(X_b,bool,Pa,X_2))
        | hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) != bot_bot(fun(X_b,bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_107_Collect__empty__eq]) ).

fof(f_160_2,plain,
    ! [U_503,U_502] :
      ( ( hAPP(fun(U_503,bool),fun(U_503,bool),collect(U_503),U_502) = bot_bot(fun(U_503,bool))
        | ? [U_501] : hBOOL(hAPP(U_503,bool,U_502,U_501)) )
      & ( ! [U_500] : ~ hBOOL(hAPP(U_503,bool,U_502,U_500))
        | hAPP(fun(U_503,bool),fun(U_503,bool),collect(U_503),U_502) != bot_bot(fun(U_503,bool)) ) ),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

fof(f_160_3,plain,
    ( ! [U_507,U_505] :
        ( hAPP(fun(U_507,bool),fun(U_507,bool),collect(U_507),U_505) = bot_bot(fun(U_507,bool))
        | ? [U_501] : hBOOL(hAPP(U_507,bool,U_505,U_501)) )
    & ! [U_506,U_504] :
        ( ! [U_500] : ~ hBOOL(hAPP(U_506,bool,U_504,U_500))
        | hAPP(fun(U_506,bool),fun(U_506,bool),collect(U_506),U_504) != bot_bot(fun(U_506,bool)) ) ),
    inference(miniscope,[status(thm)],[f_160_2]) ).

fof(f_160_4,plain,
    ( ! [U_507,U_505] :
        ( hAPP(fun(U_507,bool),fun(U_507,bool),collect(U_507),U_505) = bot_bot(fun(U_507,bool))
        | hBOOL(hAPP(U_507,bool,U_505,sK16(U_507,U_505))) )
    & ! [U_506,U_504] :
        ( ! [U_500] : ~ hBOOL(hAPP(U_506,bool,U_504,U_500))
        | hAPP(fun(U_506,bool),fun(U_506,bool),collect(U_506),U_504) != bot_bot(fun(U_506,bool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_501,sK16(U_507,U_505))],[f_160_3]) ).

fof(f_160_5,plain,
    ( ! [U_505,U_507] :
        ( hAPP(fun(U_507,bool),fun(U_507,bool),collect(U_507),U_505) = bot_bot(fun(U_507,bool))
        | hBOOL(hAPP(U_507,bool,U_505,sK16(U_507,U_505))) )
    & ! [U_500,U_506,U_504] :
        ( ~ hBOOL(hAPP(U_506,bool,U_504,U_500))
        | hAPP(fun(U_506,bool),fun(U_506,bool),collect(U_506),U_504) != bot_bot(fun(U_506,bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_160_4]) ).

cnf(f_160_6,plain,
    ( ~ hBOOL(hAPP(U_506,bool,U_504,U_500))
    | hAPP(fun(U_506,bool),fun(U_506,bool),collect(U_506),U_504) != bot_bot(fun(U_506,bool)) ),
    inference(clausify,[status(thm)],[f_160_5]) ).

cnf(f_160_7,plain,
    ( hAPP(fun(U_507,bool),fun(U_507,bool),collect(U_507),U_505) = bot_bot(fun(U_507,bool))
    | hBOOL(hAPP(U_507,bool,U_505,sK16(U_507,U_505))) ),
    inference(clausify,[status(thm)],[f_160_5]) ).

fof(f_161_1,plain,
    ! [X_b,C_1] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),bot_bot(fun(X_b,bool)))),
    inference(fof_nnf,[status(thm)],[fact_108_empty__iff]) ).

fof(f_161_2,plain,
    ! [U_509,U_508] : ~ hBOOL(hAPP(fun(U_509,bool),bool,hAPP(U_509,fun(fun(U_509,bool),bool),member(U_509),U_508),bot_bot(fun(U_509,bool)))),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

fof(f_161_3,plain,
    ! [U_509,U_508] : ~ hBOOL(hAPP(fun(U_509,bool),bool,hAPP(U_509,fun(fun(U_509,bool),bool),member(U_509),U_508),bot_bot(fun(U_509,bool)))),
    inference(definitional_conversion,[status(esa)],[f_161_2]) ).

cnf(f_161_4,plain,
    ~ hBOOL(hAPP(fun(U_509,bool),bool,hAPP(U_509,fun(fun(U_509,bool),bool),member(U_509),U_508),bot_bot(fun(U_509,bool)))),
    inference(clausify,[status(thm)],[f_161_3]) ).

fof(f_162_1,plain,
    ! [X_b,Pa] :
      ( ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)
        | ? [X_2] : hBOOL(hAPP(X_b,bool,Pa,X_2)) )
      & ( ! [X_2] : ~ hBOOL(hAPP(X_b,bool,Pa,X_2))
        | bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_109_empty__Collect__eq]) ).

fof(f_162_2,plain,
    ! [U_513,U_512] :
      ( ( bot_bot(fun(U_513,bool)) = hAPP(fun(U_513,bool),fun(U_513,bool),collect(U_513),U_512)
        | ? [U_511] : hBOOL(hAPP(U_513,bool,U_512,U_511)) )
      & ( ! [U_510] : ~ hBOOL(hAPP(U_513,bool,U_512,U_510))
        | bot_bot(fun(U_513,bool)) != hAPP(fun(U_513,bool),fun(U_513,bool),collect(U_513),U_512) ) ),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

fof(f_162_3,plain,
    ( ! [U_517,U_515] :
        ( bot_bot(fun(U_517,bool)) = hAPP(fun(U_517,bool),fun(U_517,bool),collect(U_517),U_515)
        | ? [U_511] : hBOOL(hAPP(U_517,bool,U_515,U_511)) )
    & ! [U_516,U_514] :
        ( ! [U_510] : ~ hBOOL(hAPP(U_516,bool,U_514,U_510))
        | bot_bot(fun(U_516,bool)) != hAPP(fun(U_516,bool),fun(U_516,bool),collect(U_516),U_514) ) ),
    inference(miniscope,[status(thm)],[f_162_2]) ).

fof(f_162_4,plain,
    ( ! [U_517,U_515] :
        ( bot_bot(fun(U_517,bool)) = hAPP(fun(U_517,bool),fun(U_517,bool),collect(U_517),U_515)
        | hBOOL(hAPP(U_517,bool,U_515,sK17(U_517,U_515))) )
    & ! [U_516,U_514] :
        ( ! [U_510] : ~ hBOOL(hAPP(U_516,bool,U_514,U_510))
        | bot_bot(fun(U_516,bool)) != hAPP(fun(U_516,bool),fun(U_516,bool),collect(U_516),U_514) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_511,sK17(U_517,U_515))],[f_162_3]) ).

fof(f_162_5,plain,
    ( ! [U_517,U_515] :
        ( bot_bot(fun(U_517,bool)) = hAPP(fun(U_517,bool),fun(U_517,bool),collect(U_517),U_515)
        | hBOOL(hAPP(U_517,bool,U_515,sK17(U_517,U_515))) )
    & ! [U_510,U_516,U_514] :
        ( ~ hBOOL(hAPP(U_516,bool,U_514,U_510))
        | bot_bot(fun(U_516,bool)) != hAPP(fun(U_516,bool),fun(U_516,bool),collect(U_516),U_514) ) ),
    inference(definitional_conversion,[status(esa)],[f_162_4]) ).

cnf(f_162_6,plain,
    ( ~ hBOOL(hAPP(U_516,bool,U_514,U_510))
    | bot_bot(fun(U_516,bool)) != hAPP(fun(U_516,bool),fun(U_516,bool),collect(U_516),U_514) ),
    inference(clausify,[status(thm)],[f_162_5]) ).

cnf(f_162_7,plain,
    ( bot_bot(fun(U_517,bool)) = hAPP(fun(U_517,bool),fun(U_517,bool),collect(U_517),U_515)
    | hBOOL(hAPP(U_517,bool,U_515,sK17(U_517,U_515))) ),
    inference(clausify,[status(thm)],[f_162_5]) ).

fof(f_163_1,plain,
    ! [X_b,A_3] :
      ( ( ? [X_2] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))
        | ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) )
      & ( ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool))
        | ! [X_2] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_110_ex__in__conv]) ).

fof(f_163_2,plain,
    ! [U_521,U_520] :
      ( ( ? [U_519] : hBOOL(hAPP(fun(U_521,bool),bool,hAPP(U_521,fun(fun(U_521,bool),bool),member(U_521),U_519),U_520))
        | ti(fun(U_521,bool),U_520) = bot_bot(fun(U_521,bool)) )
      & ( ti(fun(U_521,bool),U_520) != bot_bot(fun(U_521,bool))
        | ! [U_518] : ~ hBOOL(hAPP(fun(U_521,bool),bool,hAPP(U_521,fun(fun(U_521,bool),bool),member(U_521),U_518),U_520)) ) ),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

fof(f_163_3,plain,
    ( ! [U_525,U_523] :
        ( ? [U_519] : hBOOL(hAPP(fun(U_525,bool),bool,hAPP(U_525,fun(fun(U_525,bool),bool),member(U_525),U_519),U_523))
        | ti(fun(U_525,bool),U_523) = bot_bot(fun(U_525,bool)) )
    & ! [U_524,U_522] :
        ( ti(fun(U_524,bool),U_522) != bot_bot(fun(U_524,bool))
        | ! [U_518] : ~ hBOOL(hAPP(fun(U_524,bool),bool,hAPP(U_524,fun(fun(U_524,bool),bool),member(U_524),U_518),U_522)) ) ),
    inference(miniscope,[status(thm)],[f_163_2]) ).

fof(f_163_4,plain,
    ( ! [U_525,U_523] :
        ( hBOOL(hAPP(fun(U_525,bool),bool,hAPP(U_525,fun(fun(U_525,bool),bool),member(U_525),sK18(U_525,U_523)),U_523))
        | ti(fun(U_525,bool),U_523) = bot_bot(fun(U_525,bool)) )
    & ! [U_524,U_522] :
        ( ti(fun(U_524,bool),U_522) != bot_bot(fun(U_524,bool))
        | ! [U_518] : ~ hBOOL(hAPP(fun(U_524,bool),bool,hAPP(U_524,fun(fun(U_524,bool),bool),member(U_524),U_518),U_522)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_519,sK18(U_525,U_523))],[f_163_3]) ).

fof(f_163_5,plain,
    ( ! [U_523,U_525] :
        ( hBOOL(hAPP(fun(U_525,bool),bool,hAPP(U_525,fun(fun(U_525,bool),bool),member(U_525),sK18(U_525,U_523)),U_523))
        | ti(fun(U_525,bool),U_523) = bot_bot(fun(U_525,bool)) )
    & ! [U_518,U_522,U_524] :
        ( ti(fun(U_524,bool),U_522) != bot_bot(fun(U_524,bool))
        | ~ hBOOL(hAPP(fun(U_524,bool),bool,hAPP(U_524,fun(fun(U_524,bool),bool),member(U_524),U_518),U_522)) ) ),
    inference(definitional_conversion,[status(esa)],[f_163_4]) ).

cnf(f_163_6,plain,
    ( ti(fun(U_524,bool),U_522) != bot_bot(fun(U_524,bool))
    | ~ hBOOL(hAPP(fun(U_524,bool),bool,hAPP(U_524,fun(fun(U_524,bool),bool),member(U_524),U_518),U_522)) ),
    inference(clausify,[status(thm)],[f_163_5]) ).

cnf(f_163_7,plain,
    ( hBOOL(hAPP(fun(U_525,bool),bool,hAPP(U_525,fun(fun(U_525,bool),bool),member(U_525),sK18(U_525,U_523)),U_523))
    | ti(fun(U_525,bool),U_523) = bot_bot(fun(U_525,bool)) ),
    inference(clausify,[status(thm)],[f_163_5]) ).

fof(f_164_1,plain,
    ! [X_b,A_3] :
      ( ( ! [X_2] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))
        | ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) )
      & ( ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool))
        | ? [X_2] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_111_all__not__in__conv]) ).

fof(f_164_2,plain,
    ! [U_529,U_528] :
      ( ( ! [U_527] : ~ hBOOL(hAPP(fun(U_529,bool),bool,hAPP(U_529,fun(fun(U_529,bool),bool),member(U_529),U_527),U_528))
        | ti(fun(U_529,bool),U_528) != bot_bot(fun(U_529,bool)) )
      & ( ti(fun(U_529,bool),U_528) = bot_bot(fun(U_529,bool))
        | ? [U_526] : hBOOL(hAPP(fun(U_529,bool),bool,hAPP(U_529,fun(fun(U_529,bool),bool),member(U_529),U_526),U_528)) ) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

fof(f_164_3,plain,
    ( ! [U_533,U_531] :
        ( ! [U_527] : ~ hBOOL(hAPP(fun(U_533,bool),bool,hAPP(U_533,fun(fun(U_533,bool),bool),member(U_533),U_527),U_531))
        | ti(fun(U_533,bool),U_531) != bot_bot(fun(U_533,bool)) )
    & ! [U_532,U_530] :
        ( ti(fun(U_532,bool),U_530) = bot_bot(fun(U_532,bool))
        | ? [U_526] : hBOOL(hAPP(fun(U_532,bool),bool,hAPP(U_532,fun(fun(U_532,bool),bool),member(U_532),U_526),U_530)) ) ),
    inference(miniscope,[status(thm)],[f_164_2]) ).

fof(f_164_4,plain,
    ( ! [U_533,U_531] :
        ( ! [U_527] : ~ hBOOL(hAPP(fun(U_533,bool),bool,hAPP(U_533,fun(fun(U_533,bool),bool),member(U_533),U_527),U_531))
        | ti(fun(U_533,bool),U_531) != bot_bot(fun(U_533,bool)) )
    & ! [U_532,U_530] :
        ( ti(fun(U_532,bool),U_530) = bot_bot(fun(U_532,bool))
        | hBOOL(hAPP(fun(U_532,bool),bool,hAPP(U_532,fun(fun(U_532,bool),bool),member(U_532),sK19(U_532,U_530)),U_530)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_526,sK19(U_532,U_530))],[f_164_3]) ).

fof(f_164_5,plain,
    ( ! [U_527,U_531,U_533] :
        ( ~ hBOOL(hAPP(fun(U_533,bool),bool,hAPP(U_533,fun(fun(U_533,bool),bool),member(U_533),U_527),U_531))
        | ti(fun(U_533,bool),U_531) != bot_bot(fun(U_533,bool)) )
    & ! [U_530,U_532] :
        ( ti(fun(U_532,bool),U_530) = bot_bot(fun(U_532,bool))
        | hBOOL(hAPP(fun(U_532,bool),bool,hAPP(U_532,fun(fun(U_532,bool),bool),member(U_532),sK19(U_532,U_530)),U_530)) ) ),
    inference(definitional_conversion,[status(esa)],[f_164_4]) ).

cnf(f_164_6,plain,
    ( ti(fun(U_532,bool),U_530) = bot_bot(fun(U_532,bool))
    | hBOOL(hAPP(fun(U_532,bool),bool,hAPP(U_532,fun(fun(U_532,bool),bool),member(U_532),sK19(U_532,U_530)),U_530)) ),
    inference(clausify,[status(thm)],[f_164_5]) ).

cnf(f_164_7,plain,
    ( ~ hBOOL(hAPP(fun(U_533,bool),bool,hAPP(U_533,fun(fun(U_533,bool),bool),member(U_533),U_527),U_531))
    | ti(fun(U_533,bool),U_531) != bot_bot(fun(U_533,bool)) ),
    inference(clausify,[status(thm)],[f_164_5]) ).

fof(f_165_1,plain,
    ! [X_b] : bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)),
    inference(fof_nnf,[status(thm)],[fact_112_empty__def]) ).

fof(f_165_2,plain,
    ! [U_534] : bot_bot(fun(U_534,bool)) = hAPP(fun(U_534,bool),fun(U_534,bool),collect(U_534),hAPP(bool,fun(U_534,bool),combk(bool,U_534),fFalse)),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

fof(f_165_3,plain,
    ! [U_534] : bot_bot(fun(U_534,bool)) = hAPP(fun(U_534,bool),fun(U_534,bool),collect(U_534),hAPP(bool,fun(U_534,bool),combk(bool,U_534),fFalse)),
    inference(definitional_conversion,[status(esa)],[f_165_2]) ).

cnf(f_165_4,plain,
    bot_bot(fun(U_534,bool)) = hAPP(fun(U_534,bool),fun(U_534,bool),collect(U_534),hAPP(bool,fun(U_534,bool),combk(bool,U_534),fFalse)),
    inference(clausify,[status(thm)],[f_165_3]) ).

fof(f_166_1,plain,
    ! [X_b,X_c] :
      ( ! [X_2] : hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c)
      | ~ bot(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_113_bot__fun__def]) ).

fof(f_166_2,plain,
    ! [U_537,U_536] :
      ( ! [U_535] : hAPP(U_537,U_536,bot_bot(fun(U_537,U_536)),U_535) = bot_bot(U_536)
      | ~ bot(U_536) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

fof(f_166_3,plain,
    ! [U_535,U_536,U_537] :
      ( hAPP(U_537,U_536,bot_bot(fun(U_537,U_536)),U_535) = bot_bot(U_536)
      | ~ bot(U_536) ),
    inference(definitional_conversion,[status(esa)],[f_166_2]) ).

cnf(f_166_4,plain,
    ( hAPP(U_537,U_536,bot_bot(fun(U_537,U_536)),U_535) = bot_bot(U_536)
    | ~ bot(U_536) ),
    inference(clausify,[status(thm)],[f_166_3]) ).

fof(f_167_1,plain,
    ! [X_c,X_b] :
      ( ! [X_1] : hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_1) = bot_bot(X_b)
      | ~ bot(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_114_bot__apply]) ).

fof(f_167_2,plain,
    ! [U_540,U_539] :
      ( ! [U_538] : hAPP(U_540,U_539,bot_bot(fun(U_540,U_539)),U_538) = bot_bot(U_539)
      | ~ bot(U_539) ),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

fof(f_167_3,plain,
    ! [U_538,U_539,U_540] :
      ( hAPP(U_540,U_539,bot_bot(fun(U_540,U_539)),U_538) = bot_bot(U_539)
      | ~ bot(U_539) ),
    inference(definitional_conversion,[status(esa)],[f_167_2]) ).

cnf(f_167_4,plain,
    ( hAPP(U_540,U_539,bot_bot(fun(U_540,U_539)),U_538) = bot_bot(U_539)
    | ~ bot(U_539) ),
    inference(clausify,[status(thm)],[f_167_3]) ).

fof(f_168_1,plain,
    ! [X_a] :
      ( ! [A_1] :
          ( ti(X_a,A_1) = bot_bot(X_a)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),bot_bot(X_a))) )
      | ~ bot(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_115_le__bot]) ).

fof(f_168_2,plain,
    ! [U_542] :
      ( ! [U_541] :
          ( ti(U_542,U_541) = bot_bot(U_542)
          | ~ hBOOL(hAPP(U_542,bool,hAPP(U_542,fun(U_542,bool),ord_less_eq(U_542),U_541),bot_bot(U_542))) )
      | ~ bot(U_542) ),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

fof(f_168_3,plain,
    ! [U_541,U_542] :
      ( ti(U_542,U_541) = bot_bot(U_542)
      | ~ hBOOL(hAPP(U_542,bool,hAPP(U_542,fun(U_542,bool),ord_less_eq(U_542),U_541),bot_bot(U_542)))
      | ~ bot(U_542) ),
    inference(definitional_conversion,[status(esa)],[f_168_2]) ).

cnf(f_168_4,plain,
    ( ti(U_542,U_541) = bot_bot(U_542)
    | ~ hBOOL(hAPP(U_542,bool,hAPP(U_542,fun(U_542,bool),ord_less_eq(U_542),U_541),bot_bot(U_542)))
    | ~ bot(U_542) ),
    inference(clausify,[status(thm)],[f_168_3]) ).

fof(f_169_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),bot_bot(X_b)))
            | ti(X_b,A_2) != bot_bot(X_b) )
          & ( ti(X_b,A_2) = bot_bot(X_b)
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),bot_bot(X_b))) ) )
      | ~ bot(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_116_bot__unique]) ).

fof(f_169_2,plain,
    ! [U_544] :
      ( ! [U_543] :
          ( ( hBOOL(hAPP(U_544,bool,hAPP(U_544,fun(U_544,bool),ord_less_eq(U_544),U_543),bot_bot(U_544)))
            | ti(U_544,U_543) != bot_bot(U_544) )
          & ( ti(U_544,U_543) = bot_bot(U_544)
            | ~ hBOOL(hAPP(U_544,bool,hAPP(U_544,fun(U_544,bool),ord_less_eq(U_544),U_543),bot_bot(U_544))) ) )
      | ~ bot(U_544) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

fof(f_169_3,plain,
    ! [U_544] :
      ( ( ! [U_546] :
            ( hBOOL(hAPP(U_544,bool,hAPP(U_544,fun(U_544,bool),ord_less_eq(U_544),U_546),bot_bot(U_544)))
            | ti(U_544,U_546) != bot_bot(U_544) )
        & ! [U_545] :
            ( ti(U_544,U_545) = bot_bot(U_544)
            | ~ hBOOL(hAPP(U_544,bool,hAPP(U_544,fun(U_544,bool),ord_less_eq(U_544),U_545),bot_bot(U_544))) ) )
      | ~ bot(U_544) ),
    inference(miniscope,[status(thm)],[f_169_2]) ).

fof(f_169_4,plain,
    ( ! [U_544,U_546,U_545] :
        ( hBOOL(hAPP(U_544,bool,hAPP(U_544,fun(U_544,bool),ord_less_eq(U_544),U_546),bot_bot(U_544)))
        | ti(U_544,U_546) != bot_bot(U_544)
        | ~ sP25(U_544,U_546,U_545) )
    & ! [U_544,U_546,U_545] :
        ( ti(U_544,U_545) = bot_bot(U_544)
        | ~ hBOOL(hAPP(U_544,bool,hAPP(U_544,fun(U_544,bool),ord_less_eq(U_544),U_545),bot_bot(U_544)))
        | ~ sP25(U_544,U_546,U_545) )
    & ! [U_544,U_546,U_545] :
        ( sP25(U_544,U_546,U_545)
        | ~ bot(U_544) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25])],[f_169_3]) ).

cnf(f_169_5,plain,
    ( sP25(U_544,U_546,U_545)
    | ~ bot(U_544) ),
    inference(clausify,[status(thm)],[f_169_4]) ).

cnf(f_169_6,plain,
    ( ti(U_544,U_545) = bot_bot(U_544)
    | ~ hBOOL(hAPP(U_544,bool,hAPP(U_544,fun(U_544,bool),ord_less_eq(U_544),U_545),bot_bot(U_544)))
    | ~ sP25(U_544,U_546,U_545) ),
    inference(clausify,[status(thm)],[f_169_4]) ).

cnf(f_169_7,plain,
    ( hBOOL(hAPP(U_544,bool,hAPP(U_544,fun(U_544,bool),ord_less_eq(U_544),U_546),bot_bot(U_544)))
    | ti(U_544,U_546) != bot_bot(U_544)
    | ~ sP25(U_544,U_546,U_545) ),
    inference(clausify,[status(thm)],[f_169_4]) ).

fof(f_170_1,plain,
    ! [X_a] :
      ( ! [A_1] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),bot_bot(X_a)),A_1))
      | ~ bot(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_117_bot__least]) ).

fof(f_170_2,plain,
    ! [U_548] :
      ( ! [U_547] : hBOOL(hAPP(U_548,bool,hAPP(U_548,fun(U_548,bool),ord_less_eq(U_548),bot_bot(U_548)),U_547))
      | ~ bot(U_548) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

fof(f_170_3,plain,
    ! [U_547,U_548] :
      ( hBOOL(hAPP(U_548,bool,hAPP(U_548,fun(U_548,bool),ord_less_eq(U_548),bot_bot(U_548)),U_547))
      | ~ bot(U_548) ),
    inference(definitional_conversion,[status(esa)],[f_170_2]) ).

cnf(f_170_4,plain,
    ( hBOOL(hAPP(U_548,bool,hAPP(U_548,fun(U_548,bool),ord_less_eq(U_548),bot_bot(U_548)),U_547))
    | ~ bot(U_548) ),
    inference(clausify,[status(thm)],[f_170_3]) ).

fof(f_171_1,plain,
    ! [X_b,A_2,B] :
      ( ti(X_b,A_2) = ti(X_b,B)
      | hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool))) ),
    inference(fof_nnf,[status(thm)],[fact_118_singleton__inject]) ).

fof(f_171_2,plain,
    ! [U_551,U_550,U_549] :
      ( ti(U_551,U_550) = ti(U_551,U_549)
      | hAPP(fun(U_551,bool),fun(U_551,bool),hAPP(U_551,fun(fun(U_551,bool),fun(U_551,bool)),insert(U_551),U_550),bot_bot(fun(U_551,bool))) != hAPP(fun(U_551,bool),fun(U_551,bool),hAPP(U_551,fun(fun(U_551,bool),fun(U_551,bool)),insert(U_551),U_549),bot_bot(fun(U_551,bool))) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

fof(f_171_3,plain,
    ! [U_549,U_550,U_551] :
      ( ti(U_551,U_550) = ti(U_551,U_549)
      | hAPP(fun(U_551,bool),fun(U_551,bool),hAPP(U_551,fun(fun(U_551,bool),fun(U_551,bool)),insert(U_551),U_550),bot_bot(fun(U_551,bool))) != hAPP(fun(U_551,bool),fun(U_551,bool),hAPP(U_551,fun(fun(U_551,bool),fun(U_551,bool)),insert(U_551),U_549),bot_bot(fun(U_551,bool))) ),
    inference(definitional_conversion,[status(esa)],[f_171_2]) ).

cnf(f_171_4,plain,
    ( ti(U_551,U_550) = ti(U_551,U_549)
    | hAPP(fun(U_551,bool),fun(U_551,bool),hAPP(U_551,fun(fun(U_551,bool),fun(U_551,bool)),insert(U_551),U_550),bot_bot(fun(U_551,bool))) != hAPP(fun(U_551,bool),fun(U_551,bool),hAPP(U_551,fun(fun(U_551,bool),fun(U_551,bool)),insert(U_551),U_549),bot_bot(fun(U_551,bool))) ),
    inference(clausify,[status(thm)],[f_171_3]) ).

fof(f_172_1,plain,
    ! [X_b,B,A_2] :
      ( ti(X_b,B) = ti(X_b,A_2)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) ),
    inference(fof_nnf,[status(thm)],[fact_119_singletonE]) ).

fof(f_172_2,plain,
    ! [U_554,U_553,U_552] :
      ( ti(U_554,U_553) = ti(U_554,U_552)
      | ~ hBOOL(hAPP(fun(U_554,bool),bool,hAPP(U_554,fun(fun(U_554,bool),bool),member(U_554),U_553),hAPP(fun(U_554,bool),fun(U_554,bool),hAPP(U_554,fun(fun(U_554,bool),fun(U_554,bool)),insert(U_554),U_552),bot_bot(fun(U_554,bool))))) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

fof(f_172_3,plain,
    ! [U_552,U_553,U_554] :
      ( ti(U_554,U_553) = ti(U_554,U_552)
      | ~ hBOOL(hAPP(fun(U_554,bool),bool,hAPP(U_554,fun(fun(U_554,bool),bool),member(U_554),U_553),hAPP(fun(U_554,bool),fun(U_554,bool),hAPP(U_554,fun(fun(U_554,bool),fun(U_554,bool)),insert(U_554),U_552),bot_bot(fun(U_554,bool))))) ),
    inference(definitional_conversion,[status(esa)],[f_172_2]) ).

cnf(f_172_4,plain,
    ( ti(U_554,U_553) = ti(U_554,U_552)
    | ~ hBOOL(hAPP(fun(U_554,bool),bool,hAPP(U_554,fun(fun(U_554,bool),bool),member(U_554),U_553),hAPP(fun(U_554,bool),fun(U_554,bool),hAPP(U_554,fun(fun(U_554,bool),fun(U_554,bool)),insert(U_554),U_552),bot_bot(fun(U_554,bool))))) ),
    inference(clausify,[status(thm)],[f_172_3]) ).

fof(f_173_1,plain,
    ! [X_b,A_2,B,C_1,D_1] :
      ( ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_1),bot_bot(fun(X_b,bool))))
        | ( ( ti(X_b,B) != ti(X_b,C_1)
            | ti(X_b,A_2) != ti(X_b,D_1) )
          & ( ti(X_b,B) != ti(X_b,D_1)
            | ti(X_b,A_2) != ti(X_b,C_1) ) ) )
      & ( ( ti(X_b,B) = ti(X_b,C_1)
          & ti(X_b,A_2) = ti(X_b,D_1) )
        | ( ti(X_b,B) = ti(X_b,D_1)
          & ti(X_b,A_2) = ti(X_b,C_1) )
        | hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool)))) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D_1),bot_bot(fun(X_b,bool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_120_doubleton__eq__iff]) ).

fof(f_173_2,plain,
    ! [U_559,U_558,U_557,U_556,U_555] :
      ( ( hAPP(fun(U_559,bool),fun(U_559,bool),hAPP(U_559,fun(fun(U_559,bool),fun(U_559,bool)),insert(U_559),U_558),hAPP(fun(U_559,bool),fun(U_559,bool),hAPP(U_559,fun(fun(U_559,bool),fun(U_559,bool)),insert(U_559),U_557),bot_bot(fun(U_559,bool)))) = hAPP(fun(U_559,bool),fun(U_559,bool),hAPP(U_559,fun(fun(U_559,bool),fun(U_559,bool)),insert(U_559),U_556),hAPP(fun(U_559,bool),fun(U_559,bool),hAPP(U_559,fun(fun(U_559,bool),fun(U_559,bool)),insert(U_559),U_555),bot_bot(fun(U_559,bool))))
        | ( ( ti(U_559,U_557) != ti(U_559,U_556)
            | ti(U_559,U_558) != ti(U_559,U_555) )
          & ( ti(U_559,U_557) != ti(U_559,U_555)
            | ti(U_559,U_558) != ti(U_559,U_556) ) ) )
      & ( ( ti(U_559,U_557) = ti(U_559,U_556)
          & ti(U_559,U_558) = ti(U_559,U_555) )
        | ( ti(U_559,U_557) = ti(U_559,U_555)
          & ti(U_559,U_558) = ti(U_559,U_556) )
        | hAPP(fun(U_559,bool),fun(U_559,bool),hAPP(U_559,fun(fun(U_559,bool),fun(U_559,bool)),insert(U_559),U_558),hAPP(fun(U_559,bool),fun(U_559,bool),hAPP(U_559,fun(fun(U_559,bool),fun(U_559,bool)),insert(U_559),U_557),bot_bot(fun(U_559,bool)))) != hAPP(fun(U_559,bool),fun(U_559,bool),hAPP(U_559,fun(fun(U_559,bool),fun(U_559,bool)),insert(U_559),U_556),hAPP(fun(U_559,bool),fun(U_559,bool),hAPP(U_559,fun(fun(U_559,bool),fun(U_559,bool)),insert(U_559),U_555),bot_bot(fun(U_559,bool)))) ) ),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

fof(f_173_3,plain,
    ( ! [U_569,U_567,U_565,U_563,U_561] :
        ( hAPP(fun(U_569,bool),fun(U_569,bool),hAPP(U_569,fun(fun(U_569,bool),fun(U_569,bool)),insert(U_569),U_567),hAPP(fun(U_569,bool),fun(U_569,bool),hAPP(U_569,fun(fun(U_569,bool),fun(U_569,bool)),insert(U_569),U_565),bot_bot(fun(U_569,bool)))) = hAPP(fun(U_569,bool),fun(U_569,bool),hAPP(U_569,fun(fun(U_569,bool),fun(U_569,bool)),insert(U_569),U_563),hAPP(fun(U_569,bool),fun(U_569,bool),hAPP(U_569,fun(fun(U_569,bool),fun(U_569,bool)),insert(U_569),U_561),bot_bot(fun(U_569,bool))))
        | ( ( ti(U_569,U_565) != ti(U_569,U_563)
            | ti(U_569,U_567) != ti(U_569,U_561) )
          & ( ti(U_569,U_565) != ti(U_569,U_561)
            | ti(U_569,U_567) != ti(U_569,U_563) ) ) )
    & ! [U_568,U_566,U_564,U_562,U_560] :
        ( ( ti(U_568,U_564) = ti(U_568,U_562)
          & ti(U_568,U_566) = ti(U_568,U_560) )
        | ( ti(U_568,U_564) = ti(U_568,U_560)
          & ti(U_568,U_566) = ti(U_568,U_562) )
        | hAPP(fun(U_568,bool),fun(U_568,bool),hAPP(U_568,fun(fun(U_568,bool),fun(U_568,bool)),insert(U_568),U_566),hAPP(fun(U_568,bool),fun(U_568,bool),hAPP(U_568,fun(fun(U_568,bool),fun(U_568,bool)),insert(U_568),U_564),bot_bot(fun(U_568,bool)))) != hAPP(fun(U_568,bool),fun(U_568,bool),hAPP(U_568,fun(fun(U_568,bool),fun(U_568,bool)),insert(U_568),U_562),hAPP(fun(U_568,bool),fun(U_568,bool),hAPP(U_568,fun(fun(U_568,bool),fun(U_568,bool)),insert(U_568),U_560),bot_bot(fun(U_568,bool)))) ) ),
    inference(miniscope,[status(thm)],[f_173_2]) ).

fof(f_173_4,plain,
    ( ! [U_561,U_569,U_565,U_563,U_567] :
        ( ti(U_569,U_565) != ti(U_569,U_563)
        | ti(U_569,U_567) != ti(U_569,U_561)
        | ~ sP28(U_561,U_569,U_565,U_563,U_567) )
    & ! [U_561,U_569,U_565,U_563,U_567] :
        ( ti(U_569,U_565) != ti(U_569,U_561)
        | ti(U_569,U_567) != ti(U_569,U_563)
        | ~ sP28(U_561,U_569,U_565,U_563,U_567) )
    & ! [U_560,U_566,U_562,U_564,U_568] :
        ( ti(U_568,U_564) = ti(U_568,U_562)
        | ~ sP27(U_560,U_566,U_562,U_564,U_568) )
    & ! [U_560,U_566,U_562,U_564,U_568] :
        ( ti(U_568,U_566) = ti(U_568,U_560)
        | ~ sP27(U_560,U_566,U_562,U_564,U_568) )
    & ! [U_560,U_566,U_562,U_564,U_568] :
        ( ti(U_568,U_564) = ti(U_568,U_560)
        | ~ sP26(U_560,U_566,U_562,U_564,U_568) )
    & ! [U_560,U_566,U_562,U_564,U_568] :
        ( ti(U_568,U_566) = ti(U_568,U_562)
        | ~ sP26(U_560,U_566,U_562,U_564,U_568) )
    & ! [U_561,U_569,U_565,U_563,U_567] :
        ( hAPP(fun(U_569,bool),fun(U_569,bool),hAPP(U_569,fun(fun(U_569,bool),fun(U_569,bool)),insert(U_569),U_567),hAPP(fun(U_569,bool),fun(U_569,bool),hAPP(U_569,fun(fun(U_569,bool),fun(U_569,bool)),insert(U_569),U_565),bot_bot(fun(U_569,bool)))) = hAPP(fun(U_569,bool),fun(U_569,bool),hAPP(U_569,fun(fun(U_569,bool),fun(U_569,bool)),insert(U_569),U_563),hAPP(fun(U_569,bool),fun(U_569,bool),hAPP(U_569,fun(fun(U_569,bool),fun(U_569,bool)),insert(U_569),U_561),bot_bot(fun(U_569,bool))))
        | sP28(U_561,U_569,U_565,U_563,U_567) )
    & ! [U_560,U_566,U_562,U_564,U_568] :
        ( sP27(U_560,U_566,U_562,U_564,U_568)
        | sP26(U_560,U_566,U_562,U_564,U_568)
        | hAPP(fun(U_568,bool),fun(U_568,bool),hAPP(U_568,fun(fun(U_568,bool),fun(U_568,bool)),insert(U_568),U_566),hAPP(fun(U_568,bool),fun(U_568,bool),hAPP(U_568,fun(fun(U_568,bool),fun(U_568,bool)),insert(U_568),U_564),bot_bot(fun(U_568,bool)))) != hAPP(fun(U_568,bool),fun(U_568,bool),hAPP(U_568,fun(fun(U_568,bool),fun(U_568,bool)),insert(U_568),U_562),hAPP(fun(U_568,bool),fun(U_568,bool),hAPP(U_568,fun(fun(U_568,bool),fun(U_568,bool)),insert(U_568),U_560),bot_bot(fun(U_568,bool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26,sP27,sP28])],[f_173_3]) ).

cnf(f_173_5,plain,
    ( sP27(U_560,U_566,U_562,U_564,U_568)
    | sP26(U_560,U_566,U_562,U_564,U_568)
    | hAPP(fun(U_568,bool),fun(U_568,bool),hAPP(U_568,fun(fun(U_568,bool),fun(U_568,bool)),insert(U_568),U_566),hAPP(fun(U_568,bool),fun(U_568,bool),hAPP(U_568,fun(fun(U_568,bool),fun(U_568,bool)),insert(U_568),U_564),bot_bot(fun(U_568,bool)))) != hAPP(fun(U_568,bool),fun(U_568,bool),hAPP(U_568,fun(fun(U_568,bool),fun(U_568,bool)),insert(U_568),U_562),hAPP(fun(U_568,bool),fun(U_568,bool),hAPP(U_568,fun(fun(U_568,bool),fun(U_568,bool)),insert(U_568),U_560),bot_bot(fun(U_568,bool)))) ),
    inference(clausify,[status(thm)],[f_173_4]) ).

cnf(f_173_6,plain,
    ( hAPP(fun(U_569,bool),fun(U_569,bool),hAPP(U_569,fun(fun(U_569,bool),fun(U_569,bool)),insert(U_569),U_567),hAPP(fun(U_569,bool),fun(U_569,bool),hAPP(U_569,fun(fun(U_569,bool),fun(U_569,bool)),insert(U_569),U_565),bot_bot(fun(U_569,bool)))) = hAPP(fun(U_569,bool),fun(U_569,bool),hAPP(U_569,fun(fun(U_569,bool),fun(U_569,bool)),insert(U_569),U_563),hAPP(fun(U_569,bool),fun(U_569,bool),hAPP(U_569,fun(fun(U_569,bool),fun(U_569,bool)),insert(U_569),U_561),bot_bot(fun(U_569,bool))))
    | sP28(U_561,U_569,U_565,U_563,U_567) ),
    inference(clausify,[status(thm)],[f_173_4]) ).

cnf(f_173_7,plain,
    ( ti(U_568,U_566) = ti(U_568,U_562)
    | ~ sP26(U_560,U_566,U_562,U_564,U_568) ),
    inference(clausify,[status(thm)],[f_173_4]) ).

cnf(f_173_8,plain,
    ( ti(U_568,U_564) = ti(U_568,U_560)
    | ~ sP26(U_560,U_566,U_562,U_564,U_568) ),
    inference(clausify,[status(thm)],[f_173_4]) ).

cnf(f_173_9,plain,
    ( ti(U_568,U_566) = ti(U_568,U_560)
    | ~ sP27(U_560,U_566,U_562,U_564,U_568) ),
    inference(clausify,[status(thm)],[f_173_4]) ).

cnf(f_173_10,plain,
    ( ti(U_568,U_564) = ti(U_568,U_562)
    | ~ sP27(U_560,U_566,U_562,U_564,U_568) ),
    inference(clausify,[status(thm)],[f_173_4]) ).

cnf(f_173_11,plain,
    ( ti(U_569,U_565) != ti(U_569,U_561)
    | ti(U_569,U_567) != ti(U_569,U_563)
    | ~ sP28(U_561,U_569,U_565,U_563,U_567) ),
    inference(clausify,[status(thm)],[f_173_4]) ).

cnf(f_173_12,plain,
    ( ti(U_569,U_565) != ti(U_569,U_563)
    | ti(U_569,U_567) != ti(U_569,U_561)
    | ~ sP28(U_561,U_569,U_565,U_563,U_567) ),
    inference(clausify,[status(thm)],[f_173_4]) ).

fof(f_174_1,plain,
    ! [X_b,B,A_2] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))
        | ti(X_b,B) != ti(X_b,A_2) )
      & ( ti(X_b,B) = ti(X_b,A_2)
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_121_singleton__iff]) ).

fof(f_174_2,plain,
    ! [U_572,U_571,U_570] :
      ( ( hBOOL(hAPP(fun(U_572,bool),bool,hAPP(U_572,fun(fun(U_572,bool),bool),member(U_572),U_571),hAPP(fun(U_572,bool),fun(U_572,bool),hAPP(U_572,fun(fun(U_572,bool),fun(U_572,bool)),insert(U_572),U_570),bot_bot(fun(U_572,bool)))))
        | ti(U_572,U_571) != ti(U_572,U_570) )
      & ( ti(U_572,U_571) = ti(U_572,U_570)
        | ~ hBOOL(hAPP(fun(U_572,bool),bool,hAPP(U_572,fun(fun(U_572,bool),bool),member(U_572),U_571),hAPP(fun(U_572,bool),fun(U_572,bool),hAPP(U_572,fun(fun(U_572,bool),fun(U_572,bool)),insert(U_572),U_570),bot_bot(fun(U_572,bool))))) ) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

fof(f_174_3,plain,
    ( ! [U_578,U_576,U_574] :
        ( hBOOL(hAPP(fun(U_578,bool),bool,hAPP(U_578,fun(fun(U_578,bool),bool),member(U_578),U_576),hAPP(fun(U_578,bool),fun(U_578,bool),hAPP(U_578,fun(fun(U_578,bool),fun(U_578,bool)),insert(U_578),U_574),bot_bot(fun(U_578,bool)))))
        | ti(U_578,U_576) != ti(U_578,U_574) )
    & ! [U_577,U_575,U_573] :
        ( ti(U_577,U_575) = ti(U_577,U_573)
        | ~ hBOOL(hAPP(fun(U_577,bool),bool,hAPP(U_577,fun(fun(U_577,bool),bool),member(U_577),U_575),hAPP(fun(U_577,bool),fun(U_577,bool),hAPP(U_577,fun(fun(U_577,bool),fun(U_577,bool)),insert(U_577),U_573),bot_bot(fun(U_577,bool))))) ) ),
    inference(miniscope,[status(thm)],[f_174_2]) ).

fof(f_174_4,plain,
    ( ! [U_574,U_576,U_578] :
        ( hBOOL(hAPP(fun(U_578,bool),bool,hAPP(U_578,fun(fun(U_578,bool),bool),member(U_578),U_576),hAPP(fun(U_578,bool),fun(U_578,bool),hAPP(U_578,fun(fun(U_578,bool),fun(U_578,bool)),insert(U_578),U_574),bot_bot(fun(U_578,bool)))))
        | ti(U_578,U_576) != ti(U_578,U_574) )
    & ! [U_577,U_575,U_573] :
        ( ti(U_577,U_575) = ti(U_577,U_573)
        | ~ hBOOL(hAPP(fun(U_577,bool),bool,hAPP(U_577,fun(fun(U_577,bool),bool),member(U_577),U_575),hAPP(fun(U_577,bool),fun(U_577,bool),hAPP(U_577,fun(fun(U_577,bool),fun(U_577,bool)),insert(U_577),U_573),bot_bot(fun(U_577,bool))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_174_3]) ).

cnf(f_174_5,plain,
    ( ti(U_577,U_575) = ti(U_577,U_573)
    | ~ hBOOL(hAPP(fun(U_577,bool),bool,hAPP(U_577,fun(fun(U_577,bool),bool),member(U_577),U_575),hAPP(fun(U_577,bool),fun(U_577,bool),hAPP(U_577,fun(fun(U_577,bool),fun(U_577,bool)),insert(U_577),U_573),bot_bot(fun(U_577,bool))))) ),
    inference(clausify,[status(thm)],[f_174_4]) ).

cnf(f_174_6,plain,
    ( hBOOL(hAPP(fun(U_578,bool),bool,hAPP(U_578,fun(fun(U_578,bool),bool),member(U_578),U_576),hAPP(fun(U_578,bool),fun(U_578,bool),hAPP(U_578,fun(fun(U_578,bool),fun(U_578,bool)),insert(U_578),U_574),bot_bot(fun(U_578,bool)))))
    | ti(U_578,U_576) != ti(U_578,U_574) ),
    inference(clausify,[status(thm)],[f_174_4]) ).

fof(f_175_1,plain,
    ! [X_b,A_2,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3) != bot_bot(fun(X_b,bool)),
    inference(fof_nnf,[status(thm)],[fact_122_insert__not__empty]) ).

fof(f_175_2,plain,
    ! [U_581,U_580,U_579] : hAPP(fun(U_581,bool),fun(U_581,bool),hAPP(U_581,fun(fun(U_581,bool),fun(U_581,bool)),insert(U_581),U_580),U_579) != bot_bot(fun(U_581,bool)),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

fof(f_175_3,plain,
    ! [U_579,U_581,U_580] : hAPP(fun(U_581,bool),fun(U_581,bool),hAPP(U_581,fun(fun(U_581,bool),fun(U_581,bool)),insert(U_581),U_580),U_579) != bot_bot(fun(U_581,bool)),
    inference(definitional_conversion,[status(esa)],[f_175_2]) ).

cnf(f_175_4,plain,
    hAPP(fun(U_581,bool),fun(U_581,bool),hAPP(U_581,fun(fun(U_581,bool),fun(U_581,bool)),insert(U_581),U_580),U_579) != bot_bot(fun(U_581,bool)),
    inference(clausify,[status(thm)],[f_175_3]) ).

fof(f_176_1,plain,
    ! [X_b,A_2,A_3] : bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3),
    inference(fof_nnf,[status(thm)],[fact_123_empty__not__insert]) ).

fof(f_176_2,plain,
    ! [U_584,U_583,U_582] : bot_bot(fun(U_584,bool)) != hAPP(fun(U_584,bool),fun(U_584,bool),hAPP(U_584,fun(fun(U_584,bool),fun(U_584,bool)),insert(U_584),U_583),U_582),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

fof(f_176_3,plain,
    ! [U_583,U_584,U_582] : bot_bot(fun(U_584,bool)) != hAPP(fun(U_584,bool),fun(U_584,bool),hAPP(U_584,fun(fun(U_584,bool),fun(U_584,bool)),insert(U_584),U_583),U_582),
    inference(definitional_conversion,[status(esa)],[f_176_2]) ).

cnf(f_176_4,plain,
    bot_bot(fun(U_584,bool)) != hAPP(fun(U_584,bool),fun(U_584,bool),hAPP(U_584,fun(fun(U_584,bool),fun(U_584,bool)),insert(U_584),U_583),U_582),
    inference(clausify,[status(thm)],[f_176_3]) ).

fof(f_177_1,plain,
    ! [X_b,A_3] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))))
        | ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) )
      & ( ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_124_subset__empty]) ).

fof(f_177_2,plain,
    ! [U_586,U_585] :
      ( ( hBOOL(hAPP(fun(U_586,bool),bool,hAPP(fun(U_586,bool),fun(fun(U_586,bool),bool),ord_less_eq(fun(U_586,bool)),U_585),bot_bot(fun(U_586,bool))))
        | ti(fun(U_586,bool),U_585) != bot_bot(fun(U_586,bool)) )
      & ( ti(fun(U_586,bool),U_585) = bot_bot(fun(U_586,bool))
        | ~ hBOOL(hAPP(fun(U_586,bool),bool,hAPP(fun(U_586,bool),fun(fun(U_586,bool),bool),ord_less_eq(fun(U_586,bool)),U_585),bot_bot(fun(U_586,bool)))) ) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

fof(f_177_3,plain,
    ( ! [U_590,U_588] :
        ( hBOOL(hAPP(fun(U_590,bool),bool,hAPP(fun(U_590,bool),fun(fun(U_590,bool),bool),ord_less_eq(fun(U_590,bool)),U_588),bot_bot(fun(U_590,bool))))
        | ti(fun(U_590,bool),U_588) != bot_bot(fun(U_590,bool)) )
    & ! [U_589,U_587] :
        ( ti(fun(U_589,bool),U_587) = bot_bot(fun(U_589,bool))
        | ~ hBOOL(hAPP(fun(U_589,bool),bool,hAPP(fun(U_589,bool),fun(fun(U_589,bool),bool),ord_less_eq(fun(U_589,bool)),U_587),bot_bot(fun(U_589,bool)))) ) ),
    inference(miniscope,[status(thm)],[f_177_2]) ).

fof(f_177_4,plain,
    ( ! [U_588,U_590] :
        ( hBOOL(hAPP(fun(U_590,bool),bool,hAPP(fun(U_590,bool),fun(fun(U_590,bool),bool),ord_less_eq(fun(U_590,bool)),U_588),bot_bot(fun(U_590,bool))))
        | ti(fun(U_590,bool),U_588) != bot_bot(fun(U_590,bool)) )
    & ! [U_587,U_589] :
        ( ti(fun(U_589,bool),U_587) = bot_bot(fun(U_589,bool))
        | ~ hBOOL(hAPP(fun(U_589,bool),bool,hAPP(fun(U_589,bool),fun(fun(U_589,bool),bool),ord_less_eq(fun(U_589,bool)),U_587),bot_bot(fun(U_589,bool)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_177_3]) ).

cnf(f_177_5,plain,
    ( ti(fun(U_589,bool),U_587) = bot_bot(fun(U_589,bool))
    | ~ hBOOL(hAPP(fun(U_589,bool),bool,hAPP(fun(U_589,bool),fun(fun(U_589,bool),bool),ord_less_eq(fun(U_589,bool)),U_587),bot_bot(fun(U_589,bool)))) ),
    inference(clausify,[status(thm)],[f_177_4]) ).

cnf(f_177_6,plain,
    ( hBOOL(hAPP(fun(U_590,bool),bool,hAPP(fun(U_590,bool),fun(fun(U_590,bool),bool),ord_less_eq(fun(U_590,bool)),U_588),bot_bot(fun(U_590,bool))))
    | ti(fun(U_590,bool),U_588) != bot_bot(fun(U_590,bool)) ),
    inference(clausify,[status(thm)],[f_177_4]) ).

fof(f_178_1,plain,
    ! [X_c,X_b,F,A_3] :
      ( ( hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3) = bot_bot(fun(X_b,bool))
        | ti(fun(X_c,bool),A_3) != bot_bot(fun(X_c,bool)) )
      & ( ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool))
        | hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3) != bot_bot(fun(X_b,bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_125_image__is__empty]) ).

fof(f_178_2,plain,
    ! [U_594,U_593,U_592,U_591] :
      ( ( hAPP(fun(U_594,bool),fun(U_593,bool),hAPP(fun(U_594,U_593),fun(fun(U_594,bool),fun(U_593,bool)),image(U_594,U_593),U_592),U_591) = bot_bot(fun(U_593,bool))
        | ti(fun(U_594,bool),U_591) != bot_bot(fun(U_594,bool)) )
      & ( ti(fun(U_594,bool),U_591) = bot_bot(fun(U_594,bool))
        | hAPP(fun(U_594,bool),fun(U_593,bool),hAPP(fun(U_594,U_593),fun(fun(U_594,bool),fun(U_593,bool)),image(U_594,U_593),U_592),U_591) != bot_bot(fun(U_593,bool)) ) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

fof(f_178_3,plain,
    ( ! [U_602,U_600,U_598,U_596] :
        ( hAPP(fun(U_602,bool),fun(U_600,bool),hAPP(fun(U_602,U_600),fun(fun(U_602,bool),fun(U_600,bool)),image(U_602,U_600),U_598),U_596) = bot_bot(fun(U_600,bool))
        | ti(fun(U_602,bool),U_596) != bot_bot(fun(U_602,bool)) )
    & ! [U_601,U_599,U_597,U_595] :
        ( ti(fun(U_601,bool),U_595) = bot_bot(fun(U_601,bool))
        | hAPP(fun(U_601,bool),fun(U_599,bool),hAPP(fun(U_601,U_599),fun(fun(U_601,bool),fun(U_599,bool)),image(U_601,U_599),U_597),U_595) != bot_bot(fun(U_599,bool)) ) ),
    inference(miniscope,[status(thm)],[f_178_2]) ).

fof(f_178_4,plain,
    ( ! [U_598,U_596,U_600,U_602] :
        ( hAPP(fun(U_602,bool),fun(U_600,bool),hAPP(fun(U_602,U_600),fun(fun(U_602,bool),fun(U_600,bool)),image(U_602,U_600),U_598),U_596) = bot_bot(fun(U_600,bool))
        | ti(fun(U_602,bool),U_596) != bot_bot(fun(U_602,bool)) )
    & ! [U_595,U_599,U_597,U_601] :
        ( ti(fun(U_601,bool),U_595) = bot_bot(fun(U_601,bool))
        | hAPP(fun(U_601,bool),fun(U_599,bool),hAPP(fun(U_601,U_599),fun(fun(U_601,bool),fun(U_599,bool)),image(U_601,U_599),U_597),U_595) != bot_bot(fun(U_599,bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_178_3]) ).

cnf(f_178_5,plain,
    ( ti(fun(U_601,bool),U_595) = bot_bot(fun(U_601,bool))
    | hAPP(fun(U_601,bool),fun(U_599,bool),hAPP(fun(U_601,U_599),fun(fun(U_601,bool),fun(U_599,bool)),image(U_601,U_599),U_597),U_595) != bot_bot(fun(U_599,bool)) ),
    inference(clausify,[status(thm)],[f_178_4]) ).

cnf(f_178_6,plain,
    ( hAPP(fun(U_602,bool),fun(U_600,bool),hAPP(fun(U_602,U_600),fun(fun(U_602,bool),fun(U_600,bool)),image(U_602,U_600),U_598),U_596) = bot_bot(fun(U_600,bool))
    | ti(fun(U_602,bool),U_596) != bot_bot(fun(U_602,bool)) ),
    inference(clausify,[status(thm)],[f_178_4]) ).

fof(f_179_1,plain,
    ! [X_c,X_b,F] : hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),bot_bot(fun(X_c,bool))) = bot_bot(fun(X_b,bool)),
    inference(fof_nnf,[status(thm)],[fact_126_image__empty]) ).

fof(f_179_2,plain,
    ! [U_605,U_604,U_603] : hAPP(fun(U_605,bool),fun(U_604,bool),hAPP(fun(U_605,U_604),fun(fun(U_605,bool),fun(U_604,bool)),image(U_605,U_604),U_603),bot_bot(fun(U_605,bool))) = bot_bot(fun(U_604,bool)),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

fof(f_179_3,plain,
    ! [U_604,U_603,U_605] : hAPP(fun(U_605,bool),fun(U_604,bool),hAPP(fun(U_605,U_604),fun(fun(U_605,bool),fun(U_604,bool)),image(U_605,U_604),U_603),bot_bot(fun(U_605,bool))) = bot_bot(fun(U_604,bool)),
    inference(definitional_conversion,[status(esa)],[f_179_2]) ).

cnf(f_179_4,plain,
    hAPP(fun(U_605,bool),fun(U_604,bool),hAPP(fun(U_605,U_604),fun(fun(U_605,bool),fun(U_604,bool)),image(U_605,U_604),U_603),bot_bot(fun(U_605,bool))) = bot_bot(fun(U_604,bool)),
    inference(clausify,[status(thm)],[f_179_3]) ).

fof(f_180_1,plain,
    ! [X_b,X_c,F,A_3] :
      ( ( bot_bot(fun(X_b,bool)) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)
        | ti(fun(X_c,bool),A_3) != bot_bot(fun(X_c,bool)) )
      & ( ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool))
        | bot_bot(fun(X_b,bool)) != hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3) ) ),
    inference(fof_nnf,[status(thm)],[fact_127_empty__is__image]) ).

fof(f_180_2,plain,
    ! [U_609,U_608,U_607,U_606] :
      ( ( bot_bot(fun(U_609,bool)) = hAPP(fun(U_608,bool),fun(U_609,bool),hAPP(fun(U_608,U_609),fun(fun(U_608,bool),fun(U_609,bool)),image(U_608,U_609),U_607),U_606)
        | ti(fun(U_608,bool),U_606) != bot_bot(fun(U_608,bool)) )
      & ( ti(fun(U_608,bool),U_606) = bot_bot(fun(U_608,bool))
        | bot_bot(fun(U_609,bool)) != hAPP(fun(U_608,bool),fun(U_609,bool),hAPP(fun(U_608,U_609),fun(fun(U_608,bool),fun(U_609,bool)),image(U_608,U_609),U_607),U_606) ) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

fof(f_180_3,plain,
    ( ! [U_617,U_615,U_613,U_611] :
        ( bot_bot(fun(U_617,bool)) = hAPP(fun(U_615,bool),fun(U_617,bool),hAPP(fun(U_615,U_617),fun(fun(U_615,bool),fun(U_617,bool)),image(U_615,U_617),U_613),U_611)
        | ti(fun(U_615,bool),U_611) != bot_bot(fun(U_615,bool)) )
    & ! [U_616,U_614,U_612,U_610] :
        ( ti(fun(U_614,bool),U_610) = bot_bot(fun(U_614,bool))
        | bot_bot(fun(U_616,bool)) != hAPP(fun(U_614,bool),fun(U_616,bool),hAPP(fun(U_614,U_616),fun(fun(U_614,bool),fun(U_616,bool)),image(U_614,U_616),U_612),U_610) ) ),
    inference(miniscope,[status(thm)],[f_180_2]) ).

fof(f_180_4,plain,
    ( ! [U_613,U_611,U_615,U_617] :
        ( bot_bot(fun(U_617,bool)) = hAPP(fun(U_615,bool),fun(U_617,bool),hAPP(fun(U_615,U_617),fun(fun(U_615,bool),fun(U_617,bool)),image(U_615,U_617),U_613),U_611)
        | ti(fun(U_615,bool),U_611) != bot_bot(fun(U_615,bool)) )
    & ! [U_610,U_614,U_612,U_616] :
        ( ti(fun(U_614,bool),U_610) = bot_bot(fun(U_614,bool))
        | bot_bot(fun(U_616,bool)) != hAPP(fun(U_614,bool),fun(U_616,bool),hAPP(fun(U_614,U_616),fun(fun(U_614,bool),fun(U_616,bool)),image(U_614,U_616),U_612),U_610) ) ),
    inference(definitional_conversion,[status(esa)],[f_180_3]) ).

cnf(f_180_5,plain,
    ( ti(fun(U_614,bool),U_610) = bot_bot(fun(U_614,bool))
    | bot_bot(fun(U_616,bool)) != hAPP(fun(U_614,bool),fun(U_616,bool),hAPP(fun(U_614,U_616),fun(fun(U_614,bool),fun(U_616,bool)),image(U_614,U_616),U_612),U_610) ),
    inference(clausify,[status(thm)],[f_180_4]) ).

cnf(f_180_6,plain,
    ( bot_bot(fun(U_617,bool)) = hAPP(fun(U_615,bool),fun(U_617,bool),hAPP(fun(U_615,U_617),fun(fun(U_615,bool),fun(U_617,bool)),image(U_615,U_617),U_613),U_611)
    | ti(fun(U_615,bool),U_611) != bot_bot(fun(U_615,bool)) ),
    inference(clausify,[status(thm)],[f_180_4]) ).

fof(f_181_1,plain,
    ! [X_b,Pa,A_2] :
      ( ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = bot_bot(fun(X_b,bool))
        | hBOOL(hAPP(X_b,bool,Pa,A_2)) )
      & ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))
        | ~ hBOOL(hAPP(X_b,bool,Pa,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_128_Collect__conv__if]) ).

fof(f_181_2,plain,
    ! [U_620,U_619,U_618] :
      ( ( hAPP(fun(U_620,bool),fun(U_620,bool),collect(U_620),hAPP(fun(U_620,bool),fun(U_620,bool),hAPP(fun(U_620,fun(bool,bool)),fun(fun(U_620,bool),fun(U_620,bool)),combs(U_620,bool,bool),hAPP(fun(U_620,bool),fun(U_620,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_620,bool),fun(U_620,fun(bool,bool))),combb(bool,fun(bool,bool),U_620),fconj),hAPP(U_620,fun(U_620,bool),hAPP(fun(U_620,fun(U_620,bool)),fun(U_620,fun(U_620,bool)),combc(U_620,U_620,bool),fequal(U_620)),U_618))),U_619)) = bot_bot(fun(U_620,bool))
        | hBOOL(hAPP(U_620,bool,U_619,U_618)) )
      & ( hAPP(fun(U_620,bool),fun(U_620,bool),collect(U_620),hAPP(fun(U_620,bool),fun(U_620,bool),hAPP(fun(U_620,fun(bool,bool)),fun(fun(U_620,bool),fun(U_620,bool)),combs(U_620,bool,bool),hAPP(fun(U_620,bool),fun(U_620,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_620,bool),fun(U_620,fun(bool,bool))),combb(bool,fun(bool,bool),U_620),fconj),hAPP(U_620,fun(U_620,bool),hAPP(fun(U_620,fun(U_620,bool)),fun(U_620,fun(U_620,bool)),combc(U_620,U_620,bool),fequal(U_620)),U_618))),U_619)) = hAPP(fun(U_620,bool),fun(U_620,bool),hAPP(U_620,fun(fun(U_620,bool),fun(U_620,bool)),insert(U_620),U_618),bot_bot(fun(U_620,bool)))
        | ~ hBOOL(hAPP(U_620,bool,U_619,U_618)) ) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

fof(f_181_3,plain,
    ( ! [U_626,U_624,U_622] :
        ( hAPP(fun(U_626,bool),fun(U_626,bool),collect(U_626),hAPP(fun(U_626,bool),fun(U_626,bool),hAPP(fun(U_626,fun(bool,bool)),fun(fun(U_626,bool),fun(U_626,bool)),combs(U_626,bool,bool),hAPP(fun(U_626,bool),fun(U_626,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_626,bool),fun(U_626,fun(bool,bool))),combb(bool,fun(bool,bool),U_626),fconj),hAPP(U_626,fun(U_626,bool),hAPP(fun(U_626,fun(U_626,bool)),fun(U_626,fun(U_626,bool)),combc(U_626,U_626,bool),fequal(U_626)),U_622))),U_624)) = bot_bot(fun(U_626,bool))
        | hBOOL(hAPP(U_626,bool,U_624,U_622)) )
    & ! [U_625,U_623,U_621] :
        ( hAPP(fun(U_625,bool),fun(U_625,bool),collect(U_625),hAPP(fun(U_625,bool),fun(U_625,bool),hAPP(fun(U_625,fun(bool,bool)),fun(fun(U_625,bool),fun(U_625,bool)),combs(U_625,bool,bool),hAPP(fun(U_625,bool),fun(U_625,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_625,bool),fun(U_625,fun(bool,bool))),combb(bool,fun(bool,bool),U_625),fconj),hAPP(U_625,fun(U_625,bool),hAPP(fun(U_625,fun(U_625,bool)),fun(U_625,fun(U_625,bool)),combc(U_625,U_625,bool),fequal(U_625)),U_621))),U_623)) = hAPP(fun(U_625,bool),fun(U_625,bool),hAPP(U_625,fun(fun(U_625,bool),fun(U_625,bool)),insert(U_625),U_621),bot_bot(fun(U_625,bool)))
        | ~ hBOOL(hAPP(U_625,bool,U_623,U_621)) ) ),
    inference(miniscope,[status(thm)],[f_181_2]) ).

fof(f_181_4,plain,
    ( ! [U_622,U_624,U_626] :
        ( hAPP(fun(U_626,bool),fun(U_626,bool),collect(U_626),hAPP(fun(U_626,bool),fun(U_626,bool),hAPP(fun(U_626,fun(bool,bool)),fun(fun(U_626,bool),fun(U_626,bool)),combs(U_626,bool,bool),hAPP(fun(U_626,bool),fun(U_626,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_626,bool),fun(U_626,fun(bool,bool))),combb(bool,fun(bool,bool),U_626),fconj),hAPP(U_626,fun(U_626,bool),hAPP(fun(U_626,fun(U_626,bool)),fun(U_626,fun(U_626,bool)),combc(U_626,U_626,bool),fequal(U_626)),U_622))),U_624)) = bot_bot(fun(U_626,bool))
        | hBOOL(hAPP(U_626,bool,U_624,U_622)) )
    & ! [U_625,U_623,U_621] :
        ( hAPP(fun(U_625,bool),fun(U_625,bool),collect(U_625),hAPP(fun(U_625,bool),fun(U_625,bool),hAPP(fun(U_625,fun(bool,bool)),fun(fun(U_625,bool),fun(U_625,bool)),combs(U_625,bool,bool),hAPP(fun(U_625,bool),fun(U_625,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_625,bool),fun(U_625,fun(bool,bool))),combb(bool,fun(bool,bool),U_625),fconj),hAPP(U_625,fun(U_625,bool),hAPP(fun(U_625,fun(U_625,bool)),fun(U_625,fun(U_625,bool)),combc(U_625,U_625,bool),fequal(U_625)),U_621))),U_623)) = hAPP(fun(U_625,bool),fun(U_625,bool),hAPP(U_625,fun(fun(U_625,bool),fun(U_625,bool)),insert(U_625),U_621),bot_bot(fun(U_625,bool)))
        | ~ hBOOL(hAPP(U_625,bool,U_623,U_621)) ) ),
    inference(definitional_conversion,[status(esa)],[f_181_3]) ).

cnf(f_181_5,plain,
    ( hAPP(fun(U_625,bool),fun(U_625,bool),collect(U_625),hAPP(fun(U_625,bool),fun(U_625,bool),hAPP(fun(U_625,fun(bool,bool)),fun(fun(U_625,bool),fun(U_625,bool)),combs(U_625,bool,bool),hAPP(fun(U_625,bool),fun(U_625,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_625,bool),fun(U_625,fun(bool,bool))),combb(bool,fun(bool,bool),U_625),fconj),hAPP(U_625,fun(U_625,bool),hAPP(fun(U_625,fun(U_625,bool)),fun(U_625,fun(U_625,bool)),combc(U_625,U_625,bool),fequal(U_625)),U_621))),U_623)) = hAPP(fun(U_625,bool),fun(U_625,bool),hAPP(U_625,fun(fun(U_625,bool),fun(U_625,bool)),insert(U_625),U_621),bot_bot(fun(U_625,bool)))
    | ~ hBOOL(hAPP(U_625,bool,U_623,U_621)) ),
    inference(clausify,[status(thm)],[f_181_4]) ).

cnf(f_181_6,plain,
    ( hAPP(fun(U_626,bool),fun(U_626,bool),collect(U_626),hAPP(fun(U_626,bool),fun(U_626,bool),hAPP(fun(U_626,fun(bool,bool)),fun(fun(U_626,bool),fun(U_626,bool)),combs(U_626,bool,bool),hAPP(fun(U_626,bool),fun(U_626,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_626,bool),fun(U_626,fun(bool,bool))),combb(bool,fun(bool,bool),U_626),fconj),hAPP(U_626,fun(U_626,bool),hAPP(fun(U_626,fun(U_626,bool)),fun(U_626,fun(U_626,bool)),combc(U_626,U_626,bool),fequal(U_626)),U_622))),U_624)) = bot_bot(fun(U_626,bool))
    | hBOOL(hAPP(U_626,bool,U_624,U_622)) ),
    inference(clausify,[status(thm)],[f_181_4]) ).

fof(f_182_1,plain,
    ! [X_b,Pa,A_2] :
      ( ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa)) = bot_bot(fun(X_b,bool))
        | hBOOL(hAPP(X_b,bool,Pa,A_2)) )
      & ( hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))
        | ~ hBOOL(hAPP(X_b,bool,Pa,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_129_Collect__conv__if2]) ).

fof(f_182_2,plain,
    ! [U_629,U_628,U_627] :
      ( ( hAPP(fun(U_629,bool),fun(U_629,bool),collect(U_629),hAPP(fun(U_629,bool),fun(U_629,bool),hAPP(fun(U_629,fun(bool,bool)),fun(fun(U_629,bool),fun(U_629,bool)),combs(U_629,bool,bool),hAPP(fun(U_629,bool),fun(U_629,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_629,bool),fun(U_629,fun(bool,bool))),combb(bool,fun(bool,bool),U_629),fconj),hAPP(U_629,fun(U_629,bool),fequal(U_629),U_627))),U_628)) = bot_bot(fun(U_629,bool))
        | hBOOL(hAPP(U_629,bool,U_628,U_627)) )
      & ( hAPP(fun(U_629,bool),fun(U_629,bool),collect(U_629),hAPP(fun(U_629,bool),fun(U_629,bool),hAPP(fun(U_629,fun(bool,bool)),fun(fun(U_629,bool),fun(U_629,bool)),combs(U_629,bool,bool),hAPP(fun(U_629,bool),fun(U_629,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_629,bool),fun(U_629,fun(bool,bool))),combb(bool,fun(bool,bool),U_629),fconj),hAPP(U_629,fun(U_629,bool),fequal(U_629),U_627))),U_628)) = hAPP(fun(U_629,bool),fun(U_629,bool),hAPP(U_629,fun(fun(U_629,bool),fun(U_629,bool)),insert(U_629),U_627),bot_bot(fun(U_629,bool)))
        | ~ hBOOL(hAPP(U_629,bool,U_628,U_627)) ) ),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

fof(f_182_3,plain,
    ( ! [U_635,U_633,U_631] :
        ( hAPP(fun(U_635,bool),fun(U_635,bool),collect(U_635),hAPP(fun(U_635,bool),fun(U_635,bool),hAPP(fun(U_635,fun(bool,bool)),fun(fun(U_635,bool),fun(U_635,bool)),combs(U_635,bool,bool),hAPP(fun(U_635,bool),fun(U_635,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_635,bool),fun(U_635,fun(bool,bool))),combb(bool,fun(bool,bool),U_635),fconj),hAPP(U_635,fun(U_635,bool),fequal(U_635),U_631))),U_633)) = bot_bot(fun(U_635,bool))
        | hBOOL(hAPP(U_635,bool,U_633,U_631)) )
    & ! [U_634,U_632,U_630] :
        ( hAPP(fun(U_634,bool),fun(U_634,bool),collect(U_634),hAPP(fun(U_634,bool),fun(U_634,bool),hAPP(fun(U_634,fun(bool,bool)),fun(fun(U_634,bool),fun(U_634,bool)),combs(U_634,bool,bool),hAPP(fun(U_634,bool),fun(U_634,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_634,bool),fun(U_634,fun(bool,bool))),combb(bool,fun(bool,bool),U_634),fconj),hAPP(U_634,fun(U_634,bool),fequal(U_634),U_630))),U_632)) = hAPP(fun(U_634,bool),fun(U_634,bool),hAPP(U_634,fun(fun(U_634,bool),fun(U_634,bool)),insert(U_634),U_630),bot_bot(fun(U_634,bool)))
        | ~ hBOOL(hAPP(U_634,bool,U_632,U_630)) ) ),
    inference(miniscope,[status(thm)],[f_182_2]) ).

fof(f_182_4,plain,
    ( ! [U_631,U_633,U_635] :
        ( hAPP(fun(U_635,bool),fun(U_635,bool),collect(U_635),hAPP(fun(U_635,bool),fun(U_635,bool),hAPP(fun(U_635,fun(bool,bool)),fun(fun(U_635,bool),fun(U_635,bool)),combs(U_635,bool,bool),hAPP(fun(U_635,bool),fun(U_635,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_635,bool),fun(U_635,fun(bool,bool))),combb(bool,fun(bool,bool),U_635),fconj),hAPP(U_635,fun(U_635,bool),fequal(U_635),U_631))),U_633)) = bot_bot(fun(U_635,bool))
        | hBOOL(hAPP(U_635,bool,U_633,U_631)) )
    & ! [U_634,U_632,U_630] :
        ( hAPP(fun(U_634,bool),fun(U_634,bool),collect(U_634),hAPP(fun(U_634,bool),fun(U_634,bool),hAPP(fun(U_634,fun(bool,bool)),fun(fun(U_634,bool),fun(U_634,bool)),combs(U_634,bool,bool),hAPP(fun(U_634,bool),fun(U_634,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_634,bool),fun(U_634,fun(bool,bool))),combb(bool,fun(bool,bool),U_634),fconj),hAPP(U_634,fun(U_634,bool),fequal(U_634),U_630))),U_632)) = hAPP(fun(U_634,bool),fun(U_634,bool),hAPP(U_634,fun(fun(U_634,bool),fun(U_634,bool)),insert(U_634),U_630),bot_bot(fun(U_634,bool)))
        | ~ hBOOL(hAPP(U_634,bool,U_632,U_630)) ) ),
    inference(definitional_conversion,[status(esa)],[f_182_3]) ).

cnf(f_182_5,plain,
    ( hAPP(fun(U_634,bool),fun(U_634,bool),collect(U_634),hAPP(fun(U_634,bool),fun(U_634,bool),hAPP(fun(U_634,fun(bool,bool)),fun(fun(U_634,bool),fun(U_634,bool)),combs(U_634,bool,bool),hAPP(fun(U_634,bool),fun(U_634,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_634,bool),fun(U_634,fun(bool,bool))),combb(bool,fun(bool,bool),U_634),fconj),hAPP(U_634,fun(U_634,bool),fequal(U_634),U_630))),U_632)) = hAPP(fun(U_634,bool),fun(U_634,bool),hAPP(U_634,fun(fun(U_634,bool),fun(U_634,bool)),insert(U_634),U_630),bot_bot(fun(U_634,bool)))
    | ~ hBOOL(hAPP(U_634,bool,U_632,U_630)) ),
    inference(clausify,[status(thm)],[f_182_4]) ).

cnf(f_182_6,plain,
    ( hAPP(fun(U_635,bool),fun(U_635,bool),collect(U_635),hAPP(fun(U_635,bool),fun(U_635,bool),hAPP(fun(U_635,fun(bool,bool)),fun(fun(U_635,bool),fun(U_635,bool)),combs(U_635,bool,bool),hAPP(fun(U_635,bool),fun(U_635,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_635,bool),fun(U_635,fun(bool,bool))),combb(bool,fun(bool,bool),U_635),fconj),hAPP(U_635,fun(U_635,bool),fequal(U_635),U_631))),U_633)) = bot_bot(fun(U_635,bool))
    | hBOOL(hAPP(U_635,bool,U_633,U_631)) ),
    inference(clausify,[status(thm)],[f_182_4]) ).

fof(f_183_1,plain,
    ! [X_b,A_2] : hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))),
    inference(fof_nnf,[status(thm)],[fact_130_singleton__conv]) ).

fof(f_183_2,plain,
    ! [U_637,U_636] : hAPP(fun(U_637,bool),fun(U_637,bool),collect(U_637),hAPP(U_637,fun(U_637,bool),hAPP(fun(U_637,fun(U_637,bool)),fun(U_637,fun(U_637,bool)),combc(U_637,U_637,bool),fequal(U_637)),U_636)) = hAPP(fun(U_637,bool),fun(U_637,bool),hAPP(U_637,fun(fun(U_637,bool),fun(U_637,bool)),insert(U_637),U_636),bot_bot(fun(U_637,bool))),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

fof(f_183_3,plain,
    ! [U_636,U_637] : hAPP(fun(U_637,bool),fun(U_637,bool),collect(U_637),hAPP(U_637,fun(U_637,bool),hAPP(fun(U_637,fun(U_637,bool)),fun(U_637,fun(U_637,bool)),combc(U_637,U_637,bool),fequal(U_637)),U_636)) = hAPP(fun(U_637,bool),fun(U_637,bool),hAPP(U_637,fun(fun(U_637,bool),fun(U_637,bool)),insert(U_637),U_636),bot_bot(fun(U_637,bool))),
    inference(definitional_conversion,[status(esa)],[f_183_2]) ).

cnf(f_183_4,plain,
    hAPP(fun(U_637,bool),fun(U_637,bool),collect(U_637),hAPP(U_637,fun(U_637,bool),hAPP(fun(U_637,fun(U_637,bool)),fun(U_637,fun(U_637,bool)),combc(U_637,U_637,bool),fequal(U_637)),U_636)) = hAPP(fun(U_637,bool),fun(U_637,bool),hAPP(U_637,fun(fun(U_637,bool),fun(U_637,bool)),insert(U_637),U_636),bot_bot(fun(U_637,bool))),
    inference(clausify,[status(thm)],[f_183_3]) ).

fof(f_184_1,plain,
    ! [X_b,A_2] : hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))),
    inference(fof_nnf,[status(thm)],[fact_131_singleton__conv2]) ).

fof(f_184_2,plain,
    ! [U_639,U_638] : hAPP(fun(U_639,bool),fun(U_639,bool),collect(U_639),hAPP(U_639,fun(U_639,bool),fequal(U_639),U_638)) = hAPP(fun(U_639,bool),fun(U_639,bool),hAPP(U_639,fun(fun(U_639,bool),fun(U_639,bool)),insert(U_639),U_638),bot_bot(fun(U_639,bool))),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

fof(f_184_3,plain,
    ! [U_639,U_638] : hAPP(fun(U_639,bool),fun(U_639,bool),collect(U_639),hAPP(U_639,fun(U_639,bool),fequal(U_639),U_638)) = hAPP(fun(U_639,bool),fun(U_639,bool),hAPP(U_639,fun(fun(U_639,bool),fun(U_639,bool)),insert(U_639),U_638),bot_bot(fun(U_639,bool))),
    inference(definitional_conversion,[status(esa)],[f_184_2]) ).

cnf(f_184_4,plain,
    hAPP(fun(U_639,bool),fun(U_639,bool),collect(U_639),hAPP(U_639,fun(U_639,bool),fequal(U_639),U_638)) = hAPP(fun(U_639,bool),fun(U_639,bool),hAPP(U_639,fun(fun(U_639,bool),fun(U_639,bool)),insert(U_639),U_638),bot_bot(fun(U_639,bool))),
    inference(clausify,[status(thm)],[f_184_3]) ).

fof(f_185_1,plain,
    ! [X_b,A_3,X_1] :
      ( ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))
      | ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) ),
    inference(fof_nnf,[status(thm)],[fact_132_subset__singletonD]) ).

fof(f_185_2,plain,
    ! [U_642,U_641,U_640] :
      ( ti(fun(U_642,bool),U_641) = hAPP(fun(U_642,bool),fun(U_642,bool),hAPP(U_642,fun(fun(U_642,bool),fun(U_642,bool)),insert(U_642),U_640),bot_bot(fun(U_642,bool)))
      | ti(fun(U_642,bool),U_641) = bot_bot(fun(U_642,bool))
      | ~ hBOOL(hAPP(fun(U_642,bool),bool,hAPP(fun(U_642,bool),fun(fun(U_642,bool),bool),ord_less_eq(fun(U_642,bool)),U_641),hAPP(fun(U_642,bool),fun(U_642,bool),hAPP(U_642,fun(fun(U_642,bool),fun(U_642,bool)),insert(U_642),U_640),bot_bot(fun(U_642,bool))))) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

fof(f_185_3,plain,
    ! [U_641,U_640,U_642] :
      ( ti(fun(U_642,bool),U_641) = hAPP(fun(U_642,bool),fun(U_642,bool),hAPP(U_642,fun(fun(U_642,bool),fun(U_642,bool)),insert(U_642),U_640),bot_bot(fun(U_642,bool)))
      | ti(fun(U_642,bool),U_641) = bot_bot(fun(U_642,bool))
      | ~ hBOOL(hAPP(fun(U_642,bool),bool,hAPP(fun(U_642,bool),fun(fun(U_642,bool),bool),ord_less_eq(fun(U_642,bool)),U_641),hAPP(fun(U_642,bool),fun(U_642,bool),hAPP(U_642,fun(fun(U_642,bool),fun(U_642,bool)),insert(U_642),U_640),bot_bot(fun(U_642,bool))))) ),
    inference(definitional_conversion,[status(esa)],[f_185_2]) ).

cnf(f_185_4,plain,
    ( ti(fun(U_642,bool),U_641) = hAPP(fun(U_642,bool),fun(U_642,bool),hAPP(U_642,fun(fun(U_642,bool),fun(U_642,bool)),insert(U_642),U_640),bot_bot(fun(U_642,bool)))
    | ti(fun(U_642,bool),U_641) = bot_bot(fun(U_642,bool))
    | ~ hBOOL(hAPP(fun(U_642,bool),bool,hAPP(fun(U_642,bool),fun(fun(U_642,bool),bool),ord_less_eq(fun(U_642,bool)),U_641),hAPP(fun(U_642,bool),fun(U_642,bool),hAPP(U_642,fun(fun(U_642,bool),fun(U_642,bool)),insert(U_642),U_640),bot_bot(fun(U_642,bool))))) ),
    inference(clausify,[status(thm)],[f_185_3]) ).

fof(f_186_1,plain,
    ! [X_c,X_b,C_1,X_1,A_3] :
      ( hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C_1),bot_bot(fun(X_c,bool)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_133_image__constant]) ).

fof(f_186_2,plain,
    ! [U_647,U_646,U_645,U_644,U_643] :
      ( hAPP(fun(U_646,bool),fun(U_647,bool),hAPP(fun(U_646,U_647),fun(fun(U_646,bool),fun(U_647,bool)),image(U_646,U_647),hAPP(U_647,fun(U_646,U_647),combk(U_647,U_646),U_645)),U_643) = hAPP(fun(U_647,bool),fun(U_647,bool),hAPP(U_647,fun(fun(U_647,bool),fun(U_647,bool)),insert(U_647),U_645),bot_bot(fun(U_647,bool)))
      | ~ hBOOL(hAPP(fun(U_646,bool),bool,hAPP(U_646,fun(fun(U_646,bool),bool),member(U_646),U_644),U_643)) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

fof(f_186_3,plain,
    ! [U_645,U_644,U_643,U_646,U_647] :
      ( hAPP(fun(U_646,bool),fun(U_647,bool),hAPP(fun(U_646,U_647),fun(fun(U_646,bool),fun(U_647,bool)),image(U_646,U_647),hAPP(U_647,fun(U_646,U_647),combk(U_647,U_646),U_645)),U_643) = hAPP(fun(U_647,bool),fun(U_647,bool),hAPP(U_647,fun(fun(U_647,bool),fun(U_647,bool)),insert(U_647),U_645),bot_bot(fun(U_647,bool)))
      | ~ hBOOL(hAPP(fun(U_646,bool),bool,hAPP(U_646,fun(fun(U_646,bool),bool),member(U_646),U_644),U_643)) ),
    inference(definitional_conversion,[status(esa)],[f_186_2]) ).

cnf(f_186_4,plain,
    ( hAPP(fun(U_646,bool),fun(U_647,bool),hAPP(fun(U_646,U_647),fun(fun(U_646,bool),fun(U_647,bool)),image(U_646,U_647),hAPP(U_647,fun(U_646,U_647),combk(U_647,U_646),U_645)),U_643) = hAPP(fun(U_647,bool),fun(U_647,bool),hAPP(U_647,fun(fun(U_647,bool),fun(U_647,bool)),insert(U_647),U_645),bot_bot(fun(U_647,bool)))
    | ~ hBOOL(hAPP(fun(U_646,bool),bool,hAPP(U_646,fun(fun(U_646,bool),bool),member(U_646),U_644),U_643)) ),
    inference(clausify,[status(thm)],[f_186_3]) ).

fof(f_187_1,plain,
    ! [X_c,X_b,C_1,A_3] :
      ( ( hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C_1),bot_bot(fun(X_c,bool)))
        | ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) )
      & ( hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C_1)),A_3) = bot_bot(fun(X_c,bool))
        | ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_134_image__constant__conv]) ).

fof(f_187_2,plain,
    ! [U_651,U_650,U_649,U_648] :
      ( ( hAPP(fun(U_650,bool),fun(U_651,bool),hAPP(fun(U_650,U_651),fun(fun(U_650,bool),fun(U_651,bool)),image(U_650,U_651),hAPP(U_651,fun(U_650,U_651),combk(U_651,U_650),U_649)),U_648) = hAPP(fun(U_651,bool),fun(U_651,bool),hAPP(U_651,fun(fun(U_651,bool),fun(U_651,bool)),insert(U_651),U_649),bot_bot(fun(U_651,bool)))
        | ti(fun(U_650,bool),U_648) = bot_bot(fun(U_650,bool)) )
      & ( hAPP(fun(U_650,bool),fun(U_651,bool),hAPP(fun(U_650,U_651),fun(fun(U_650,bool),fun(U_651,bool)),image(U_650,U_651),hAPP(U_651,fun(U_650,U_651),combk(U_651,U_650),U_649)),U_648) = bot_bot(fun(U_651,bool))
        | ti(fun(U_650,bool),U_648) != bot_bot(fun(U_650,bool)) ) ),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

fof(f_187_3,plain,
    ( ! [U_659,U_657,U_655,U_653] :
        ( hAPP(fun(U_657,bool),fun(U_659,bool),hAPP(fun(U_657,U_659),fun(fun(U_657,bool),fun(U_659,bool)),image(U_657,U_659),hAPP(U_659,fun(U_657,U_659),combk(U_659,U_657),U_655)),U_653) = hAPP(fun(U_659,bool),fun(U_659,bool),hAPP(U_659,fun(fun(U_659,bool),fun(U_659,bool)),insert(U_659),U_655),bot_bot(fun(U_659,bool)))
        | ti(fun(U_657,bool),U_653) = bot_bot(fun(U_657,bool)) )
    & ! [U_658,U_656,U_654,U_652] :
        ( hAPP(fun(U_656,bool),fun(U_658,bool),hAPP(fun(U_656,U_658),fun(fun(U_656,bool),fun(U_658,bool)),image(U_656,U_658),hAPP(U_658,fun(U_656,U_658),combk(U_658,U_656),U_654)),U_652) = bot_bot(fun(U_658,bool))
        | ti(fun(U_656,bool),U_652) != bot_bot(fun(U_656,bool)) ) ),
    inference(miniscope,[status(thm)],[f_187_2]) ).

fof(f_187_4,plain,
    ( ! [U_653,U_655,U_657,U_659] :
        ( hAPP(fun(U_657,bool),fun(U_659,bool),hAPP(fun(U_657,U_659),fun(fun(U_657,bool),fun(U_659,bool)),image(U_657,U_659),hAPP(U_659,fun(U_657,U_659),combk(U_659,U_657),U_655)),U_653) = hAPP(fun(U_659,bool),fun(U_659,bool),hAPP(U_659,fun(fun(U_659,bool),fun(U_659,bool)),insert(U_659),U_655),bot_bot(fun(U_659,bool)))
        | ti(fun(U_657,bool),U_653) = bot_bot(fun(U_657,bool)) )
    & ! [U_654,U_652,U_656,U_658] :
        ( hAPP(fun(U_656,bool),fun(U_658,bool),hAPP(fun(U_656,U_658),fun(fun(U_656,bool),fun(U_658,bool)),image(U_656,U_658),hAPP(U_658,fun(U_656,U_658),combk(U_658,U_656),U_654)),U_652) = bot_bot(fun(U_658,bool))
        | ti(fun(U_656,bool),U_652) != bot_bot(fun(U_656,bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_187_3]) ).

cnf(f_187_5,plain,
    ( hAPP(fun(U_656,bool),fun(U_658,bool),hAPP(fun(U_656,U_658),fun(fun(U_656,bool),fun(U_658,bool)),image(U_656,U_658),hAPP(U_658,fun(U_656,U_658),combk(U_658,U_656),U_654)),U_652) = bot_bot(fun(U_658,bool))
    | ti(fun(U_656,bool),U_652) != bot_bot(fun(U_656,bool)) ),
    inference(clausify,[status(thm)],[f_187_4]) ).

cnf(f_187_6,plain,
    ( hAPP(fun(U_657,bool),fun(U_659,bool),hAPP(fun(U_657,U_659),fun(fun(U_657,bool),fun(U_659,bool)),image(U_657,U_659),hAPP(U_659,fun(U_657,U_659),combk(U_659,U_657),U_655)),U_653) = hAPP(fun(U_659,bool),fun(U_659,bool),hAPP(U_659,fun(fun(U_659,bool),fun(U_659,bool)),insert(U_659),U_655),bot_bot(fun(U_659,bool)))
    | ti(fun(U_657,bool),U_653) = bot_bot(fun(U_657,bool)) ),
    inference(clausify,[status(thm)],[f_187_4]) ).

fof(f_188_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_135_linorder__le__cases]) ).

fof(f_188_2,plain,
    ! [U_662] :
      ( ! [U_661,U_660] :
          ( hBOOL(hAPP(U_662,bool,hAPP(U_662,fun(U_662,bool),ord_less_eq(U_662),U_660),U_661))
          | hBOOL(hAPP(U_662,bool,hAPP(U_662,fun(U_662,bool),ord_less_eq(U_662),U_661),U_660)) )
      | ~ linorder(U_662) ),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

fof(f_188_3,plain,
    ! [U_660,U_661,U_662] :
      ( hBOOL(hAPP(U_662,bool,hAPP(U_662,fun(U_662,bool),ord_less_eq(U_662),U_660),U_661))
      | hBOOL(hAPP(U_662,bool,hAPP(U_662,fun(U_662,bool),ord_less_eq(U_662),U_661),U_660))
      | ~ linorder(U_662) ),
    inference(definitional_conversion,[status(esa)],[f_188_2]) ).

cnf(f_188_4,plain,
    ( hBOOL(hAPP(U_662,bool,hAPP(U_662,fun(U_662,bool),ord_less_eq(U_662),U_660),U_661))
    | hBOOL(hAPP(U_662,bool,hAPP(U_662,fun(U_662,bool),ord_less_eq(U_662),U_661),U_660))
    | ~ linorder(U_662) ),
    inference(clausify,[status(thm)],[f_188_3]) ).

fof(f_189_1,plain,
    ! [X_a] :
      ( ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_136_xt1_I6_J]) ).

fof(f_189_2,plain,
    ! [U_666] :
      ( ! [U_665,U_664,U_663] :
          ( hBOOL(hAPP(U_666,bool,hAPP(U_666,fun(U_666,bool),ord_less_eq(U_666),U_665),U_663))
          | ~ hBOOL(hAPP(U_666,bool,hAPP(U_666,fun(U_666,bool),ord_less_eq(U_666),U_665),U_664))
          | ~ hBOOL(hAPP(U_666,bool,hAPP(U_666,fun(U_666,bool),ord_less_eq(U_666),U_664),U_663)) )
      | ~ order(U_666) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

fof(f_189_3,plain,
    ! [U_665,U_666,U_663,U_664] :
      ( hBOOL(hAPP(U_666,bool,hAPP(U_666,fun(U_666,bool),ord_less_eq(U_666),U_665),U_663))
      | ~ hBOOL(hAPP(U_666,bool,hAPP(U_666,fun(U_666,bool),ord_less_eq(U_666),U_665),U_664))
      | ~ hBOOL(hAPP(U_666,bool,hAPP(U_666,fun(U_666,bool),ord_less_eq(U_666),U_664),U_663))
      | ~ order(U_666) ),
    inference(definitional_conversion,[status(esa)],[f_189_2]) ).

cnf(f_189_4,plain,
    ( hBOOL(hAPP(U_666,bool,hAPP(U_666,fun(U_666,bool),ord_less_eq(U_666),U_665),U_663))
    | ~ hBOOL(hAPP(U_666,bool,hAPP(U_666,fun(U_666,bool),ord_less_eq(U_666),U_665),U_664))
    | ~ hBOOL(hAPP(U_666,bool,hAPP(U_666,fun(U_666,bool),ord_less_eq(U_666),U_664),U_663))
    | ~ order(U_666) ),
    inference(clausify,[status(thm)],[f_189_3]) ).

fof(f_190_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( ti(X_a,X) = ti(X_a,Y)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_137_xt1_I5_J]) ).

fof(f_190_2,plain,
    ! [U_669] :
      ( ! [U_668,U_667] :
          ( ti(U_669,U_667) = ti(U_669,U_668)
          | ~ hBOOL(hAPP(U_669,bool,hAPP(U_669,fun(U_669,bool),ord_less_eq(U_669),U_667),U_668))
          | ~ hBOOL(hAPP(U_669,bool,hAPP(U_669,fun(U_669,bool),ord_less_eq(U_669),U_668),U_667)) )
      | ~ order(U_669) ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

fof(f_190_3,plain,
    ! [U_667,U_668,U_669] :
      ( ti(U_669,U_667) = ti(U_669,U_668)
      | ~ hBOOL(hAPP(U_669,bool,hAPP(U_669,fun(U_669,bool),ord_less_eq(U_669),U_667),U_668))
      | ~ hBOOL(hAPP(U_669,bool,hAPP(U_669,fun(U_669,bool),ord_less_eq(U_669),U_668),U_667))
      | ~ order(U_669) ),
    inference(definitional_conversion,[status(esa)],[f_190_2]) ).

cnf(f_190_4,plain,
    ( ti(U_669,U_667) = ti(U_669,U_668)
    | ~ hBOOL(hAPP(U_669,bool,hAPP(U_669,fun(U_669,bool),ord_less_eq(U_669),U_667),U_668))
    | ~ hBOOL(hAPP(U_669,bool,hAPP(U_669,fun(U_669,bool),ord_less_eq(U_669),U_668),U_667))
    | ~ order(U_669) ),
    inference(clausify,[status(thm)],[f_190_3]) ).

fof(f_191_1,plain,
    ! [X_a] :
      ( ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_138_order__trans]) ).

fof(f_191_2,plain,
    ! [U_673] :
      ( ! [U_672,U_671,U_670] :
          ( hBOOL(hAPP(U_673,bool,hAPP(U_673,fun(U_673,bool),ord_less_eq(U_673),U_671),U_672))
          | ~ hBOOL(hAPP(U_673,bool,hAPP(U_673,fun(U_673,bool),ord_less_eq(U_673),U_670),U_672))
          | ~ hBOOL(hAPP(U_673,bool,hAPP(U_673,fun(U_673,bool),ord_less_eq(U_673),U_671),U_670)) )
      | ~ preorder(U_673) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

fof(f_191_3,plain,
    ! [U_673,U_670,U_672,U_671] :
      ( hBOOL(hAPP(U_673,bool,hAPP(U_673,fun(U_673,bool),ord_less_eq(U_673),U_671),U_672))
      | ~ hBOOL(hAPP(U_673,bool,hAPP(U_673,fun(U_673,bool),ord_less_eq(U_673),U_670),U_672))
      | ~ hBOOL(hAPP(U_673,bool,hAPP(U_673,fun(U_673,bool),ord_less_eq(U_673),U_671),U_670))
      | ~ preorder(U_673) ),
    inference(definitional_conversion,[status(esa)],[f_191_2]) ).

cnf(f_191_4,plain,
    ( hBOOL(hAPP(U_673,bool,hAPP(U_673,fun(U_673,bool),ord_less_eq(U_673),U_671),U_672))
    | ~ hBOOL(hAPP(U_673,bool,hAPP(U_673,fun(U_673,bool),ord_less_eq(U_673),U_670),U_672))
    | ~ hBOOL(hAPP(U_673,bool,hAPP(U_673,fun(U_673,bool),ord_less_eq(U_673),U_671),U_670))
    | ~ preorder(U_673) ),
    inference(clausify,[status(thm)],[f_191_3]) ).

fof(f_192_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ti(X_a,X) = ti(X_a,Y)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_139_order__antisym]) ).

fof(f_192_2,plain,
    ! [U_676] :
      ( ! [U_675,U_674] :
          ( ti(U_676,U_675) = ti(U_676,U_674)
          | ~ hBOOL(hAPP(U_676,bool,hAPP(U_676,fun(U_676,bool),ord_less_eq(U_676),U_674),U_675))
          | ~ hBOOL(hAPP(U_676,bool,hAPP(U_676,fun(U_676,bool),ord_less_eq(U_676),U_675),U_674)) )
      | ~ order(U_676) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

fof(f_192_3,plain,
    ! [U_676,U_674,U_675] :
      ( ti(U_676,U_675) = ti(U_676,U_674)
      | ~ hBOOL(hAPP(U_676,bool,hAPP(U_676,fun(U_676,bool),ord_less_eq(U_676),U_674),U_675))
      | ~ hBOOL(hAPP(U_676,bool,hAPP(U_676,fun(U_676,bool),ord_less_eq(U_676),U_675),U_674))
      | ~ order(U_676) ),
    inference(definitional_conversion,[status(esa)],[f_192_2]) ).

cnf(f_192_4,plain,
    ( ti(U_676,U_675) = ti(U_676,U_674)
    | ~ hBOOL(hAPP(U_676,bool,hAPP(U_676,fun(U_676,bool),ord_less_eq(U_676),U_674),U_675))
    | ~ hBOOL(hAPP(U_676,bool,hAPP(U_676,fun(U_676,bool),ord_less_eq(U_676),U_675),U_674))
    | ~ order(U_676) ),
    inference(clausify,[status(thm)],[f_192_3]) ).

fof(f_193_1,plain,
    ! [X_a] :
      ( ! [C,B_1,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))
          | ti(X_a,B_1) != ti(X_a,C)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_1)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_140_xt1_I4_J]) ).

fof(f_193_2,plain,
    ! [U_680] :
      ( ! [U_679,U_678,U_677] :
          ( hBOOL(hAPP(U_680,bool,hAPP(U_680,fun(U_680,bool),ord_less_eq(U_680),U_679),U_677))
          | ti(U_680,U_678) != ti(U_680,U_679)
          | ~ hBOOL(hAPP(U_680,bool,hAPP(U_680,fun(U_680,bool),ord_less_eq(U_680),U_678),U_677)) )
      | ~ order(U_680) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

fof(f_193_3,plain,
    ! [U_680,U_678,U_677,U_679] :
      ( hBOOL(hAPP(U_680,bool,hAPP(U_680,fun(U_680,bool),ord_less_eq(U_680),U_679),U_677))
      | ti(U_680,U_678) != ti(U_680,U_679)
      | ~ hBOOL(hAPP(U_680,bool,hAPP(U_680,fun(U_680,bool),ord_less_eq(U_680),U_678),U_677))
      | ~ order(U_680) ),
    inference(definitional_conversion,[status(esa)],[f_193_2]) ).

cnf(f_193_4,plain,
    ( hBOOL(hAPP(U_680,bool,hAPP(U_680,fun(U_680,bool),ord_less_eq(U_680),U_679),U_677))
    | ti(U_680,U_678) != ti(U_680,U_679)
    | ~ hBOOL(hAPP(U_680,bool,hAPP(U_680,fun(U_680,bool),ord_less_eq(U_680),U_678),U_677))
    | ~ order(U_680) ),
    inference(clausify,[status(thm)],[f_193_3]) ).

fof(f_194_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))
          | B_1 != C
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_141_ord__le__eq__trans]) ).

fof(f_194_2,plain,
    ! [U_684] :
      ( ! [U_683,U_682,U_681] :
          ( hBOOL(hAPP(U_684,bool,hAPP(U_684,fun(U_684,bool),ord_less_eq(U_684),U_682),U_683))
          | U_681 != U_683
          | ~ hBOOL(hAPP(U_684,bool,hAPP(U_684,fun(U_684,bool),ord_less_eq(U_684),U_682),U_681)) )
      | ~ ord(U_684) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

fof(f_194_3,plain,
    ! [U_684,U_681,U_683,U_682] :
      ( hBOOL(hAPP(U_684,bool,hAPP(U_684,fun(U_684,bool),ord_less_eq(U_684),U_682),U_683))
      | U_681 != U_683
      | ~ hBOOL(hAPP(U_684,bool,hAPP(U_684,fun(U_684,bool),ord_less_eq(U_684),U_682),U_681))
      | ~ ord(U_684) ),
    inference(definitional_conversion,[status(esa)],[f_194_2]) ).

cnf(f_194_4,plain,
    ( hBOOL(hAPP(U_684,bool,hAPP(U_684,fun(U_684,bool),ord_less_eq(U_684),U_682),U_683))
    | U_681 != U_683
    | ~ hBOOL(hAPP(U_684,bool,hAPP(U_684,fun(U_684,bool),ord_less_eq(U_684),U_682),U_681))
    | ~ ord(U_684) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

fof(f_195_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B_1))
          | ti(X_a,A_1) != ti(X_a,B_1) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_142_xt1_I3_J]) ).

fof(f_195_2,plain,
    ! [U_688] :
      ( ! [U_687,U_686,U_685] :
          ( hBOOL(hAPP(U_688,bool,hAPP(U_688,fun(U_688,bool),ord_less_eq(U_688),U_687),U_686))
          | ~ hBOOL(hAPP(U_688,bool,hAPP(U_688,fun(U_688,bool),ord_less_eq(U_688),U_687),U_685))
          | ti(U_688,U_686) != ti(U_688,U_685) )
      | ~ order(U_688) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

fof(f_195_3,plain,
    ! [U_686,U_688,U_687,U_685] :
      ( hBOOL(hAPP(U_688,bool,hAPP(U_688,fun(U_688,bool),ord_less_eq(U_688),U_687),U_686))
      | ~ hBOOL(hAPP(U_688,bool,hAPP(U_688,fun(U_688,bool),ord_less_eq(U_688),U_687),U_685))
      | ti(U_688,U_686) != ti(U_688,U_685)
      | ~ order(U_688) ),
    inference(definitional_conversion,[status(esa)],[f_195_2]) ).

cnf(f_195_4,plain,
    ( hBOOL(hAPP(U_688,bool,hAPP(U_688,fun(U_688,bool),ord_less_eq(U_688),U_687),U_686))
    | ~ hBOOL(hAPP(U_688,bool,hAPP(U_688,fun(U_688,bool),ord_less_eq(U_688),U_687),U_685))
    | ti(U_688,U_686) != ti(U_688,U_685)
    | ~ order(U_688) ),
    inference(clausify,[status(thm)],[f_195_3]) ).

fof(f_196_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C))
          | A_1 != B_1 )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_143_ord__eq__le__trans]) ).

fof(f_196_2,plain,
    ! [U_692] :
      ( ! [U_691,U_690,U_689] :
          ( hBOOL(hAPP(U_692,bool,hAPP(U_692,fun(U_692,bool),ord_less_eq(U_692),U_690),U_691))
          | ~ hBOOL(hAPP(U_692,bool,hAPP(U_692,fun(U_692,bool),ord_less_eq(U_692),U_689),U_691))
          | U_690 != U_689 )
      | ~ ord(U_692) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

fof(f_196_3,plain,
    ! [U_690,U_692,U_691,U_689] :
      ( hBOOL(hAPP(U_692,bool,hAPP(U_692,fun(U_692,bool),ord_less_eq(U_692),U_690),U_691))
      | ~ hBOOL(hAPP(U_692,bool,hAPP(U_692,fun(U_692,bool),ord_less_eq(U_692),U_689),U_691))
      | U_690 != U_689
      | ~ ord(U_692) ),
    inference(definitional_conversion,[status(esa)],[f_196_2]) ).

cnf(f_196_4,plain,
    ( hBOOL(hAPP(U_692,bool,hAPP(U_692,fun(U_692,bool),ord_less_eq(U_692),U_690),U_691))
    | ~ hBOOL(hAPP(U_692,bool,hAPP(U_692,fun(U_692,bool),ord_less_eq(U_692),U_689),U_691))
    | U_690 != U_689
    | ~ ord(U_692) ),
    inference(clausify,[status(thm)],[f_196_3]) ).

fof(f_197_1,plain,
    ! [X_b] :
      ( ! [Y_1,X_1] :
          ( ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1))
              | ti(X_b,X_1) != ti(X_b,Y_1) )
            & ( ti(X_b,X_1) = ti(X_b,Y_1)
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) ) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_144_order__antisym__conv]) ).

fof(f_197_2,plain,
    ! [U_695] :
      ( ! [U_694,U_693] :
          ( ( ( hBOOL(hAPP(U_695,bool,hAPP(U_695,fun(U_695,bool),ord_less_eq(U_695),U_693),U_694))
              | ti(U_695,U_693) != ti(U_695,U_694) )
            & ( ti(U_695,U_693) = ti(U_695,U_694)
              | ~ hBOOL(hAPP(U_695,bool,hAPP(U_695,fun(U_695,bool),ord_less_eq(U_695),U_693),U_694)) ) )
          | ~ hBOOL(hAPP(U_695,bool,hAPP(U_695,fun(U_695,bool),ord_less_eq(U_695),U_694),U_693)) )
      | ~ order(U_695) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

fof(f_197_3,plain,
    ( ! [U_695,U_693,U_694] :
        ( hBOOL(hAPP(U_695,bool,hAPP(U_695,fun(U_695,bool),ord_less_eq(U_695),U_693),U_694))
        | ti(U_695,U_693) != ti(U_695,U_694)
        | ~ sP29(U_695,U_693,U_694) )
    & ! [U_695,U_693,U_694] :
        ( ti(U_695,U_693) = ti(U_695,U_694)
        | ~ hBOOL(hAPP(U_695,bool,hAPP(U_695,fun(U_695,bool),ord_less_eq(U_695),U_693),U_694))
        | ~ sP29(U_695,U_693,U_694) )
    & ! [U_695,U_693,U_694] :
        ( sP29(U_695,U_693,U_694)
        | ~ hBOOL(hAPP(U_695,bool,hAPP(U_695,fun(U_695,bool),ord_less_eq(U_695),U_694),U_693))
        | ~ order(U_695) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29])],[f_197_2]) ).

cnf(f_197_4,plain,
    ( sP29(U_695,U_693,U_694)
    | ~ hBOOL(hAPP(U_695,bool,hAPP(U_695,fun(U_695,bool),ord_less_eq(U_695),U_694),U_693))
    | ~ order(U_695) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

cnf(f_197_5,plain,
    ( ti(U_695,U_693) = ti(U_695,U_694)
    | ~ hBOOL(hAPP(U_695,bool,hAPP(U_695,fun(U_695,bool),ord_less_eq(U_695),U_693),U_694))
    | ~ sP29(U_695,U_693,U_694) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

cnf(f_197_6,plain,
    ( hBOOL(hAPP(U_695,bool,hAPP(U_695,fun(U_695,bool),ord_less_eq(U_695),U_693),U_694))
    | ti(U_695,U_693) != ti(U_695,U_694)
    | ~ sP29(U_695,U_693,U_694) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

fof(f_198_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
          | X != Y )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_145_order__eq__refl]) ).

fof(f_198_2,plain,
    ! [U_698] :
      ( ! [U_697,U_696] :
          ( hBOOL(hAPP(U_698,bool,hAPP(U_698,fun(U_698,bool),ord_less_eq(U_698),U_697),U_696))
          | U_697 != U_696 )
      | ~ preorder(U_698) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

fof(f_198_3,plain,
    ! [U_698,U_696,U_697] :
      ( hBOOL(hAPP(U_698,bool,hAPP(U_698,fun(U_698,bool),ord_less_eq(U_698),U_697),U_696))
      | U_697 != U_696
      | ~ preorder(U_698) ),
    inference(definitional_conversion,[status(esa)],[f_198_2]) ).

cnf(f_198_4,plain,
    ( hBOOL(hAPP(U_698,bool,hAPP(U_698,fun(U_698,bool),ord_less_eq(U_698),U_697),U_696))
    | U_697 != U_696
    | ~ preorder(U_698) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

fof(f_199_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_1] :
          ( ( ti(X_b,X_1) = ti(X_b,Y_1)
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) )
          & ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) )
            | ti(X_b,X_1) != ti(X_b,Y_1) ) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_146_order__eq__iff]) ).

fof(f_199_2,plain,
    ! [U_701] :
      ( ! [U_700,U_699] :
          ( ( ti(U_701,U_700) = ti(U_701,U_699)
            | ~ hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_699),U_700))
            | ~ hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_700),U_699)) )
          & ( ( hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_699),U_700))
              & hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_700),U_699)) )
            | ti(U_701,U_700) != ti(U_701,U_699) ) )
      | ~ order(U_701) ),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

fof(f_199_3,plain,
    ! [U_701] :
      ( ( ! [U_705,U_703] :
            ( ti(U_701,U_705) = ti(U_701,U_703)
            | ~ hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_703),U_705))
            | ~ hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_705),U_703)) )
        & ! [U_704,U_702] :
            ( ( hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_702),U_704))
              & hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_704),U_702)) )
            | ti(U_701,U_704) != ti(U_701,U_702) ) )
      | ~ order(U_701) ),
    inference(miniscope,[status(thm)],[f_199_2]) ).

fof(f_199_4,plain,
    ( ! [U_704,U_701,U_702] :
        ( hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_702),U_704))
        | ~ sP30(U_704,U_701,U_702) )
    & ! [U_704,U_701,U_702] :
        ( hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_704),U_702))
        | ~ sP30(U_704,U_701,U_702) )
    & ! [U_704,U_701,U_702,U_705,U_703] :
        ( ti(U_701,U_705) = ti(U_701,U_703)
        | ~ hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_703),U_705))
        | ~ hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_705),U_703))
        | ~ sP31(U_704,U_701,U_702,U_705,U_703) )
    & ! [U_704,U_701,U_702,U_705,U_703] :
        ( sP30(U_704,U_701,U_702)
        | ti(U_701,U_704) != ti(U_701,U_702)
        | ~ sP31(U_704,U_701,U_702,U_705,U_703) )
    & ! [U_704,U_701,U_702,U_705,U_703] :
        ( sP31(U_704,U_701,U_702,U_705,U_703)
        | ~ order(U_701) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30,sP31])],[f_199_3]) ).

cnf(f_199_5,plain,
    ( sP31(U_704,U_701,U_702,U_705,U_703)
    | ~ order(U_701) ),
    inference(clausify,[status(thm)],[f_199_4]) ).

cnf(f_199_6,plain,
    ( sP30(U_704,U_701,U_702)
    | ti(U_701,U_704) != ti(U_701,U_702)
    | ~ sP31(U_704,U_701,U_702,U_705,U_703) ),
    inference(clausify,[status(thm)],[f_199_4]) ).

cnf(f_199_7,plain,
    ( ti(U_701,U_705) = ti(U_701,U_703)
    | ~ hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_703),U_705))
    | ~ hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_705),U_703))
    | ~ sP31(U_704,U_701,U_702,U_705,U_703) ),
    inference(clausify,[status(thm)],[f_199_4]) ).

cnf(f_199_8,plain,
    ( hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_704),U_702))
    | ~ sP30(U_704,U_701,U_702) ),
    inference(clausify,[status(thm)],[f_199_4]) ).

cnf(f_199_9,plain,
    ( hBOOL(hAPP(U_701,bool,hAPP(U_701,fun(U_701,bool),ord_less_eq(U_701),U_702),U_704))
    | ~ sP30(U_704,U_701,U_702) ),
    inference(clausify,[status(thm)],[f_199_4]) ).

fof(f_200_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_147_linorder__linear]) ).

fof(f_200_2,plain,
    ! [U_708] :
      ( ! [U_707,U_706] :
          ( hBOOL(hAPP(U_708,bool,hAPP(U_708,fun(U_708,bool),ord_less_eq(U_708),U_706),U_707))
          | hBOOL(hAPP(U_708,bool,hAPP(U_708,fun(U_708,bool),ord_less_eq(U_708),U_707),U_706)) )
      | ~ linorder(U_708) ),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

fof(f_200_3,plain,
    ! [U_708,U_707,U_706] :
      ( hBOOL(hAPP(U_708,bool,hAPP(U_708,fun(U_708,bool),ord_less_eq(U_708),U_706),U_707))
      | hBOOL(hAPP(U_708,bool,hAPP(U_708,fun(U_708,bool),ord_less_eq(U_708),U_707),U_706))
      | ~ linorder(U_708) ),
    inference(definitional_conversion,[status(esa)],[f_200_2]) ).

cnf(f_200_4,plain,
    ( hBOOL(hAPP(U_708,bool,hAPP(U_708,fun(U_708,bool),ord_less_eq(U_708),U_706),U_707))
    | hBOOL(hAPP(U_708,bool,hAPP(U_708,fun(U_708,bool),ord_less_eq(U_708),U_707),U_706))
    | ~ linorder(U_708) ),
    inference(clausify,[status(thm)],[f_200_3]) ).

fof(f_201_1,plain,
    ! [X_b,Pa,A_3,F_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2))
      | ? [A_5,F_3] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),F_3)))
          & hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3))
          & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),F_3))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_3))
          & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_3)) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),F_2),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_148_finite__subset__induct]) ).

fof(f_201_2,plain,
    ! [U_714,U_713,U_712,U_711] :
      ( hBOOL(hAPP(fun(U_714,bool),bool,U_713,U_711))
      | ? [U_710,U_709] :
          ( ~ hBOOL(hAPP(fun(U_714,bool),bool,U_713,hAPP(fun(U_714,bool),fun(U_714,bool),hAPP(U_714,fun(fun(U_714,bool),fun(U_714,bool)),insert(U_714),U_710),U_709)))
          & hBOOL(hAPP(fun(U_714,bool),bool,U_713,U_709))
          & ~ hBOOL(hAPP(fun(U_714,bool),bool,hAPP(U_714,fun(fun(U_714,bool),bool),member(U_714),U_710),U_709))
          & hBOOL(hAPP(fun(U_714,bool),bool,hAPP(U_714,fun(fun(U_714,bool),bool),member(U_714),U_710),U_712))
          & hBOOL(hAPP(fun(U_714,bool),bool,finite_finite(U_714),U_709)) )
      | ~ hBOOL(hAPP(fun(U_714,bool),bool,U_713,bot_bot(fun(U_714,bool))))
      | ~ hBOOL(hAPP(fun(U_714,bool),bool,hAPP(fun(U_714,bool),fun(fun(U_714,bool),bool),ord_less_eq(fun(U_714,bool)),U_711),U_712))
      | ~ hBOOL(hAPP(fun(U_714,bool),bool,finite_finite(U_714),U_711)) ),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

fof(f_201_3,plain,
    ! [U_714,U_713,U_712,U_711] :
      ( hBOOL(hAPP(fun(U_714,bool),bool,U_713,U_711))
      | ? [U_709] :
          ( ~ hBOOL(hAPP(fun(U_714,bool),bool,U_713,hAPP(fun(U_714,bool),fun(U_714,bool),hAPP(U_714,fun(fun(U_714,bool),fun(U_714,bool)),insert(U_714),sK20(U_714,U_713,U_712,U_711)),U_709)))
          & hBOOL(hAPP(fun(U_714,bool),bool,U_713,U_709))
          & ~ hBOOL(hAPP(fun(U_714,bool),bool,hAPP(U_714,fun(fun(U_714,bool),bool),member(U_714),sK20(U_714,U_713,U_712,U_711)),U_709))
          & hBOOL(hAPP(fun(U_714,bool),bool,hAPP(U_714,fun(fun(U_714,bool),bool),member(U_714),sK20(U_714,U_713,U_712,U_711)),U_712))
          & hBOOL(hAPP(fun(U_714,bool),bool,finite_finite(U_714),U_709)) )
      | ~ hBOOL(hAPP(fun(U_714,bool),bool,U_713,bot_bot(fun(U_714,bool))))
      | ~ hBOOL(hAPP(fun(U_714,bool),bool,hAPP(fun(U_714,bool),fun(fun(U_714,bool),bool),ord_less_eq(fun(U_714,bool)),U_711),U_712))
      | ~ hBOOL(hAPP(fun(U_714,bool),bool,finite_finite(U_714),U_711)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_710,sK20(U_714,U_713,U_712,U_711))],[f_201_2]) ).

fof(f_201_4,plain,
    ! [U_714,U_713,U_712,U_711] :
      ( hBOOL(hAPP(fun(U_714,bool),bool,U_713,U_711))
      | ( ~ hBOOL(hAPP(fun(U_714,bool),bool,U_713,hAPP(fun(U_714,bool),fun(U_714,bool),hAPP(U_714,fun(fun(U_714,bool),fun(U_714,bool)),insert(U_714),sK20(U_714,U_713,U_712,U_711)),sK21(U_714,U_713,U_712,U_711))))
        & hBOOL(hAPP(fun(U_714,bool),bool,U_713,sK21(U_714,U_713,U_712,U_711)))
        & ~ hBOOL(hAPP(fun(U_714,bool),bool,hAPP(U_714,fun(fun(U_714,bool),bool),member(U_714),sK20(U_714,U_713,U_712,U_711)),sK21(U_714,U_713,U_712,U_711)))
        & hBOOL(hAPP(fun(U_714,bool),bool,hAPP(U_714,fun(fun(U_714,bool),bool),member(U_714),sK20(U_714,U_713,U_712,U_711)),U_712))
        & hBOOL(hAPP(fun(U_714,bool),bool,finite_finite(U_714),sK21(U_714,U_713,U_712,U_711))) )
      | ~ hBOOL(hAPP(fun(U_714,bool),bool,U_713,bot_bot(fun(U_714,bool))))
      | ~ hBOOL(hAPP(fun(U_714,bool),bool,hAPP(fun(U_714,bool),fun(fun(U_714,bool),bool),ord_less_eq(fun(U_714,bool)),U_711),U_712))
      | ~ hBOOL(hAPP(fun(U_714,bool),bool,finite_finite(U_714),U_711)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_709,sK21(U_714,U_713,U_712,U_711))],[f_201_3]) ).

fof(f_201_5,plain,
    ( ! [U_713,U_711,U_712,U_714] :
        ( ~ hBOOL(hAPP(fun(U_714,bool),bool,U_713,hAPP(fun(U_714,bool),fun(U_714,bool),hAPP(U_714,fun(fun(U_714,bool),fun(U_714,bool)),insert(U_714),sK20(U_714,U_713,U_712,U_711)),sK21(U_714,U_713,U_712,U_711))))
        | ~ sP32(U_713,U_711,U_712,U_714) )
    & ! [U_713,U_711,U_712,U_714] :
        ( hBOOL(hAPP(fun(U_714,bool),bool,U_713,sK21(U_714,U_713,U_712,U_711)))
        | ~ sP32(U_713,U_711,U_712,U_714) )
    & ! [U_713,U_711,U_712,U_714] :
        ( ~ hBOOL(hAPP(fun(U_714,bool),bool,hAPP(U_714,fun(fun(U_714,bool),bool),member(U_714),sK20(U_714,U_713,U_712,U_711)),sK21(U_714,U_713,U_712,U_711)))
        | ~ sP32(U_713,U_711,U_712,U_714) )
    & ! [U_713,U_711,U_712,U_714] :
        ( hBOOL(hAPP(fun(U_714,bool),bool,hAPP(U_714,fun(fun(U_714,bool),bool),member(U_714),sK20(U_714,U_713,U_712,U_711)),U_712))
        | ~ sP32(U_713,U_711,U_712,U_714) )
    & ! [U_713,U_711,U_712,U_714] :
        ( hBOOL(hAPP(fun(U_714,bool),bool,finite_finite(U_714),sK21(U_714,U_713,U_712,U_711)))
        | ~ sP32(U_713,U_711,U_712,U_714) )
    & ! [U_713,U_711,U_712,U_714] :
        ( hBOOL(hAPP(fun(U_714,bool),bool,U_713,U_711))
        | sP32(U_713,U_711,U_712,U_714)
        | ~ hBOOL(hAPP(fun(U_714,bool),bool,U_713,bot_bot(fun(U_714,bool))))
        | ~ hBOOL(hAPP(fun(U_714,bool),bool,hAPP(fun(U_714,bool),fun(fun(U_714,bool),bool),ord_less_eq(fun(U_714,bool)),U_711),U_712))
        | ~ hBOOL(hAPP(fun(U_714,bool),bool,finite_finite(U_714),U_711)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32])],[f_201_4]) ).

cnf(f_201_6,plain,
    ( hBOOL(hAPP(fun(U_714,bool),bool,U_713,U_711))
    | sP32(U_713,U_711,U_712,U_714)
    | ~ hBOOL(hAPP(fun(U_714,bool),bool,U_713,bot_bot(fun(U_714,bool))))
    | ~ hBOOL(hAPP(fun(U_714,bool),bool,hAPP(fun(U_714,bool),fun(fun(U_714,bool),bool),ord_less_eq(fun(U_714,bool)),U_711),U_712))
    | ~ hBOOL(hAPP(fun(U_714,bool),bool,finite_finite(U_714),U_711)) ),
    inference(clausify,[status(thm)],[f_201_5]) ).

cnf(f_201_7,plain,
    ( hBOOL(hAPP(fun(U_714,bool),bool,finite_finite(U_714),sK21(U_714,U_713,U_712,U_711)))
    | ~ sP32(U_713,U_711,U_712,U_714) ),
    inference(clausify,[status(thm)],[f_201_5]) ).

cnf(f_201_8,plain,
    ( hBOOL(hAPP(fun(U_714,bool),bool,hAPP(U_714,fun(fun(U_714,bool),bool),member(U_714),sK20(U_714,U_713,U_712,U_711)),U_712))
    | ~ sP32(U_713,U_711,U_712,U_714) ),
    inference(clausify,[status(thm)],[f_201_5]) ).

cnf(f_201_9,plain,
    ( ~ hBOOL(hAPP(fun(U_714,bool),bool,hAPP(U_714,fun(fun(U_714,bool),bool),member(U_714),sK20(U_714,U_713,U_712,U_711)),sK21(U_714,U_713,U_712,U_711)))
    | ~ sP32(U_713,U_711,U_712,U_714) ),
    inference(clausify,[status(thm)],[f_201_5]) ).

cnf(f_201_10,plain,
    ( hBOOL(hAPP(fun(U_714,bool),bool,U_713,sK21(U_714,U_713,U_712,U_711)))
    | ~ sP32(U_713,U_711,U_712,U_714) ),
    inference(clausify,[status(thm)],[f_201_5]) ).

cnf(f_201_11,plain,
    ( ~ hBOOL(hAPP(fun(U_714,bool),bool,U_713,hAPP(fun(U_714,bool),fun(U_714,bool),hAPP(U_714,fun(fun(U_714,bool),fun(U_714,bool)),insert(U_714),sK20(U_714,U_713,U_712,U_711)),sK21(U_714,U_713,U_712,U_711))))
    | ~ sP32(U_713,U_711,U_712,U_714) ),
    inference(clausify,[status(thm)],[f_201_5]) ).

fof(f_202_1,plain,
    ! [Pn,G_1] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,Pn)),bot_bot(fun(x_a,bool)))))
      | ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,Pn)),G_1)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,Pn)))),bot_bot(fun(x_a,bool))))) ),
    inference(fof_nnf,[status(thm)],[fact_149_assms_I2_J]) ).

fof(f_202_2,plain,
    ! [U_716,U_715] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_715),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,U_716)),bot_bot(fun(x_a,bool)))))
      | ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,U_716)),U_715)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,U_716)))),bot_bot(fun(x_a,bool))))) ),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

fof(f_202_3,plain,
    ! [U_716,U_715] :
      ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_715),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,U_716)),bot_bot(fun(x_a,bool)))))
      | ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,U_716)),U_715)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,U_716)))),bot_bot(fun(x_a,bool))))) ),
    inference(definitional_conversion,[status(esa)],[f_202_2]) ).

cnf(f_202_4,plain,
    ( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,U_715),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,U_716)),bot_bot(fun(x_a,bool)))))
    | ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,U_716)),U_715)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,U_716)))),bot_bot(fun(x_a,bool))))) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

fof(f_203_1,plain,
    ! [X_b,Pa,F_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2))
      | ? [X_2,F_3] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_3)))
          & hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3))
          & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3))
          & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_3)) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_150_finite__induct]) ).

fof(f_203_2,plain,
    ! [U_721,U_720,U_719] :
      ( hBOOL(hAPP(fun(U_721,bool),bool,U_720,U_719))
      | ? [U_718,U_717] :
          ( ~ hBOOL(hAPP(fun(U_721,bool),bool,U_720,hAPP(fun(U_721,bool),fun(U_721,bool),hAPP(U_721,fun(fun(U_721,bool),fun(U_721,bool)),insert(U_721),U_718),U_717)))
          & hBOOL(hAPP(fun(U_721,bool),bool,U_720,U_717))
          & ~ hBOOL(hAPP(fun(U_721,bool),bool,hAPP(U_721,fun(fun(U_721,bool),bool),member(U_721),U_718),U_717))
          & hBOOL(hAPP(fun(U_721,bool),bool,finite_finite(U_721),U_717)) )
      | ~ hBOOL(hAPP(fun(U_721,bool),bool,U_720,bot_bot(fun(U_721,bool))))
      | ~ hBOOL(hAPP(fun(U_721,bool),bool,finite_finite(U_721),U_719)) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

fof(f_203_3,plain,
    ! [U_721,U_720,U_719] :
      ( hBOOL(hAPP(fun(U_721,bool),bool,U_720,U_719))
      | ? [U_717] :
          ( ~ hBOOL(hAPP(fun(U_721,bool),bool,U_720,hAPP(fun(U_721,bool),fun(U_721,bool),hAPP(U_721,fun(fun(U_721,bool),fun(U_721,bool)),insert(U_721),sK22(U_721,U_720,U_719)),U_717)))
          & hBOOL(hAPP(fun(U_721,bool),bool,U_720,U_717))
          & ~ hBOOL(hAPP(fun(U_721,bool),bool,hAPP(U_721,fun(fun(U_721,bool),bool),member(U_721),sK22(U_721,U_720,U_719)),U_717))
          & hBOOL(hAPP(fun(U_721,bool),bool,finite_finite(U_721),U_717)) )
      | ~ hBOOL(hAPP(fun(U_721,bool),bool,U_720,bot_bot(fun(U_721,bool))))
      | ~ hBOOL(hAPP(fun(U_721,bool),bool,finite_finite(U_721),U_719)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_718,sK22(U_721,U_720,U_719))],[f_203_2]) ).

fof(f_203_4,plain,
    ! [U_721,U_720,U_719] :
      ( hBOOL(hAPP(fun(U_721,bool),bool,U_720,U_719))
      | ( ~ hBOOL(hAPP(fun(U_721,bool),bool,U_720,hAPP(fun(U_721,bool),fun(U_721,bool),hAPP(U_721,fun(fun(U_721,bool),fun(U_721,bool)),insert(U_721),sK22(U_721,U_720,U_719)),sK23(U_721,U_720,U_719))))
        & hBOOL(hAPP(fun(U_721,bool),bool,U_720,sK23(U_721,U_720,U_719)))
        & ~ hBOOL(hAPP(fun(U_721,bool),bool,hAPP(U_721,fun(fun(U_721,bool),bool),member(U_721),sK22(U_721,U_720,U_719)),sK23(U_721,U_720,U_719)))
        & hBOOL(hAPP(fun(U_721,bool),bool,finite_finite(U_721),sK23(U_721,U_720,U_719))) )
      | ~ hBOOL(hAPP(fun(U_721,bool),bool,U_720,bot_bot(fun(U_721,bool))))
      | ~ hBOOL(hAPP(fun(U_721,bool),bool,finite_finite(U_721),U_719)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_717,sK23(U_721,U_720,U_719))],[f_203_3]) ).

fof(f_203_5,plain,
    ( ! [U_720,U_721,U_719] :
        ( ~ hBOOL(hAPP(fun(U_721,bool),bool,U_720,hAPP(fun(U_721,bool),fun(U_721,bool),hAPP(U_721,fun(fun(U_721,bool),fun(U_721,bool)),insert(U_721),sK22(U_721,U_720,U_719)),sK23(U_721,U_720,U_719))))
        | ~ sP33(U_720,U_721,U_719) )
    & ! [U_720,U_721,U_719] :
        ( hBOOL(hAPP(fun(U_721,bool),bool,U_720,sK23(U_721,U_720,U_719)))
        | ~ sP33(U_720,U_721,U_719) )
    & ! [U_720,U_721,U_719] :
        ( ~ hBOOL(hAPP(fun(U_721,bool),bool,hAPP(U_721,fun(fun(U_721,bool),bool),member(U_721),sK22(U_721,U_720,U_719)),sK23(U_721,U_720,U_719)))
        | ~ sP33(U_720,U_721,U_719) )
    & ! [U_720,U_721,U_719] :
        ( hBOOL(hAPP(fun(U_721,bool),bool,finite_finite(U_721),sK23(U_721,U_720,U_719)))
        | ~ sP33(U_720,U_721,U_719) )
    & ! [U_720,U_721,U_719] :
        ( hBOOL(hAPP(fun(U_721,bool),bool,U_720,U_719))
        | sP33(U_720,U_721,U_719)
        | ~ hBOOL(hAPP(fun(U_721,bool),bool,U_720,bot_bot(fun(U_721,bool))))
        | ~ hBOOL(hAPP(fun(U_721,bool),bool,finite_finite(U_721),U_719)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33])],[f_203_4]) ).

cnf(f_203_6,plain,
    ( hBOOL(hAPP(fun(U_721,bool),bool,U_720,U_719))
    | sP33(U_720,U_721,U_719)
    | ~ hBOOL(hAPP(fun(U_721,bool),bool,U_720,bot_bot(fun(U_721,bool))))
    | ~ hBOOL(hAPP(fun(U_721,bool),bool,finite_finite(U_721),U_719)) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

cnf(f_203_7,plain,
    ( hBOOL(hAPP(fun(U_721,bool),bool,finite_finite(U_721),sK23(U_721,U_720,U_719)))
    | ~ sP33(U_720,U_721,U_719) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

cnf(f_203_8,plain,
    ( ~ hBOOL(hAPP(fun(U_721,bool),bool,hAPP(U_721,fun(fun(U_721,bool),bool),member(U_721),sK22(U_721,U_720,U_719)),sK23(U_721,U_720,U_719)))
    | ~ sP33(U_720,U_721,U_719) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

cnf(f_203_9,plain,
    ( hBOOL(hAPP(fun(U_721,bool),bool,U_720,sK23(U_721,U_720,U_719)))
    | ~ sP33(U_720,U_721,U_719) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

cnf(f_203_10,plain,
    ( ~ hBOOL(hAPP(fun(U_721,bool),bool,U_720,hAPP(fun(U_721,bool),fun(U_721,bool),hAPP(U_721,fun(fun(U_721,bool),fun(U_721,bool)),insert(U_721),sK22(U_721,U_720,U_719)),sK23(U_721,U_720,U_719))))
    | ~ sP33(U_720,U_721,U_719) ),
    inference(clausify,[status(thm)],[f_203_5]) ).

fof(f_204_1,plain,
    ! [X_b,A_2] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2))
        | ( ! [A_4,A_5] :
              ( ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_4))
              | ti(fun(X_b,bool),A_2) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),A_4) )
          & ti(fun(X_b,bool),A_2) != bot_bot(fun(X_b,bool)) ) )
      & ( ? [A_4,A_5] :
            ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_4))
            & ti(fun(X_b,bool),A_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),A_4) )
        | ti(fun(X_b,bool),A_2) = bot_bot(fun(X_b,bool))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_151_finite_Osimps]) ).

fof(f_204_2,plain,
    ! [U_727,U_726] :
      ( ( hBOOL(hAPP(fun(U_727,bool),bool,finite_finite(U_727),U_726))
        | ( ! [U_725,U_724] :
              ( ~ hBOOL(hAPP(fun(U_727,bool),bool,finite_finite(U_727),U_725))
              | ti(fun(U_727,bool),U_726) != hAPP(fun(U_727,bool),fun(U_727,bool),hAPP(U_727,fun(fun(U_727,bool),fun(U_727,bool)),insert(U_727),U_724),U_725) )
          & ti(fun(U_727,bool),U_726) != bot_bot(fun(U_727,bool)) ) )
      & ( ? [U_723,U_722] :
            ( hBOOL(hAPP(fun(U_727,bool),bool,finite_finite(U_727),U_723))
            & ti(fun(U_727,bool),U_726) = hAPP(fun(U_727,bool),fun(U_727,bool),hAPP(U_727,fun(fun(U_727,bool),fun(U_727,bool)),insert(U_727),U_722),U_723) )
        | ti(fun(U_727,bool),U_726) = bot_bot(fun(U_727,bool))
        | ~ hBOOL(hAPP(fun(U_727,bool),bool,finite_finite(U_727),U_726)) ) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

fof(f_204_3,plain,
    ( ! [U_731,U_729] :
        ( hBOOL(hAPP(fun(U_731,bool),bool,finite_finite(U_731),U_729))
        | ( ! [U_725] :
              ( ! [U_724] : ti(fun(U_731,bool),U_729) != hAPP(fun(U_731,bool),fun(U_731,bool),hAPP(U_731,fun(fun(U_731,bool),fun(U_731,bool)),insert(U_731),U_724),U_725)
              | ~ hBOOL(hAPP(fun(U_731,bool),bool,finite_finite(U_731),U_725)) )
          & ti(fun(U_731,bool),U_729) != bot_bot(fun(U_731,bool)) ) )
    & ! [U_730,U_728] :
        ( ? [U_723] :
            ( ? [U_722] : ti(fun(U_730,bool),U_728) = hAPP(fun(U_730,bool),fun(U_730,bool),hAPP(U_730,fun(fun(U_730,bool),fun(U_730,bool)),insert(U_730),U_722),U_723)
            & hBOOL(hAPP(fun(U_730,bool),bool,finite_finite(U_730),U_723)) )
        | ti(fun(U_730,bool),U_728) = bot_bot(fun(U_730,bool))
        | ~ hBOOL(hAPP(fun(U_730,bool),bool,finite_finite(U_730),U_728)) ) ),
    inference(miniscope,[status(thm)],[f_204_2]) ).

fof(f_204_4,plain,
    ( ! [U_731,U_729] :
        ( hBOOL(hAPP(fun(U_731,bool),bool,finite_finite(U_731),U_729))
        | ( ! [U_725] :
              ( ! [U_724] : ti(fun(U_731,bool),U_729) != hAPP(fun(U_731,bool),fun(U_731,bool),hAPP(U_731,fun(fun(U_731,bool),fun(U_731,bool)),insert(U_731),U_724),U_725)
              | ~ hBOOL(hAPP(fun(U_731,bool),bool,finite_finite(U_731),U_725)) )
          & ti(fun(U_731,bool),U_729) != bot_bot(fun(U_731,bool)) ) )
    & ! [U_730,U_728] :
        ( ( ? [U_722] : ti(fun(U_730,bool),U_728) = hAPP(fun(U_730,bool),fun(U_730,bool),hAPP(U_730,fun(fun(U_730,bool),fun(U_730,bool)),insert(U_730),U_722),sK24(U_730,U_728))
          & hBOOL(hAPP(fun(U_730,bool),bool,finite_finite(U_730),sK24(U_730,U_728))) )
        | ti(fun(U_730,bool),U_728) = bot_bot(fun(U_730,bool))
        | ~ hBOOL(hAPP(fun(U_730,bool),bool,finite_finite(U_730),U_728)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_723,sK24(U_730,U_728))],[f_204_3]) ).

fof(f_204_5,plain,
    ( ! [U_731,U_729] :
        ( hBOOL(hAPP(fun(U_731,bool),bool,finite_finite(U_731),U_729))
        | ( ! [U_725] :
              ( ! [U_724] : ti(fun(U_731,bool),U_729) != hAPP(fun(U_731,bool),fun(U_731,bool),hAPP(U_731,fun(fun(U_731,bool),fun(U_731,bool)),insert(U_731),U_724),U_725)
              | ~ hBOOL(hAPP(fun(U_731,bool),bool,finite_finite(U_731),U_725)) )
          & ti(fun(U_731,bool),U_729) != bot_bot(fun(U_731,bool)) ) )
    & ! [U_730,U_728] :
        ( ( ti(fun(U_730,bool),U_728) = hAPP(fun(U_730,bool),fun(U_730,bool),hAPP(U_730,fun(fun(U_730,bool),fun(U_730,bool)),insert(U_730),sK25(U_730,U_728)),sK24(U_730,U_728))
          & hBOOL(hAPP(fun(U_730,bool),bool,finite_finite(U_730),sK24(U_730,U_728))) )
        | ti(fun(U_730,bool),U_728) = bot_bot(fun(U_730,bool))
        | ~ hBOOL(hAPP(fun(U_730,bool),bool,finite_finite(U_730),U_728)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_722,sK25(U_730,U_728))],[f_204_4]) ).

fof(f_204_6,plain,
    ( ! [U_725,U_724,U_729,U_731] :
        ( ti(fun(U_731,bool),U_729) != hAPP(fun(U_731,bool),fun(U_731,bool),hAPP(U_731,fun(fun(U_731,bool),fun(U_731,bool)),insert(U_731),U_724),U_725)
        | ~ hBOOL(hAPP(fun(U_731,bool),bool,finite_finite(U_731),U_725))
        | ~ sP35(U_725,U_724,U_729,U_731) )
    & ! [U_725,U_724,U_729,U_731] :
        ( ti(fun(U_731,bool),U_729) != bot_bot(fun(U_731,bool))
        | ~ sP35(U_725,U_724,U_729,U_731) )
    & ! [U_728,U_730] :
        ( ti(fun(U_730,bool),U_728) = hAPP(fun(U_730,bool),fun(U_730,bool),hAPP(U_730,fun(fun(U_730,bool),fun(U_730,bool)),insert(U_730),sK25(U_730,U_728)),sK24(U_730,U_728))
        | ~ sP34(U_728,U_730) )
    & ! [U_728,U_730] :
        ( hBOOL(hAPP(fun(U_730,bool),bool,finite_finite(U_730),sK24(U_730,U_728)))
        | ~ sP34(U_728,U_730) )
    & ! [U_725,U_724,U_729,U_731] :
        ( hBOOL(hAPP(fun(U_731,bool),bool,finite_finite(U_731),U_729))
        | sP35(U_725,U_724,U_729,U_731) )
    & ! [U_728,U_730] :
        ( sP34(U_728,U_730)
        | ti(fun(U_730,bool),U_728) = bot_bot(fun(U_730,bool))
        | ~ hBOOL(hAPP(fun(U_730,bool),bool,finite_finite(U_730),U_728)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP34,sP35])],[f_204_5]) ).

cnf(f_204_7,plain,
    ( sP34(U_728,U_730)
    | ti(fun(U_730,bool),U_728) = bot_bot(fun(U_730,bool))
    | ~ hBOOL(hAPP(fun(U_730,bool),bool,finite_finite(U_730),U_728)) ),
    inference(clausify,[status(thm)],[f_204_6]) ).

cnf(f_204_8,plain,
    ( hBOOL(hAPP(fun(U_731,bool),bool,finite_finite(U_731),U_729))
    | sP35(U_725,U_724,U_729,U_731) ),
    inference(clausify,[status(thm)],[f_204_6]) ).

cnf(f_204_9,plain,
    ( hBOOL(hAPP(fun(U_730,bool),bool,finite_finite(U_730),sK24(U_730,U_728)))
    | ~ sP34(U_728,U_730) ),
    inference(clausify,[status(thm)],[f_204_6]) ).

cnf(f_204_10,plain,
    ( ti(fun(U_730,bool),U_728) = hAPP(fun(U_730,bool),fun(U_730,bool),hAPP(U_730,fun(fun(U_730,bool),fun(U_730,bool)),insert(U_730),sK25(U_730,U_728)),sK24(U_730,U_728))
    | ~ sP34(U_728,U_730) ),
    inference(clausify,[status(thm)],[f_204_6]) ).

cnf(f_204_11,plain,
    ( ti(fun(U_731,bool),U_729) != bot_bot(fun(U_731,bool))
    | ~ sP35(U_725,U_724,U_729,U_731) ),
    inference(clausify,[status(thm)],[f_204_6]) ).

cnf(f_204_12,plain,
    ( ti(fun(U_731,bool),U_729) != hAPP(fun(U_731,bool),fun(U_731,bool),hAPP(U_731,fun(fun(U_731,bool),fun(U_731,bool)),insert(U_731),U_724),U_725)
    | ~ hBOOL(hAPP(fun(U_731,bool),bool,finite_finite(U_731),U_725))
    | ~ sP35(U_725,U_724,U_729,U_731) ),
    inference(clausify,[status(thm)],[f_204_6]) ).

fof(f_205_1,plain,
    ! [U,F] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U))))
      | ? [N_2] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),hAPP(nat,nat,F,N_2))) ),
    inference(fof_nnf,[status(thm)],[fact_152_finite__less__ub]) ).

fof(f_205_2,plain,
    ! [U_734,U_733] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),U_733)),U_734))))
      | ? [U_732] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_732),hAPP(nat,nat,U_733,U_732))) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

fof(f_205_3,plain,
    ! [U_734,U_733] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),U_733)),U_734))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK26(U_734,U_733)),hAPP(nat,nat,U_733,sK26(U_734,U_733)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_732,sK26(U_734,U_733))],[f_205_2]) ).

fof(f_205_4,plain,
    ! [U_733,U_734] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),U_733)),U_734))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK26(U_734,U_733)),hAPP(nat,nat,U_733,sK26(U_734,U_733)))) ),
    inference(definitional_conversion,[status(esa)],[f_205_3]) ).

cnf(f_205_5,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),U_733)),U_734))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK26(U_734,U_733)),hAPP(nat,nat,U_733,sK26(U_734,U_733)))) ),
    inference(clausify,[status(thm)],[f_205_4]) ).

fof(f_206_1,plain,
    ! [X_b,X_1] : hAPP(fun(X_b,bool),X_b,the_elem(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1),
    inference(fof_nnf,[status(thm)],[fact_153_the__elem__eq]) ).

fof(f_206_2,plain,
    ! [U_736,U_735] : hAPP(fun(U_736,bool),U_736,the_elem(U_736),hAPP(fun(U_736,bool),fun(U_736,bool),hAPP(U_736,fun(fun(U_736,bool),fun(U_736,bool)),insert(U_736),U_735),bot_bot(fun(U_736,bool)))) = ti(U_736,U_735),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

fof(f_206_3,plain,
    ! [U_736,U_735] : hAPP(fun(U_736,bool),U_736,the_elem(U_736),hAPP(fun(U_736,bool),fun(U_736,bool),hAPP(U_736,fun(fun(U_736,bool),fun(U_736,bool)),insert(U_736),U_735),bot_bot(fun(U_736,bool)))) = ti(U_736,U_735),
    inference(definitional_conversion,[status(esa)],[f_206_2]) ).

cnf(f_206_4,plain,
    hAPP(fun(U_736,bool),U_736,the_elem(U_736),hAPP(fun(U_736,bool),fun(U_736,bool),hAPP(U_736,fun(fun(U_736,bool),fun(U_736,bool)),insert(U_736),U_735),bot_bot(fun(U_736,bool)))) = ti(U_736,U_735),
    inference(clausify,[status(thm)],[f_206_3]) ).

fof(f_207_1,plain,
    ! [X_b,A_3] :
      ( ( ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool))
        | ! [X_2,B_4] :
            ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_4))
            | ti(fun(X_b,bool),A_3) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B_4) ) )
      & ( ? [X_2,B_4] :
            ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_4))
            & ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B_4) )
        | ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_154_nonempty__iff]) ).

fof(f_207_2,plain,
    ! [U_742,U_741] :
      ( ( ti(fun(U_742,bool),U_741) != bot_bot(fun(U_742,bool))
        | ! [U_740,U_739] :
            ( hBOOL(hAPP(fun(U_742,bool),bool,hAPP(U_742,fun(fun(U_742,bool),bool),member(U_742),U_740),U_739))
            | ti(fun(U_742,bool),U_741) != hAPP(fun(U_742,bool),fun(U_742,bool),hAPP(U_742,fun(fun(U_742,bool),fun(U_742,bool)),insert(U_742),U_740),U_739) ) )
      & ( ? [U_738,U_737] :
            ( ~ hBOOL(hAPP(fun(U_742,bool),bool,hAPP(U_742,fun(fun(U_742,bool),bool),member(U_742),U_738),U_737))
            & ti(fun(U_742,bool),U_741) = hAPP(fun(U_742,bool),fun(U_742,bool),hAPP(U_742,fun(fun(U_742,bool),fun(U_742,bool)),insert(U_742),U_738),U_737) )
        | ti(fun(U_742,bool),U_741) = bot_bot(fun(U_742,bool)) ) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

fof(f_207_3,plain,
    ( ! [U_746,U_744] :
        ( ti(fun(U_746,bool),U_744) != bot_bot(fun(U_746,bool))
        | ! [U_740,U_739] :
            ( hBOOL(hAPP(fun(U_746,bool),bool,hAPP(U_746,fun(fun(U_746,bool),bool),member(U_746),U_740),U_739))
            | ti(fun(U_746,bool),U_744) != hAPP(fun(U_746,bool),fun(U_746,bool),hAPP(U_746,fun(fun(U_746,bool),fun(U_746,bool)),insert(U_746),U_740),U_739) ) )
    & ! [U_745,U_743] :
        ( ? [U_738,U_737] :
            ( ~ hBOOL(hAPP(fun(U_745,bool),bool,hAPP(U_745,fun(fun(U_745,bool),bool),member(U_745),U_738),U_737))
            & ti(fun(U_745,bool),U_743) = hAPP(fun(U_745,bool),fun(U_745,bool),hAPP(U_745,fun(fun(U_745,bool),fun(U_745,bool)),insert(U_745),U_738),U_737) )
        | ti(fun(U_745,bool),U_743) = bot_bot(fun(U_745,bool)) ) ),
    inference(miniscope,[status(thm)],[f_207_2]) ).

fof(f_207_4,plain,
    ( ! [U_746,U_744] :
        ( ti(fun(U_746,bool),U_744) != bot_bot(fun(U_746,bool))
        | ! [U_740,U_739] :
            ( hBOOL(hAPP(fun(U_746,bool),bool,hAPP(U_746,fun(fun(U_746,bool),bool),member(U_746),U_740),U_739))
            | ti(fun(U_746,bool),U_744) != hAPP(fun(U_746,bool),fun(U_746,bool),hAPP(U_746,fun(fun(U_746,bool),fun(U_746,bool)),insert(U_746),U_740),U_739) ) )
    & ! [U_745,U_743] :
        ( ? [U_737] :
            ( ~ hBOOL(hAPP(fun(U_745,bool),bool,hAPP(U_745,fun(fun(U_745,bool),bool),member(U_745),sK27(U_745,U_743)),U_737))
            & ti(fun(U_745,bool),U_743) = hAPP(fun(U_745,bool),fun(U_745,bool),hAPP(U_745,fun(fun(U_745,bool),fun(U_745,bool)),insert(U_745),sK27(U_745,U_743)),U_737) )
        | ti(fun(U_745,bool),U_743) = bot_bot(fun(U_745,bool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_738,sK27(U_745,U_743))],[f_207_3]) ).

fof(f_207_5,plain,
    ( ! [U_746,U_744] :
        ( ti(fun(U_746,bool),U_744) != bot_bot(fun(U_746,bool))
        | ! [U_740,U_739] :
            ( hBOOL(hAPP(fun(U_746,bool),bool,hAPP(U_746,fun(fun(U_746,bool),bool),member(U_746),U_740),U_739))
            | ti(fun(U_746,bool),U_744) != hAPP(fun(U_746,bool),fun(U_746,bool),hAPP(U_746,fun(fun(U_746,bool),fun(U_746,bool)),insert(U_746),U_740),U_739) ) )
    & ! [U_745,U_743] :
        ( ( ~ hBOOL(hAPP(fun(U_745,bool),bool,hAPP(U_745,fun(fun(U_745,bool),bool),member(U_745),sK27(U_745,U_743)),sK28(U_745,U_743)))
          & ti(fun(U_745,bool),U_743) = hAPP(fun(U_745,bool),fun(U_745,bool),hAPP(U_745,fun(fun(U_745,bool),fun(U_745,bool)),insert(U_745),sK27(U_745,U_743)),sK28(U_745,U_743)) )
        | ti(fun(U_745,bool),U_743) = bot_bot(fun(U_745,bool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_737,sK28(U_745,U_743))],[f_207_4]) ).

fof(f_207_6,plain,
    ( ! [U_743,U_745] :
        ( ~ hBOOL(hAPP(fun(U_745,bool),bool,hAPP(U_745,fun(fun(U_745,bool),bool),member(U_745),sK27(U_745,U_743)),sK28(U_745,U_743)))
        | ~ sP36(U_743,U_745) )
    & ! [U_743,U_745] :
        ( ti(fun(U_745,bool),U_743) = hAPP(fun(U_745,bool),fun(U_745,bool),hAPP(U_745,fun(fun(U_745,bool),fun(U_745,bool)),insert(U_745),sK27(U_745,U_743)),sK28(U_745,U_743))
        | ~ sP36(U_743,U_745) )
    & ! [U_739,U_740,U_744,U_746] :
        ( ti(fun(U_746,bool),U_744) != bot_bot(fun(U_746,bool))
        | hBOOL(hAPP(fun(U_746,bool),bool,hAPP(U_746,fun(fun(U_746,bool),bool),member(U_746),U_740),U_739))
        | ti(fun(U_746,bool),U_744) != hAPP(fun(U_746,bool),fun(U_746,bool),hAPP(U_746,fun(fun(U_746,bool),fun(U_746,bool)),insert(U_746),U_740),U_739) )
    & ! [U_743,U_745] :
        ( sP36(U_743,U_745)
        | ti(fun(U_745,bool),U_743) = bot_bot(fun(U_745,bool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36])],[f_207_5]) ).

cnf(f_207_7,plain,
    ( sP36(U_743,U_745)
    | ti(fun(U_745,bool),U_743) = bot_bot(fun(U_745,bool)) ),
    inference(clausify,[status(thm)],[f_207_6]) ).

cnf(f_207_8,plain,
    ( ti(fun(U_746,bool),U_744) != bot_bot(fun(U_746,bool))
    | hBOOL(hAPP(fun(U_746,bool),bool,hAPP(U_746,fun(fun(U_746,bool),bool),member(U_746),U_740),U_739))
    | ti(fun(U_746,bool),U_744) != hAPP(fun(U_746,bool),fun(U_746,bool),hAPP(U_746,fun(fun(U_746,bool),fun(U_746,bool)),insert(U_746),U_740),U_739) ),
    inference(clausify,[status(thm)],[f_207_6]) ).

cnf(f_207_9,plain,
    ( ti(fun(U_745,bool),U_743) = hAPP(fun(U_745,bool),fun(U_745,bool),hAPP(U_745,fun(fun(U_745,bool),fun(U_745,bool)),insert(U_745),sK27(U_745,U_743)),sK28(U_745,U_743))
    | ~ sP36(U_743,U_745) ),
    inference(clausify,[status(thm)],[f_207_6]) ).

cnf(f_207_10,plain,
    ( ~ hBOOL(hAPP(fun(U_745,bool),bool,hAPP(U_745,fun(fun(U_745,bool),bool),member(U_745),sK27(U_745,U_743)),sK28(U_745,U_743)))
    | ~ sP36(U_743,U_745) ),
    inference(clausify,[status(thm)],[f_207_6]) ).

fof(f_208_1,plain,
    ! [X_b,X_c] :
      ( ! [F,G] :
          ( hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G))
          | ? [X_2] : ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))) )
      | ~ ord(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_155_le__funI]) ).

fof(f_208_2,plain,
    ! [U_751,U_750] :
      ( ! [U_749,U_748] :
          ( hBOOL(hAPP(fun(U_751,U_750),bool,hAPP(fun(U_751,U_750),fun(fun(U_751,U_750),bool),ord_less_eq(fun(U_751,U_750)),U_749),U_748))
          | ? [U_747] : ~ hBOOL(hAPP(U_750,bool,hAPP(U_750,fun(U_750,bool),ord_less_eq(U_750),hAPP(U_751,U_750,U_749,U_747)),hAPP(U_751,U_750,U_748,U_747))) )
      | ~ ord(U_750) ),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

fof(f_208_3,plain,
    ! [U_751,U_750] :
      ( ! [U_749,U_748] :
          ( hBOOL(hAPP(fun(U_751,U_750),bool,hAPP(fun(U_751,U_750),fun(fun(U_751,U_750),bool),ord_less_eq(fun(U_751,U_750)),U_749),U_748))
          | ~ hBOOL(hAPP(U_750,bool,hAPP(U_750,fun(U_750,bool),ord_less_eq(U_750),hAPP(U_751,U_750,U_749,sK29(U_751,U_750,U_749,U_748))),hAPP(U_751,U_750,U_748,sK29(U_751,U_750,U_749,U_748)))) )
      | ~ ord(U_750) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_747,sK29(U_751,U_750,U_749,U_748))],[f_208_2]) ).

fof(f_208_4,plain,
    ! [U_748,U_750,U_749,U_751] :
      ( hBOOL(hAPP(fun(U_751,U_750),bool,hAPP(fun(U_751,U_750),fun(fun(U_751,U_750),bool),ord_less_eq(fun(U_751,U_750)),U_749),U_748))
      | ~ hBOOL(hAPP(U_750,bool,hAPP(U_750,fun(U_750,bool),ord_less_eq(U_750),hAPP(U_751,U_750,U_749,sK29(U_751,U_750,U_749,U_748))),hAPP(U_751,U_750,U_748,sK29(U_751,U_750,U_749,U_748))))
      | ~ ord(U_750) ),
    inference(definitional_conversion,[status(esa)],[f_208_3]) ).

cnf(f_208_5,plain,
    ( hBOOL(hAPP(fun(U_751,U_750),bool,hAPP(fun(U_751,U_750),fun(fun(U_751,U_750),bool),ord_less_eq(fun(U_751,U_750)),U_749),U_748))
    | ~ hBOOL(hAPP(U_750,bool,hAPP(U_750,fun(U_750,bool),ord_less_eq(U_750),hAPP(U_751,U_750,U_749,sK29(U_751,U_750,U_749,U_748))),hAPP(U_751,U_750,U_748,sK29(U_751,U_750,U_749,U_748))))
    | ~ ord(U_750) ),
    inference(clausify,[status(thm)],[f_208_4]) ).

fof(f_209_1,plain,
    ! [Pn] :
      ( hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,Pn))))
      | ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn),u)) ),
    inference(fof_nnf,[status(thm)],[fact_156_assms_I4_J]) ).

fof(f_209_2,plain,
    ! [U_752] :
      ( hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,U_752))))
      | ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),U_752),u)) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

fof(f_209_3,plain,
    ! [U_752] :
      ( hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,U_752))))
      | ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),U_752),u)) ),
    inference(definitional_conversion,[status(esa)],[f_209_2]) ).

cnf(f_209_4,plain,
    ( hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,U_752))))
    | ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),U_752),u)) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

fof(f_210_1,plain,
    ! [X_b] :
      ( ! [A_2,B,C_1,D_1] :
          ( ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B))
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),D_1)) )
            & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),D_1))
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B)) ) )
          | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1) )
      | ~ ordered_ab_group_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_157_diff__eq__diff__less__eq]) ).

fof(f_210_2,plain,
    ! [U_757] :
      ( ! [U_756,U_755,U_754,U_753] :
          ( ( ( hBOOL(hAPP(U_757,bool,hAPP(U_757,fun(U_757,bool),ord_less_eq(U_757),U_756),U_755))
              | ~ hBOOL(hAPP(U_757,bool,hAPP(U_757,fun(U_757,bool),ord_less_eq(U_757),U_754),U_753)) )
            & ( hBOOL(hAPP(U_757,bool,hAPP(U_757,fun(U_757,bool),ord_less_eq(U_757),U_754),U_753))
              | ~ hBOOL(hAPP(U_757,bool,hAPP(U_757,fun(U_757,bool),ord_less_eq(U_757),U_756),U_755)) ) )
          | hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),minus_minus(U_757),U_756),U_755) != hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),minus_minus(U_757),U_754),U_753) )
      | ~ ordered_ab_group_add(U_757) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

fof(f_210_3,plain,
    ( ! [U_755,U_754,U_757,U_753,U_756] :
        ( hBOOL(hAPP(U_757,bool,hAPP(U_757,fun(U_757,bool),ord_less_eq(U_757),U_756),U_755))
        | ~ hBOOL(hAPP(U_757,bool,hAPP(U_757,fun(U_757,bool),ord_less_eq(U_757),U_754),U_753))
        | ~ sP37(U_755,U_754,U_757,U_753,U_756) )
    & ! [U_755,U_754,U_757,U_753,U_756] :
        ( hBOOL(hAPP(U_757,bool,hAPP(U_757,fun(U_757,bool),ord_less_eq(U_757),U_754),U_753))
        | ~ hBOOL(hAPP(U_757,bool,hAPP(U_757,fun(U_757,bool),ord_less_eq(U_757),U_756),U_755))
        | ~ sP37(U_755,U_754,U_757,U_753,U_756) )
    & ! [U_755,U_754,U_757,U_753,U_756] :
        ( sP37(U_755,U_754,U_757,U_753,U_756)
        | hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),minus_minus(U_757),U_756),U_755) != hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),minus_minus(U_757),U_754),U_753)
        | ~ ordered_ab_group_add(U_757) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP37])],[f_210_2]) ).

cnf(f_210_4,plain,
    ( sP37(U_755,U_754,U_757,U_753,U_756)
    | hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),minus_minus(U_757),U_756),U_755) != hAPP(U_757,U_757,hAPP(U_757,fun(U_757,U_757),minus_minus(U_757),U_754),U_753)
    | ~ ordered_ab_group_add(U_757) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

cnf(f_210_5,plain,
    ( hBOOL(hAPP(U_757,bool,hAPP(U_757,fun(U_757,bool),ord_less_eq(U_757),U_754),U_753))
    | ~ hBOOL(hAPP(U_757,bool,hAPP(U_757,fun(U_757,bool),ord_less_eq(U_757),U_756),U_755))
    | ~ sP37(U_755,U_754,U_757,U_753,U_756) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

cnf(f_210_6,plain,
    ( hBOOL(hAPP(U_757,bool,hAPP(U_757,fun(U_757,bool),ord_less_eq(U_757),U_756),U_755))
    | ~ hBOOL(hAPP(U_757,bool,hAPP(U_757,fun(U_757,bool),ord_less_eq(U_757),U_754),U_753))
    | ~ sP37(U_755,U_754,U_757,U_753,U_756) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

fof(f_211_1,plain,
    ! [X_b,B_2,A_3,F,F_2] :
      ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_2,B_2)),hAPP(fun(X_b,bool),X_b,F_2,A_3)) = hAPP(fun(X_b,bool),X_b,F_2,A_3)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))
      | ti(fun(X_b,bool),B_2) = bot_bot(fun(X_b,bool))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_158_folding__one__idem_Osubset__idem]) ).

fof(f_211_2,plain,
    ! [U_762,U_761,U_760,U_759,U_758] :
      ( hAPP(U_762,U_762,hAPP(U_762,fun(U_762,U_762),U_759,hAPP(fun(U_762,bool),U_762,U_758,U_761)),hAPP(fun(U_762,bool),U_762,U_758,U_760)) = hAPP(fun(U_762,bool),U_762,U_758,U_760)
      | ~ hBOOL(hAPP(fun(U_762,bool),bool,hAPP(fun(U_762,bool),fun(fun(U_762,bool),bool),ord_less_eq(fun(U_762,bool)),U_761),U_760))
      | ti(fun(U_762,bool),U_761) = bot_bot(fun(U_762,bool))
      | ~ hBOOL(hAPP(fun(U_762,bool),bool,finite_finite(U_762),U_760))
      | ~ hBOOL(hAPP(fun(fun(U_762,bool),U_762),bool,hAPP(fun(U_762,fun(U_762,U_762)),fun(fun(fun(U_762,bool),U_762),bool),finite2073411215e_idem(U_762),U_759),U_758)) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

fof(f_211_3,plain,
    ! [U_760,U_762,U_758,U_761,U_759] :
      ( hAPP(U_762,U_762,hAPP(U_762,fun(U_762,U_762),U_759,hAPP(fun(U_762,bool),U_762,U_758,U_761)),hAPP(fun(U_762,bool),U_762,U_758,U_760)) = hAPP(fun(U_762,bool),U_762,U_758,U_760)
      | ~ hBOOL(hAPP(fun(U_762,bool),bool,hAPP(fun(U_762,bool),fun(fun(U_762,bool),bool),ord_less_eq(fun(U_762,bool)),U_761),U_760))
      | ti(fun(U_762,bool),U_761) = bot_bot(fun(U_762,bool))
      | ~ hBOOL(hAPP(fun(U_762,bool),bool,finite_finite(U_762),U_760))
      | ~ hBOOL(hAPP(fun(fun(U_762,bool),U_762),bool,hAPP(fun(U_762,fun(U_762,U_762)),fun(fun(fun(U_762,bool),U_762),bool),finite2073411215e_idem(U_762),U_759),U_758)) ),
    inference(definitional_conversion,[status(esa)],[f_211_2]) ).

cnf(f_211_4,plain,
    ( hAPP(U_762,U_762,hAPP(U_762,fun(U_762,U_762),U_759,hAPP(fun(U_762,bool),U_762,U_758,U_761)),hAPP(fun(U_762,bool),U_762,U_758,U_760)) = hAPP(fun(U_762,bool),U_762,U_758,U_760)
    | ~ hBOOL(hAPP(fun(U_762,bool),bool,hAPP(fun(U_762,bool),fun(fun(U_762,bool),bool),ord_less_eq(fun(U_762,bool)),U_761),U_760))
    | ti(fun(U_762,bool),U_761) = bot_bot(fun(U_762,bool))
    | ~ hBOOL(hAPP(fun(U_762,bool),bool,finite_finite(U_762),U_760))
    | ~ hBOOL(hAPP(fun(fun(U_762,bool),U_762),bool,hAPP(fun(U_762,fun(U_762,U_762)),fun(fun(fun(U_762,bool),U_762),bool),finite2073411215e_idem(U_762),U_759),U_758)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

fof(f_212_1,plain,
    ! [X_b,X_1,A_3,F,F_2] :
      ( hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3))
      | ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_159_folding__one__idem_Oinsert__idem]) ).

fof(f_212_2,plain,
    ! [U_767,U_766,U_765,U_764,U_763] :
      ( hAPP(fun(U_767,bool),U_767,U_763,hAPP(fun(U_767,bool),fun(U_767,bool),hAPP(U_767,fun(fun(U_767,bool),fun(U_767,bool)),insert(U_767),U_766),U_765)) = hAPP(U_767,U_767,hAPP(U_767,fun(U_767,U_767),U_764,U_766),hAPP(fun(U_767,bool),U_767,U_763,U_765))
      | ti(fun(U_767,bool),U_765) = bot_bot(fun(U_767,bool))
      | ~ hBOOL(hAPP(fun(U_767,bool),bool,finite_finite(U_767),U_765))
      | ~ hBOOL(hAPP(fun(fun(U_767,bool),U_767),bool,hAPP(fun(U_767,fun(U_767,U_767)),fun(fun(fun(U_767,bool),U_767),bool),finite2073411215e_idem(U_767),U_764),U_763)) ),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

fof(f_212_3,plain,
    ! [U_763,U_767,U_766,U_765,U_764] :
      ( hAPP(fun(U_767,bool),U_767,U_763,hAPP(fun(U_767,bool),fun(U_767,bool),hAPP(U_767,fun(fun(U_767,bool),fun(U_767,bool)),insert(U_767),U_766),U_765)) = hAPP(U_767,U_767,hAPP(U_767,fun(U_767,U_767),U_764,U_766),hAPP(fun(U_767,bool),U_767,U_763,U_765))
      | ti(fun(U_767,bool),U_765) = bot_bot(fun(U_767,bool))
      | ~ hBOOL(hAPP(fun(U_767,bool),bool,finite_finite(U_767),U_765))
      | ~ hBOOL(hAPP(fun(fun(U_767,bool),U_767),bool,hAPP(fun(U_767,fun(U_767,U_767)),fun(fun(fun(U_767,bool),U_767),bool),finite2073411215e_idem(U_767),U_764),U_763)) ),
    inference(definitional_conversion,[status(esa)],[f_212_2]) ).

cnf(f_212_4,plain,
    ( hAPP(fun(U_767,bool),U_767,U_763,hAPP(fun(U_767,bool),fun(U_767,bool),hAPP(U_767,fun(fun(U_767,bool),fun(U_767,bool)),insert(U_767),U_766),U_765)) = hAPP(U_767,U_767,hAPP(U_767,fun(U_767,U_767),U_764,U_766),hAPP(fun(U_767,bool),U_767,U_763,U_765))
    | ti(fun(U_767,bool),U_765) = bot_bot(fun(U_767,bool))
    | ~ hBOOL(hAPP(fun(U_767,bool),bool,finite_finite(U_767),U_765))
    | ~ hBOOL(hAPP(fun(fun(U_767,bool),U_767),bool,hAPP(fun(U_767,fun(U_767,U_767)),fun(fun(fun(U_767,bool),U_767),bool),finite2073411215e_idem(U_767),U_764),U_763)) ),
    inference(clausify,[status(thm)],[f_212_3]) ).

fof(f_213_1,plain,
    ! [X_b,Pa,F_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2))
      | ? [X_2,F_3] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_3)))
          & hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3))
          & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3))
          & ti(fun(X_b,bool),F_3) != bot_bot(fun(X_b,bool))
          & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_3)) )
      | ? [X_2] : ~ hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))
      | ti(fun(X_b,bool),F_2) = bot_bot(fun(X_b,bool))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_160_finite__ne__induct]) ).

fof(f_213_2,plain,
    ! [U_773,U_772,U_771] :
      ( hBOOL(hAPP(fun(U_773,bool),bool,U_772,U_771))
      | ? [U_770,U_769] :
          ( ~ hBOOL(hAPP(fun(U_773,bool),bool,U_772,hAPP(fun(U_773,bool),fun(U_773,bool),hAPP(U_773,fun(fun(U_773,bool),fun(U_773,bool)),insert(U_773),U_770),U_769)))
          & hBOOL(hAPP(fun(U_773,bool),bool,U_772,U_769))
          & ~ hBOOL(hAPP(fun(U_773,bool),bool,hAPP(U_773,fun(fun(U_773,bool),bool),member(U_773),U_770),U_769))
          & ti(fun(U_773,bool),U_769) != bot_bot(fun(U_773,bool))
          & hBOOL(hAPP(fun(U_773,bool),bool,finite_finite(U_773),U_769)) )
      | ? [U_768] : ~ hBOOL(hAPP(fun(U_773,bool),bool,U_772,hAPP(fun(U_773,bool),fun(U_773,bool),hAPP(U_773,fun(fun(U_773,bool),fun(U_773,bool)),insert(U_773),U_768),bot_bot(fun(U_773,bool)))))
      | ti(fun(U_773,bool),U_771) = bot_bot(fun(U_773,bool))
      | ~ hBOOL(hAPP(fun(U_773,bool),bool,finite_finite(U_773),U_771)) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

fof(f_213_3,plain,
    ! [U_773,U_772,U_771] :
      ( hBOOL(hAPP(fun(U_773,bool),bool,U_772,U_771))
      | ? [U_770,U_769] :
          ( ~ hBOOL(hAPP(fun(U_773,bool),bool,U_772,hAPP(fun(U_773,bool),fun(U_773,bool),hAPP(U_773,fun(fun(U_773,bool),fun(U_773,bool)),insert(U_773),U_770),U_769)))
          & hBOOL(hAPP(fun(U_773,bool),bool,U_772,U_769))
          & ~ hBOOL(hAPP(fun(U_773,bool),bool,hAPP(U_773,fun(fun(U_773,bool),bool),member(U_773),U_770),U_769))
          & ti(fun(U_773,bool),U_769) != bot_bot(fun(U_773,bool))
          & hBOOL(hAPP(fun(U_773,bool),bool,finite_finite(U_773),U_769)) )
      | ~ hBOOL(hAPP(fun(U_773,bool),bool,U_772,hAPP(fun(U_773,bool),fun(U_773,bool),hAPP(U_773,fun(fun(U_773,bool),fun(U_773,bool)),insert(U_773),sK30(U_773,U_772,U_771)),bot_bot(fun(U_773,bool)))))
      | ti(fun(U_773,bool),U_771) = bot_bot(fun(U_773,bool))
      | ~ hBOOL(hAPP(fun(U_773,bool),bool,finite_finite(U_773),U_771)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_768,sK30(U_773,U_772,U_771))],[f_213_2]) ).

fof(f_213_4,plain,
    ! [U_773,U_772,U_771] :
      ( hBOOL(hAPP(fun(U_773,bool),bool,U_772,U_771))
      | ? [U_769] :
          ( ~ hBOOL(hAPP(fun(U_773,bool),bool,U_772,hAPP(fun(U_773,bool),fun(U_773,bool),hAPP(U_773,fun(fun(U_773,bool),fun(U_773,bool)),insert(U_773),sK31(U_773,U_772,U_771)),U_769)))
          & hBOOL(hAPP(fun(U_773,bool),bool,U_772,U_769))
          & ~ hBOOL(hAPP(fun(U_773,bool),bool,hAPP(U_773,fun(fun(U_773,bool),bool),member(U_773),sK31(U_773,U_772,U_771)),U_769))
          & ti(fun(U_773,bool),U_769) != bot_bot(fun(U_773,bool))
          & hBOOL(hAPP(fun(U_773,bool),bool,finite_finite(U_773),U_769)) )
      | ~ hBOOL(hAPP(fun(U_773,bool),bool,U_772,hAPP(fun(U_773,bool),fun(U_773,bool),hAPP(U_773,fun(fun(U_773,bool),fun(U_773,bool)),insert(U_773),sK30(U_773,U_772,U_771)),bot_bot(fun(U_773,bool)))))
      | ti(fun(U_773,bool),U_771) = bot_bot(fun(U_773,bool))
      | ~ hBOOL(hAPP(fun(U_773,bool),bool,finite_finite(U_773),U_771)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_770,sK31(U_773,U_772,U_771))],[f_213_3]) ).

fof(f_213_5,plain,
    ! [U_773,U_772,U_771] :
      ( hBOOL(hAPP(fun(U_773,bool),bool,U_772,U_771))
      | ( ~ hBOOL(hAPP(fun(U_773,bool),bool,U_772,hAPP(fun(U_773,bool),fun(U_773,bool),hAPP(U_773,fun(fun(U_773,bool),fun(U_773,bool)),insert(U_773),sK31(U_773,U_772,U_771)),sK32(U_773,U_772,U_771))))
        & hBOOL(hAPP(fun(U_773,bool),bool,U_772,sK32(U_773,U_772,U_771)))
        & ~ hBOOL(hAPP(fun(U_773,bool),bool,hAPP(U_773,fun(fun(U_773,bool),bool),member(U_773),sK31(U_773,U_772,U_771)),sK32(U_773,U_772,U_771)))
        & ti(fun(U_773,bool),sK32(U_773,U_772,U_771)) != bot_bot(fun(U_773,bool))
        & hBOOL(hAPP(fun(U_773,bool),bool,finite_finite(U_773),sK32(U_773,U_772,U_771))) )
      | ~ hBOOL(hAPP(fun(U_773,bool),bool,U_772,hAPP(fun(U_773,bool),fun(U_773,bool),hAPP(U_773,fun(fun(U_773,bool),fun(U_773,bool)),insert(U_773),sK30(U_773,U_772,U_771)),bot_bot(fun(U_773,bool)))))
      | ti(fun(U_773,bool),U_771) = bot_bot(fun(U_773,bool))
      | ~ hBOOL(hAPP(fun(U_773,bool),bool,finite_finite(U_773),U_771)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_769,sK32(U_773,U_772,U_771))],[f_213_4]) ).

fof(f_213_6,plain,
    ( ! [U_771,U_772,U_773] :
        ( ~ hBOOL(hAPP(fun(U_773,bool),bool,U_772,hAPP(fun(U_773,bool),fun(U_773,bool),hAPP(U_773,fun(fun(U_773,bool),fun(U_773,bool)),insert(U_773),sK31(U_773,U_772,U_771)),sK32(U_773,U_772,U_771))))
        | ~ sP38(U_771,U_772,U_773) )
    & ! [U_771,U_772,U_773] :
        ( hBOOL(hAPP(fun(U_773,bool),bool,U_772,sK32(U_773,U_772,U_771)))
        | ~ sP38(U_771,U_772,U_773) )
    & ! [U_771,U_772,U_773] :
        ( ~ hBOOL(hAPP(fun(U_773,bool),bool,hAPP(U_773,fun(fun(U_773,bool),bool),member(U_773),sK31(U_773,U_772,U_771)),sK32(U_773,U_772,U_771)))
        | ~ sP38(U_771,U_772,U_773) )
    & ! [U_771,U_772,U_773] :
        ( ti(fun(U_773,bool),sK32(U_773,U_772,U_771)) != bot_bot(fun(U_773,bool))
        | ~ sP38(U_771,U_772,U_773) )
    & ! [U_771,U_772,U_773] :
        ( hBOOL(hAPP(fun(U_773,bool),bool,finite_finite(U_773),sK32(U_773,U_772,U_771)))
        | ~ sP38(U_771,U_772,U_773) )
    & ! [U_771,U_772,U_773] :
        ( hBOOL(hAPP(fun(U_773,bool),bool,U_772,U_771))
        | sP38(U_771,U_772,U_773)
        | ~ hBOOL(hAPP(fun(U_773,bool),bool,U_772,hAPP(fun(U_773,bool),fun(U_773,bool),hAPP(U_773,fun(fun(U_773,bool),fun(U_773,bool)),insert(U_773),sK30(U_773,U_772,U_771)),bot_bot(fun(U_773,bool)))))
        | ti(fun(U_773,bool),U_771) = bot_bot(fun(U_773,bool))
        | ~ hBOOL(hAPP(fun(U_773,bool),bool,finite_finite(U_773),U_771)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38])],[f_213_5]) ).

cnf(f_213_7,plain,
    ( hBOOL(hAPP(fun(U_773,bool),bool,U_772,U_771))
    | sP38(U_771,U_772,U_773)
    | ~ hBOOL(hAPP(fun(U_773,bool),bool,U_772,hAPP(fun(U_773,bool),fun(U_773,bool),hAPP(U_773,fun(fun(U_773,bool),fun(U_773,bool)),insert(U_773),sK30(U_773,U_772,U_771)),bot_bot(fun(U_773,bool)))))
    | ti(fun(U_773,bool),U_771) = bot_bot(fun(U_773,bool))
    | ~ hBOOL(hAPP(fun(U_773,bool),bool,finite_finite(U_773),U_771)) ),
    inference(clausify,[status(thm)],[f_213_6]) ).

cnf(f_213_8,plain,
    ( hBOOL(hAPP(fun(U_773,bool),bool,finite_finite(U_773),sK32(U_773,U_772,U_771)))
    | ~ sP38(U_771,U_772,U_773) ),
    inference(clausify,[status(thm)],[f_213_6]) ).

cnf(f_213_9,plain,
    ( ti(fun(U_773,bool),sK32(U_773,U_772,U_771)) != bot_bot(fun(U_773,bool))
    | ~ sP38(U_771,U_772,U_773) ),
    inference(clausify,[status(thm)],[f_213_6]) ).

cnf(f_213_10,plain,
    ( ~ hBOOL(hAPP(fun(U_773,bool),bool,hAPP(U_773,fun(fun(U_773,bool),bool),member(U_773),sK31(U_773,U_772,U_771)),sK32(U_773,U_772,U_771)))
    | ~ sP38(U_771,U_772,U_773) ),
    inference(clausify,[status(thm)],[f_213_6]) ).

cnf(f_213_11,plain,
    ( hBOOL(hAPP(fun(U_773,bool),bool,U_772,sK32(U_773,U_772,U_771)))
    | ~ sP38(U_771,U_772,U_773) ),
    inference(clausify,[status(thm)],[f_213_6]) ).

cnf(f_213_12,plain,
    ( ~ hBOOL(hAPP(fun(U_773,bool),bool,U_772,hAPP(fun(U_773,bool),fun(U_773,bool),hAPP(U_773,fun(fun(U_773,bool),fun(U_773,bool)),insert(U_773),sK31(U_773,U_772,U_771)),sK32(U_773,U_772,U_771))))
    | ~ sP38(U_771,U_772,U_773) ),
    inference(clausify,[status(thm)],[f_213_6]) ).

fof(f_214_1,plain,
    ! [X_b,X_3] : hAPP(fun(X_b,bool),X_b,the_elem(X_b),X_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),fequal(fun(X_b,bool)),X_3)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))),
    inference(fof_nnf,[status(thm)],[fact_161_the__elem__def]) ).

fof(f_214_2,plain,
    ! [U_775,U_774] : hAPP(fun(U_775,bool),U_775,the_elem(U_775),U_774) = hAPP(fun(U_775,bool),U_775,the(U_775),hAPP(fun(U_775,fun(U_775,bool)),fun(U_775,bool),hAPP(fun(fun(U_775,bool),bool),fun(fun(U_775,fun(U_775,bool)),fun(U_775,bool)),combb(fun(U_775,bool),bool,U_775),hAPP(fun(U_775,bool),fun(fun(U_775,bool),bool),fequal(fun(U_775,bool)),U_774)),hAPP(fun(U_775,bool),fun(U_775,fun(U_775,bool)),hAPP(fun(U_775,fun(fun(U_775,bool),fun(U_775,bool))),fun(fun(U_775,bool),fun(U_775,fun(U_775,bool))),combc(U_775,fun(U_775,bool),fun(U_775,bool)),insert(U_775)),bot_bot(fun(U_775,bool))))),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

fof(f_214_3,plain,
    ! [U_775,U_774] : hAPP(fun(U_775,bool),U_775,the_elem(U_775),U_774) = hAPP(fun(U_775,bool),U_775,the(U_775),hAPP(fun(U_775,fun(U_775,bool)),fun(U_775,bool),hAPP(fun(fun(U_775,bool),bool),fun(fun(U_775,fun(U_775,bool)),fun(U_775,bool)),combb(fun(U_775,bool),bool,U_775),hAPP(fun(U_775,bool),fun(fun(U_775,bool),bool),fequal(fun(U_775,bool)),U_774)),hAPP(fun(U_775,bool),fun(U_775,fun(U_775,bool)),hAPP(fun(U_775,fun(fun(U_775,bool),fun(U_775,bool))),fun(fun(U_775,bool),fun(U_775,fun(U_775,bool))),combc(U_775,fun(U_775,bool),fun(U_775,bool)),insert(U_775)),bot_bot(fun(U_775,bool))))),
    inference(definitional_conversion,[status(esa)],[f_214_2]) ).

cnf(f_214_4,plain,
    hAPP(fun(U_775,bool),U_775,the_elem(U_775),U_774) = hAPP(fun(U_775,bool),U_775,the(U_775),hAPP(fun(U_775,fun(U_775,bool)),fun(U_775,bool),hAPP(fun(fun(U_775,bool),bool),fun(fun(U_775,fun(U_775,bool)),fun(U_775,bool)),combb(fun(U_775,bool),bool,U_775),hAPP(fun(U_775,bool),fun(fun(U_775,bool),bool),fequal(fun(U_775,bool)),U_774)),hAPP(fun(U_775,bool),fun(U_775,fun(U_775,bool)),hAPP(fun(U_775,fun(fun(U_775,bool),fun(U_775,bool))),fun(fun(U_775,bool),fun(U_775,fun(U_775,bool))),combc(U_775,fun(U_775,bool),fun(U_775,bool)),insert(U_775)),bot_bot(fun(U_775,bool))))),
    inference(clausify,[status(thm)],[f_214_3]) ).

fof(f_215_1,plain,
    ! [X_b,X_1,A_3,F,F_2] :
      ( hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3))
      | ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool))
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_162_folding__one_Oinsert]) ).

fof(f_215_2,plain,
    ! [U_780,U_779,U_778,U_777,U_776] :
      ( hAPP(fun(U_780,bool),U_780,U_776,hAPP(fun(U_780,bool),fun(U_780,bool),hAPP(U_780,fun(fun(U_780,bool),fun(U_780,bool)),insert(U_780),U_779),U_778)) = hAPP(U_780,U_780,hAPP(U_780,fun(U_780,U_780),U_777,U_779),hAPP(fun(U_780,bool),U_780,U_776,U_778))
      | ti(fun(U_780,bool),U_778) = bot_bot(fun(U_780,bool))
      | hBOOL(hAPP(fun(U_780,bool),bool,hAPP(U_780,fun(fun(U_780,bool),bool),member(U_780),U_779),U_778))
      | ~ hBOOL(hAPP(fun(U_780,bool),bool,finite_finite(U_780),U_778))
      | ~ hBOOL(hAPP(fun(fun(U_780,bool),U_780),bool,hAPP(fun(U_780,fun(U_780,U_780)),fun(fun(fun(U_780,bool),U_780),bool),finite_folding_one(U_780),U_777),U_776)) ),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

fof(f_215_3,plain,
    ! [U_776,U_777,U_778,U_780,U_779] :
      ( hAPP(fun(U_780,bool),U_780,U_776,hAPP(fun(U_780,bool),fun(U_780,bool),hAPP(U_780,fun(fun(U_780,bool),fun(U_780,bool)),insert(U_780),U_779),U_778)) = hAPP(U_780,U_780,hAPP(U_780,fun(U_780,U_780),U_777,U_779),hAPP(fun(U_780,bool),U_780,U_776,U_778))
      | ti(fun(U_780,bool),U_778) = bot_bot(fun(U_780,bool))
      | hBOOL(hAPP(fun(U_780,bool),bool,hAPP(U_780,fun(fun(U_780,bool),bool),member(U_780),U_779),U_778))
      | ~ hBOOL(hAPP(fun(U_780,bool),bool,finite_finite(U_780),U_778))
      | ~ hBOOL(hAPP(fun(fun(U_780,bool),U_780),bool,hAPP(fun(U_780,fun(U_780,U_780)),fun(fun(fun(U_780,bool),U_780),bool),finite_folding_one(U_780),U_777),U_776)) ),
    inference(definitional_conversion,[status(esa)],[f_215_2]) ).

cnf(f_215_4,plain,
    ( hAPP(fun(U_780,bool),U_780,U_776,hAPP(fun(U_780,bool),fun(U_780,bool),hAPP(U_780,fun(fun(U_780,bool),fun(U_780,bool)),insert(U_780),U_779),U_778)) = hAPP(U_780,U_780,hAPP(U_780,fun(U_780,U_780),U_777,U_779),hAPP(fun(U_780,bool),U_780,U_776,U_778))
    | ti(fun(U_780,bool),U_778) = bot_bot(fun(U_780,bool))
    | hBOOL(hAPP(fun(U_780,bool),bool,hAPP(U_780,fun(fun(U_780,bool),bool),member(U_780),U_779),U_778))
    | ~ hBOOL(hAPP(fun(U_780,bool),bool,finite_finite(U_780),U_778))
    | ~ hBOOL(hAPP(fun(fun(U_780,bool),U_780),bool,hAPP(fun(U_780,fun(U_780,U_780)),fun(fun(fun(U_780,bool),U_780),bool),finite_folding_one(U_780),U_777),U_776)) ),
    inference(clausify,[status(thm)],[f_215_3]) ).

fof(f_216_1,plain,
    ! [X_b,B_2,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_163_finite__Diff]) ).

fof(f_216_2,plain,
    ! [U_783,U_782,U_781] :
      ( hBOOL(hAPP(fun(U_783,bool),bool,finite_finite(U_783),hAPP(fun(U_783,bool),fun(U_783,bool),hAPP(fun(U_783,bool),fun(fun(U_783,bool),fun(U_783,bool)),minus_minus(fun(U_783,bool)),U_781),U_782)))
      | ~ hBOOL(hAPP(fun(U_783,bool),bool,finite_finite(U_783),U_781)) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

fof(f_216_3,plain,
    ! [U_782,U_781,U_783] :
      ( hBOOL(hAPP(fun(U_783,bool),bool,finite_finite(U_783),hAPP(fun(U_783,bool),fun(U_783,bool),hAPP(fun(U_783,bool),fun(fun(U_783,bool),fun(U_783,bool)),minus_minus(fun(U_783,bool)),U_781),U_782)))
      | ~ hBOOL(hAPP(fun(U_783,bool),bool,finite_finite(U_783),U_781)) ),
    inference(definitional_conversion,[status(esa)],[f_216_2]) ).

cnf(f_216_4,plain,
    ( hBOOL(hAPP(fun(U_783,bool),bool,finite_finite(U_783),hAPP(fun(U_783,bool),fun(U_783,bool),hAPP(fun(U_783,bool),fun(fun(U_783,bool),fun(U_783,bool)),minus_minus(fun(U_783,bool)),U_781),U_782)))
    | ~ hBOOL(hAPP(fun(U_783,bool),bool,finite_finite(U_783),U_781)) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

fof(f_217_1,plain,
    ! [X_b,X_1,F,F_2] :
      ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1) = ti(X_b,X_1)
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_164_folding__one__idem_Oidem]) ).

fof(f_217_2,plain,
    ! [U_787,U_786,U_785,U_784] :
      ( hAPP(U_787,U_787,hAPP(U_787,fun(U_787,U_787),U_785,U_786),U_786) = ti(U_787,U_786)
      | ~ hBOOL(hAPP(fun(fun(U_787,bool),U_787),bool,hAPP(fun(U_787,fun(U_787,U_787)),fun(fun(fun(U_787,bool),U_787),bool),finite2073411215e_idem(U_787),U_785),U_784)) ),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

fof(f_217_3,plain,
    ! [U_787,U_786,U_785] :
      ( ! [U_784] : ~ hBOOL(hAPP(fun(fun(U_787,bool),U_787),bool,hAPP(fun(U_787,fun(U_787,U_787)),fun(fun(fun(U_787,bool),U_787),bool),finite2073411215e_idem(U_787),U_785),U_784))
      | hAPP(U_787,U_787,hAPP(U_787,fun(U_787,U_787),U_785,U_786),U_786) = ti(U_787,U_786) ),
    inference(miniscope,[status(thm)],[f_217_2]) ).

fof(f_217_4,plain,
    ! [U_785,U_784,U_786,U_787] :
      ( ~ hBOOL(hAPP(fun(fun(U_787,bool),U_787),bool,hAPP(fun(U_787,fun(U_787,U_787)),fun(fun(fun(U_787,bool),U_787),bool),finite2073411215e_idem(U_787),U_785),U_784))
      | hAPP(U_787,U_787,hAPP(U_787,fun(U_787,U_787),U_785,U_786),U_786) = ti(U_787,U_786) ),
    inference(definitional_conversion,[status(esa)],[f_217_3]) ).

cnf(f_217_5,plain,
    ( ~ hBOOL(hAPP(fun(fun(U_787,bool),U_787),bool,hAPP(fun(U_787,fun(U_787,U_787)),fun(fun(fun(U_787,bool),U_787),bool),finite2073411215e_idem(U_787),U_785),U_784))
    | hAPP(U_787,U_787,hAPP(U_787,fun(U_787,U_787),U_785,U_786),U_786) = ti(U_787,U_786) ),
    inference(clausify,[status(thm)],[f_217_4]) ).

fof(f_218_1,plain,
    ! [X_b,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),A_3) = bot_bot(fun(X_b,bool)),
    inference(fof_nnf,[status(thm)],[fact_165_Diff__cancel]) ).

fof(f_218_2,plain,
    ! [U_789,U_788] : hAPP(fun(U_789,bool),fun(U_789,bool),hAPP(fun(U_789,bool),fun(fun(U_789,bool),fun(U_789,bool)),minus_minus(fun(U_789,bool)),U_788),U_788) = bot_bot(fun(U_789,bool)),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

fof(f_218_3,plain,
    ! [U_788,U_789] : hAPP(fun(U_789,bool),fun(U_789,bool),hAPP(fun(U_789,bool),fun(fun(U_789,bool),fun(U_789,bool)),minus_minus(fun(U_789,bool)),U_788),U_788) = bot_bot(fun(U_789,bool)),
    inference(definitional_conversion,[status(esa)],[f_218_2]) ).

cnf(f_218_4,plain,
    hAPP(fun(U_789,bool),fun(U_789,bool),hAPP(fun(U_789,bool),fun(fun(U_789,bool),fun(U_789,bool)),minus_minus(fun(U_789,bool)),U_788),U_788) = bot_bot(fun(U_789,bool)),
    inference(clausify,[status(thm)],[f_218_3]) ).

fof(f_219_1,plain,
    ! [X_b,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_3),
    inference(fof_nnf,[status(thm)],[fact_166_Diff__empty]) ).

fof(f_219_2,plain,
    ! [U_791,U_790] : hAPP(fun(U_791,bool),fun(U_791,bool),hAPP(fun(U_791,bool),fun(fun(U_791,bool),fun(U_791,bool)),minus_minus(fun(U_791,bool)),U_790),bot_bot(fun(U_791,bool))) = ti(fun(U_791,bool),U_790),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

fof(f_219_3,plain,
    ! [U_790,U_791] : hAPP(fun(U_791,bool),fun(U_791,bool),hAPP(fun(U_791,bool),fun(fun(U_791,bool),fun(U_791,bool)),minus_minus(fun(U_791,bool)),U_790),bot_bot(fun(U_791,bool))) = ti(fun(U_791,bool),U_790),
    inference(definitional_conversion,[status(esa)],[f_219_2]) ).

cnf(f_219_4,plain,
    hAPP(fun(U_791,bool),fun(U_791,bool),hAPP(fun(U_791,bool),fun(fun(U_791,bool),fun(U_791,bool)),minus_minus(fun(U_791,bool)),U_790),bot_bot(fun(U_791,bool))) = ti(fun(U_791,bool),U_790),
    inference(clausify,[status(thm)],[f_219_3]) ).

fof(f_220_1,plain,
    ! [X_b,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3) = bot_bot(fun(X_b,bool)),
    inference(fof_nnf,[status(thm)],[fact_167_empty__Diff]) ).

fof(f_220_2,plain,
    ! [U_793,U_792] : hAPP(fun(U_793,bool),fun(U_793,bool),hAPP(fun(U_793,bool),fun(fun(U_793,bool),fun(U_793,bool)),minus_minus(fun(U_793,bool)),bot_bot(fun(U_793,bool))),U_792) = bot_bot(fun(U_793,bool)),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

fof(f_220_3,plain,
    ! [U_792,U_793] : hAPP(fun(U_793,bool),fun(U_793,bool),hAPP(fun(U_793,bool),fun(fun(U_793,bool),fun(U_793,bool)),minus_minus(fun(U_793,bool)),bot_bot(fun(U_793,bool))),U_792) = bot_bot(fun(U_793,bool)),
    inference(definitional_conversion,[status(esa)],[f_220_2]) ).

cnf(f_220_4,plain,
    hAPP(fun(U_793,bool),fun(U_793,bool),hAPP(fun(U_793,bool),fun(fun(U_793,bool),fun(U_793,bool)),minus_minus(fun(U_793,bool)),bot_bot(fun(U_793,bool))),U_792) = bot_bot(fun(U_793,bool)),
    inference(clausify,[status(thm)],[f_220_3]) ).

fof(f_221_1,plain,
    ! [X_b,A_3,B_2] :
      ( ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) )
        & ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) ) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_168_finite__Diff2]) ).

fof(f_221_2,plain,
    ! [U_796,U_795,U_794] :
      ( ( ( hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),hAPP(fun(U_796,bool),fun(U_796,bool),hAPP(fun(U_796,bool),fun(fun(U_796,bool),fun(U_796,bool)),minus_minus(fun(U_796,bool)),U_795),U_794)))
          | ~ hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),U_795)) )
        & ( hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),U_795))
          | ~ hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),hAPP(fun(U_796,bool),fun(U_796,bool),hAPP(fun(U_796,bool),fun(fun(U_796,bool),fun(U_796,bool)),minus_minus(fun(U_796,bool)),U_795),U_794))) ) )
      | ~ hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),U_794)) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

fof(f_221_3,plain,
    ( ! [U_796,U_794,U_795] :
        ( hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),hAPP(fun(U_796,bool),fun(U_796,bool),hAPP(fun(U_796,bool),fun(fun(U_796,bool),fun(U_796,bool)),minus_minus(fun(U_796,bool)),U_795),U_794)))
        | ~ hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),U_795))
        | ~ sP39(U_796,U_794,U_795) )
    & ! [U_796,U_794,U_795] :
        ( hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),U_795))
        | ~ hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),hAPP(fun(U_796,bool),fun(U_796,bool),hAPP(fun(U_796,bool),fun(fun(U_796,bool),fun(U_796,bool)),minus_minus(fun(U_796,bool)),U_795),U_794)))
        | ~ sP39(U_796,U_794,U_795) )
    & ! [U_796,U_794,U_795] :
        ( sP39(U_796,U_794,U_795)
        | ~ hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),U_794)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39])],[f_221_2]) ).

cnf(f_221_4,plain,
    ( sP39(U_796,U_794,U_795)
    | ~ hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),U_794)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_5,plain,
    ( hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),U_795))
    | ~ hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),hAPP(fun(U_796,bool),fun(U_796,bool),hAPP(fun(U_796,bool),fun(fun(U_796,bool),fun(U_796,bool)),minus_minus(fun(U_796,bool)),U_795),U_794)))
    | ~ sP39(U_796,U_794,U_795) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_6,plain,
    ( hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),hAPP(fun(U_796,bool),fun(U_796,bool),hAPP(fun(U_796,bool),fun(fun(U_796,bool),fun(U_796,bool)),minus_minus(fun(U_796,bool)),U_795),U_794)))
    | ~ hBOOL(hAPP(fun(U_796,bool),bool,finite_finite(U_796),U_795))
    | ~ sP39(U_796,U_794,U_795) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

fof(f_222_1,plain,
    ! [X_b,A_3,X_1,B_2] :
      ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_169_insert__Diff1]) ).

fof(f_222_2,plain,
    ! [U_800,U_799,U_798,U_797] :
      ( hAPP(fun(U_800,bool),fun(U_800,bool),hAPP(fun(U_800,bool),fun(fun(U_800,bool),fun(U_800,bool)),minus_minus(fun(U_800,bool)),hAPP(fun(U_800,bool),fun(U_800,bool),hAPP(U_800,fun(fun(U_800,bool),fun(U_800,bool)),insert(U_800),U_798),U_799)),U_797) = hAPP(fun(U_800,bool),fun(U_800,bool),hAPP(fun(U_800,bool),fun(fun(U_800,bool),fun(U_800,bool)),minus_minus(fun(U_800,bool)),U_799),U_797)
      | ~ hBOOL(hAPP(fun(U_800,bool),bool,hAPP(U_800,fun(fun(U_800,bool),bool),member(U_800),U_798),U_797)) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

fof(f_222_3,plain,
    ! [U_798,U_797,U_799,U_800] :
      ( hAPP(fun(U_800,bool),fun(U_800,bool),hAPP(fun(U_800,bool),fun(fun(U_800,bool),fun(U_800,bool)),minus_minus(fun(U_800,bool)),hAPP(fun(U_800,bool),fun(U_800,bool),hAPP(U_800,fun(fun(U_800,bool),fun(U_800,bool)),insert(U_800),U_798),U_799)),U_797) = hAPP(fun(U_800,bool),fun(U_800,bool),hAPP(fun(U_800,bool),fun(fun(U_800,bool),fun(U_800,bool)),minus_minus(fun(U_800,bool)),U_799),U_797)
      | ~ hBOOL(hAPP(fun(U_800,bool),bool,hAPP(U_800,fun(fun(U_800,bool),bool),member(U_800),U_798),U_797)) ),
    inference(definitional_conversion,[status(esa)],[f_222_2]) ).

cnf(f_222_4,plain,
    ( hAPP(fun(U_800,bool),fun(U_800,bool),hAPP(fun(U_800,bool),fun(fun(U_800,bool),fun(U_800,bool)),minus_minus(fun(U_800,bool)),hAPP(fun(U_800,bool),fun(U_800,bool),hAPP(U_800,fun(fun(U_800,bool),fun(U_800,bool)),insert(U_800),U_798),U_799)),U_797) = hAPP(fun(U_800,bool),fun(U_800,bool),hAPP(fun(U_800,bool),fun(fun(U_800,bool),fun(U_800,bool)),minus_minus(fun(U_800,bool)),U_799),U_797)
    | ~ hBOOL(hAPP(fun(U_800,bool),bool,hAPP(U_800,fun(fun(U_800,bool),bool),member(U_800),U_798),U_797)) ),
    inference(clausify,[status(thm)],[f_222_3]) ).

fof(f_223_1,plain,
    ! [X_b,A_3,X_1,B_2] :
      ( ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))
        | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) )
      & ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_170_insert__Diff__if]) ).

fof(f_223_2,plain,
    ! [U_804,U_803,U_802,U_801] :
      ( ( hAPP(fun(U_804,bool),fun(U_804,bool),hAPP(fun(U_804,bool),fun(fun(U_804,bool),fun(U_804,bool)),minus_minus(fun(U_804,bool)),hAPP(fun(U_804,bool),fun(U_804,bool),hAPP(U_804,fun(fun(U_804,bool),fun(U_804,bool)),insert(U_804),U_802),U_803)),U_801) = hAPP(fun(U_804,bool),fun(U_804,bool),hAPP(U_804,fun(fun(U_804,bool),fun(U_804,bool)),insert(U_804),U_802),hAPP(fun(U_804,bool),fun(U_804,bool),hAPP(fun(U_804,bool),fun(fun(U_804,bool),fun(U_804,bool)),minus_minus(fun(U_804,bool)),U_803),U_801))
        | hBOOL(hAPP(fun(U_804,bool),bool,hAPP(U_804,fun(fun(U_804,bool),bool),member(U_804),U_802),U_801)) )
      & ( hAPP(fun(U_804,bool),fun(U_804,bool),hAPP(fun(U_804,bool),fun(fun(U_804,bool),fun(U_804,bool)),minus_minus(fun(U_804,bool)),hAPP(fun(U_804,bool),fun(U_804,bool),hAPP(U_804,fun(fun(U_804,bool),fun(U_804,bool)),insert(U_804),U_802),U_803)),U_801) = hAPP(fun(U_804,bool),fun(U_804,bool),hAPP(fun(U_804,bool),fun(fun(U_804,bool),fun(U_804,bool)),minus_minus(fun(U_804,bool)),U_803),U_801)
        | ~ hBOOL(hAPP(fun(U_804,bool),bool,hAPP(U_804,fun(fun(U_804,bool),bool),member(U_804),U_802),U_801)) ) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

fof(f_223_3,plain,
    ( ! [U_812,U_810,U_808,U_806] :
        ( hAPP(fun(U_812,bool),fun(U_812,bool),hAPP(fun(U_812,bool),fun(fun(U_812,bool),fun(U_812,bool)),minus_minus(fun(U_812,bool)),hAPP(fun(U_812,bool),fun(U_812,bool),hAPP(U_812,fun(fun(U_812,bool),fun(U_812,bool)),insert(U_812),U_808),U_810)),U_806) = hAPP(fun(U_812,bool),fun(U_812,bool),hAPP(U_812,fun(fun(U_812,bool),fun(U_812,bool)),insert(U_812),U_808),hAPP(fun(U_812,bool),fun(U_812,bool),hAPP(fun(U_812,bool),fun(fun(U_812,bool),fun(U_812,bool)),minus_minus(fun(U_812,bool)),U_810),U_806))
        | hBOOL(hAPP(fun(U_812,bool),bool,hAPP(U_812,fun(fun(U_812,bool),bool),member(U_812),U_808),U_806)) )
    & ! [U_811,U_809,U_807,U_805] :
        ( hAPP(fun(U_811,bool),fun(U_811,bool),hAPP(fun(U_811,bool),fun(fun(U_811,bool),fun(U_811,bool)),minus_minus(fun(U_811,bool)),hAPP(fun(U_811,bool),fun(U_811,bool),hAPP(U_811,fun(fun(U_811,bool),fun(U_811,bool)),insert(U_811),U_807),U_809)),U_805) = hAPP(fun(U_811,bool),fun(U_811,bool),hAPP(fun(U_811,bool),fun(fun(U_811,bool),fun(U_811,bool)),minus_minus(fun(U_811,bool)),U_809),U_805)
        | ~ hBOOL(hAPP(fun(U_811,bool),bool,hAPP(U_811,fun(fun(U_811,bool),bool),member(U_811),U_807),U_805)) ) ),
    inference(miniscope,[status(thm)],[f_223_2]) ).

fof(f_223_4,plain,
    ( ! [U_808,U_806,U_810,U_812] :
        ( hAPP(fun(U_812,bool),fun(U_812,bool),hAPP(fun(U_812,bool),fun(fun(U_812,bool),fun(U_812,bool)),minus_minus(fun(U_812,bool)),hAPP(fun(U_812,bool),fun(U_812,bool),hAPP(U_812,fun(fun(U_812,bool),fun(U_812,bool)),insert(U_812),U_808),U_810)),U_806) = hAPP(fun(U_812,bool),fun(U_812,bool),hAPP(U_812,fun(fun(U_812,bool),fun(U_812,bool)),insert(U_812),U_808),hAPP(fun(U_812,bool),fun(U_812,bool),hAPP(fun(U_812,bool),fun(fun(U_812,bool),fun(U_812,bool)),minus_minus(fun(U_812,bool)),U_810),U_806))
        | hBOOL(hAPP(fun(U_812,bool),bool,hAPP(U_812,fun(fun(U_812,bool),bool),member(U_812),U_808),U_806)) )
    & ! [U_811,U_805,U_809,U_807] :
        ( hAPP(fun(U_811,bool),fun(U_811,bool),hAPP(fun(U_811,bool),fun(fun(U_811,bool),fun(U_811,bool)),minus_minus(fun(U_811,bool)),hAPP(fun(U_811,bool),fun(U_811,bool),hAPP(U_811,fun(fun(U_811,bool),fun(U_811,bool)),insert(U_811),U_807),U_809)),U_805) = hAPP(fun(U_811,bool),fun(U_811,bool),hAPP(fun(U_811,bool),fun(fun(U_811,bool),fun(U_811,bool)),minus_minus(fun(U_811,bool)),U_809),U_805)
        | ~ hBOOL(hAPP(fun(U_811,bool),bool,hAPP(U_811,fun(fun(U_811,bool),bool),member(U_811),U_807),U_805)) ) ),
    inference(definitional_conversion,[status(esa)],[f_223_3]) ).

cnf(f_223_5,plain,
    ( hAPP(fun(U_811,bool),fun(U_811,bool),hAPP(fun(U_811,bool),fun(fun(U_811,bool),fun(U_811,bool)),minus_minus(fun(U_811,bool)),hAPP(fun(U_811,bool),fun(U_811,bool),hAPP(U_811,fun(fun(U_811,bool),fun(U_811,bool)),insert(U_811),U_807),U_809)),U_805) = hAPP(fun(U_811,bool),fun(U_811,bool),hAPP(fun(U_811,bool),fun(fun(U_811,bool),fun(U_811,bool)),minus_minus(fun(U_811,bool)),U_809),U_805)
    | ~ hBOOL(hAPP(fun(U_811,bool),bool,hAPP(U_811,fun(fun(U_811,bool),bool),member(U_811),U_807),U_805)) ),
    inference(clausify,[status(thm)],[f_223_4]) ).

cnf(f_223_6,plain,
    ( hAPP(fun(U_812,bool),fun(U_812,bool),hAPP(fun(U_812,bool),fun(fun(U_812,bool),fun(U_812,bool)),minus_minus(fun(U_812,bool)),hAPP(fun(U_812,bool),fun(U_812,bool),hAPP(U_812,fun(fun(U_812,bool),fun(U_812,bool)),insert(U_812),U_808),U_810)),U_806) = hAPP(fun(U_812,bool),fun(U_812,bool),hAPP(U_812,fun(fun(U_812,bool),fun(U_812,bool)),insert(U_812),U_808),hAPP(fun(U_812,bool),fun(U_812,bool),hAPP(fun(U_812,bool),fun(fun(U_812,bool),fun(U_812,bool)),minus_minus(fun(U_812,bool)),U_810),U_806))
    | hBOOL(hAPP(fun(U_812,bool),bool,hAPP(U_812,fun(fun(U_812,bool),bool),member(U_812),U_808),U_806)) ),
    inference(clausify,[status(thm)],[f_223_4]) ).

fof(f_224_1,plain,
    ! [X_b,C_2,A_3,B_2] :
      ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_2),A_3)) = ti(fun(X_b,bool),A_3)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),C_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_171_double__diff]) ).

fof(f_224_2,plain,
    ! [U_816,U_815,U_814,U_813] :
      ( hAPP(fun(U_816,bool),fun(U_816,bool),hAPP(fun(U_816,bool),fun(fun(U_816,bool),fun(U_816,bool)),minus_minus(fun(U_816,bool)),U_813),hAPP(fun(U_816,bool),fun(U_816,bool),hAPP(fun(U_816,bool),fun(fun(U_816,bool),fun(U_816,bool)),minus_minus(fun(U_816,bool)),U_815),U_814)) = ti(fun(U_816,bool),U_814)
      | ~ hBOOL(hAPP(fun(U_816,bool),bool,hAPP(fun(U_816,bool),fun(fun(U_816,bool),bool),ord_less_eq(fun(U_816,bool)),U_813),U_815))
      | ~ hBOOL(hAPP(fun(U_816,bool),bool,hAPP(fun(U_816,bool),fun(fun(U_816,bool),bool),ord_less_eq(fun(U_816,bool)),U_814),U_813)) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

fof(f_224_3,plain,
    ! [U_814,U_813,U_815,U_816] :
      ( hAPP(fun(U_816,bool),fun(U_816,bool),hAPP(fun(U_816,bool),fun(fun(U_816,bool),fun(U_816,bool)),minus_minus(fun(U_816,bool)),U_813),hAPP(fun(U_816,bool),fun(U_816,bool),hAPP(fun(U_816,bool),fun(fun(U_816,bool),fun(U_816,bool)),minus_minus(fun(U_816,bool)),U_815),U_814)) = ti(fun(U_816,bool),U_814)
      | ~ hBOOL(hAPP(fun(U_816,bool),bool,hAPP(fun(U_816,bool),fun(fun(U_816,bool),bool),ord_less_eq(fun(U_816,bool)),U_813),U_815))
      | ~ hBOOL(hAPP(fun(U_816,bool),bool,hAPP(fun(U_816,bool),fun(fun(U_816,bool),bool),ord_less_eq(fun(U_816,bool)),U_814),U_813)) ),
    inference(definitional_conversion,[status(esa)],[f_224_2]) ).

cnf(f_224_4,plain,
    ( hAPP(fun(U_816,bool),fun(U_816,bool),hAPP(fun(U_816,bool),fun(fun(U_816,bool),fun(U_816,bool)),minus_minus(fun(U_816,bool)),U_813),hAPP(fun(U_816,bool),fun(U_816,bool),hAPP(fun(U_816,bool),fun(fun(U_816,bool),fun(U_816,bool)),minus_minus(fun(U_816,bool)),U_815),U_814)) = ti(fun(U_816,bool),U_814)
    | ~ hBOOL(hAPP(fun(U_816,bool),bool,hAPP(fun(U_816,bool),fun(fun(U_816,bool),bool),ord_less_eq(fun(U_816,bool)),U_813),U_815))
    | ~ hBOOL(hAPP(fun(U_816,bool),bool,hAPP(fun(U_816,bool),fun(fun(U_816,bool),bool),ord_less_eq(fun(U_816,bool)),U_814),U_813)) ),
    inference(clausify,[status(thm)],[f_224_3]) ).

fof(f_225_1,plain,
    ! [X_b,D_2,B_2,A_3,C_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_2),D_2)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),D_2),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_172_Diff__mono]) ).

fof(f_225_2,plain,
    ! [U_821,U_820,U_819,U_818,U_817] :
      ( hBOOL(hAPP(fun(U_821,bool),bool,hAPP(fun(U_821,bool),fun(fun(U_821,bool),bool),ord_less_eq(fun(U_821,bool)),hAPP(fun(U_821,bool),fun(U_821,bool),hAPP(fun(U_821,bool),fun(fun(U_821,bool),fun(U_821,bool)),minus_minus(fun(U_821,bool)),U_818),U_819)),hAPP(fun(U_821,bool),fun(U_821,bool),hAPP(fun(U_821,bool),fun(fun(U_821,bool),fun(U_821,bool)),minus_minus(fun(U_821,bool)),U_817),U_820)))
      | ~ hBOOL(hAPP(fun(U_821,bool),bool,hAPP(fun(U_821,bool),fun(fun(U_821,bool),bool),ord_less_eq(fun(U_821,bool)),U_820),U_819))
      | ~ hBOOL(hAPP(fun(U_821,bool),bool,hAPP(fun(U_821,bool),fun(fun(U_821,bool),bool),ord_less_eq(fun(U_821,bool)),U_818),U_817)) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

fof(f_225_3,plain,
    ! [U_819,U_817,U_818,U_821,U_820] :
      ( hBOOL(hAPP(fun(U_821,bool),bool,hAPP(fun(U_821,bool),fun(fun(U_821,bool),bool),ord_less_eq(fun(U_821,bool)),hAPP(fun(U_821,bool),fun(U_821,bool),hAPP(fun(U_821,bool),fun(fun(U_821,bool),fun(U_821,bool)),minus_minus(fun(U_821,bool)),U_818),U_819)),hAPP(fun(U_821,bool),fun(U_821,bool),hAPP(fun(U_821,bool),fun(fun(U_821,bool),fun(U_821,bool)),minus_minus(fun(U_821,bool)),U_817),U_820)))
      | ~ hBOOL(hAPP(fun(U_821,bool),bool,hAPP(fun(U_821,bool),fun(fun(U_821,bool),bool),ord_less_eq(fun(U_821,bool)),U_820),U_819))
      | ~ hBOOL(hAPP(fun(U_821,bool),bool,hAPP(fun(U_821,bool),fun(fun(U_821,bool),bool),ord_less_eq(fun(U_821,bool)),U_818),U_817)) ),
    inference(definitional_conversion,[status(esa)],[f_225_2]) ).

cnf(f_225_4,plain,
    ( hBOOL(hAPP(fun(U_821,bool),bool,hAPP(fun(U_821,bool),fun(fun(U_821,bool),bool),ord_less_eq(fun(U_821,bool)),hAPP(fun(U_821,bool),fun(U_821,bool),hAPP(fun(U_821,bool),fun(fun(U_821,bool),fun(U_821,bool)),minus_minus(fun(U_821,bool)),U_818),U_819)),hAPP(fun(U_821,bool),fun(U_821,bool),hAPP(fun(U_821,bool),fun(fun(U_821,bool),fun(U_821,bool)),minus_minus(fun(U_821,bool)),U_817),U_820)))
    | ~ hBOOL(hAPP(fun(U_821,bool),bool,hAPP(fun(U_821,bool),fun(fun(U_821,bool),bool),ord_less_eq(fun(U_821,bool)),U_820),U_819))
    | ~ hBOOL(hAPP(fun(U_821,bool),bool,hAPP(fun(U_821,bool),fun(fun(U_821,bool),bool),ord_less_eq(fun(U_821,bool)),U_818),U_817)) ),
    inference(clausify,[status(thm)],[f_225_3]) ).

fof(f_226_1,plain,
    ! [X_b,A_3,B_2] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),A_3)),
    inference(fof_nnf,[status(thm)],[fact_173_Diff__subset]) ).

fof(f_226_2,plain,
    ! [U_824,U_823,U_822] : hBOOL(hAPP(fun(U_824,bool),bool,hAPP(fun(U_824,bool),fun(fun(U_824,bool),bool),ord_less_eq(fun(U_824,bool)),hAPP(fun(U_824,bool),fun(U_824,bool),hAPP(fun(U_824,bool),fun(fun(U_824,bool),fun(U_824,bool)),minus_minus(fun(U_824,bool)),U_823),U_822)),U_823)),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

fof(f_226_3,plain,
    ! [U_824,U_823,U_822] : hBOOL(hAPP(fun(U_824,bool),bool,hAPP(fun(U_824,bool),fun(fun(U_824,bool),bool),ord_less_eq(fun(U_824,bool)),hAPP(fun(U_824,bool),fun(U_824,bool),hAPP(fun(U_824,bool),fun(fun(U_824,bool),fun(U_824,bool)),minus_minus(fun(U_824,bool)),U_823),U_822)),U_823)),
    inference(definitional_conversion,[status(esa)],[f_226_2]) ).

cnf(f_226_4,plain,
    hBOOL(hAPP(fun(U_824,bool),bool,hAPP(fun(U_824,bool),fun(fun(U_824,bool),bool),ord_less_eq(fun(U_824,bool)),hAPP(fun(U_824,bool),fun(U_824,bool),hAPP(fun(U_824,bool),fun(fun(U_824,bool),fun(U_824,bool)),minus_minus(fun(U_824,bool)),U_823),U_822)),U_823)),
    inference(clausify,[status(thm)],[f_226_3]) ).

fof(f_227_1,plain,
    ! [X_b,X_1,A_3,F,F_2] :
      ( ( ( hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))
          | hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) )
        & ( hAPP(fun(X_b,bool),X_b,F_2,A_3) = ti(X_b,X_1)
          | hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) ) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_174_folding__one_Oremove]) ).

fof(f_227_2,plain,
    ! [U_829,U_828,U_827,U_826,U_825] :
      ( ( ( hAPP(fun(U_829,bool),U_829,U_825,U_827) = hAPP(U_829,U_829,hAPP(U_829,fun(U_829,U_829),U_826,U_828),hAPP(fun(U_829,bool),U_829,U_825,hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(fun(U_829,bool),fun(fun(U_829,bool),fun(U_829,bool)),minus_minus(fun(U_829,bool)),U_827),hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(U_829,fun(fun(U_829,bool),fun(U_829,bool)),insert(U_829),U_828),bot_bot(fun(U_829,bool))))))
          | hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(fun(U_829,bool),fun(fun(U_829,bool),fun(U_829,bool)),minus_minus(fun(U_829,bool)),U_827),hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(U_829,fun(fun(U_829,bool),fun(U_829,bool)),insert(U_829),U_828),bot_bot(fun(U_829,bool)))) = bot_bot(fun(U_829,bool)) )
        & ( hAPP(fun(U_829,bool),U_829,U_825,U_827) = ti(U_829,U_828)
          | hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(fun(U_829,bool),fun(fun(U_829,bool),fun(U_829,bool)),minus_minus(fun(U_829,bool)),U_827),hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(U_829,fun(fun(U_829,bool),fun(U_829,bool)),insert(U_829),U_828),bot_bot(fun(U_829,bool)))) != bot_bot(fun(U_829,bool)) ) )
      | ~ hBOOL(hAPP(fun(U_829,bool),bool,hAPP(U_829,fun(fun(U_829,bool),bool),member(U_829),U_828),U_827))
      | ~ hBOOL(hAPP(fun(U_829,bool),bool,finite_finite(U_829),U_827))
      | ~ hBOOL(hAPP(fun(fun(U_829,bool),U_829),bool,hAPP(fun(U_829,fun(U_829,U_829)),fun(fun(fun(U_829,bool),U_829),bool),finite_folding_one(U_829),U_826),U_825)) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

fof(f_227_3,plain,
    ( ! [U_825,U_826,U_827,U_828,U_829] :
        ( hAPP(fun(U_829,bool),U_829,U_825,U_827) = hAPP(U_829,U_829,hAPP(U_829,fun(U_829,U_829),U_826,U_828),hAPP(fun(U_829,bool),U_829,U_825,hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(fun(U_829,bool),fun(fun(U_829,bool),fun(U_829,bool)),minus_minus(fun(U_829,bool)),U_827),hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(U_829,fun(fun(U_829,bool),fun(U_829,bool)),insert(U_829),U_828),bot_bot(fun(U_829,bool))))))
        | hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(fun(U_829,bool),fun(fun(U_829,bool),fun(U_829,bool)),minus_minus(fun(U_829,bool)),U_827),hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(U_829,fun(fun(U_829,bool),fun(U_829,bool)),insert(U_829),U_828),bot_bot(fun(U_829,bool)))) = bot_bot(fun(U_829,bool))
        | ~ sP40(U_825,U_826,U_827,U_828,U_829) )
    & ! [U_825,U_826,U_827,U_828,U_829] :
        ( hAPP(fun(U_829,bool),U_829,U_825,U_827) = ti(U_829,U_828)
        | hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(fun(U_829,bool),fun(fun(U_829,bool),fun(U_829,bool)),minus_minus(fun(U_829,bool)),U_827),hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(U_829,fun(fun(U_829,bool),fun(U_829,bool)),insert(U_829),U_828),bot_bot(fun(U_829,bool)))) != bot_bot(fun(U_829,bool))
        | ~ sP40(U_825,U_826,U_827,U_828,U_829) )
    & ! [U_825,U_826,U_827,U_828,U_829] :
        ( sP40(U_825,U_826,U_827,U_828,U_829)
        | ~ hBOOL(hAPP(fun(U_829,bool),bool,hAPP(U_829,fun(fun(U_829,bool),bool),member(U_829),U_828),U_827))
        | ~ hBOOL(hAPP(fun(U_829,bool),bool,finite_finite(U_829),U_827))
        | ~ hBOOL(hAPP(fun(fun(U_829,bool),U_829),bool,hAPP(fun(U_829,fun(U_829,U_829)),fun(fun(fun(U_829,bool),U_829),bool),finite_folding_one(U_829),U_826),U_825)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_227_2]) ).

cnf(f_227_4,plain,
    ( sP40(U_825,U_826,U_827,U_828,U_829)
    | ~ hBOOL(hAPP(fun(U_829,bool),bool,hAPP(U_829,fun(fun(U_829,bool),bool),member(U_829),U_828),U_827))
    | ~ hBOOL(hAPP(fun(U_829,bool),bool,finite_finite(U_829),U_827))
    | ~ hBOOL(hAPP(fun(fun(U_829,bool),U_829),bool,hAPP(fun(U_829,fun(U_829,U_829)),fun(fun(fun(U_829,bool),U_829),bool),finite_folding_one(U_829),U_826),U_825)) ),
    inference(clausify,[status(thm)],[f_227_3]) ).

cnf(f_227_5,plain,
    ( hAPP(fun(U_829,bool),U_829,U_825,U_827) = ti(U_829,U_828)
    | hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(fun(U_829,bool),fun(fun(U_829,bool),fun(U_829,bool)),minus_minus(fun(U_829,bool)),U_827),hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(U_829,fun(fun(U_829,bool),fun(U_829,bool)),insert(U_829),U_828),bot_bot(fun(U_829,bool)))) != bot_bot(fun(U_829,bool))
    | ~ sP40(U_825,U_826,U_827,U_828,U_829) ),
    inference(clausify,[status(thm)],[f_227_3]) ).

cnf(f_227_6,plain,
    ( hAPP(fun(U_829,bool),U_829,U_825,U_827) = hAPP(U_829,U_829,hAPP(U_829,fun(U_829,U_829),U_826,U_828),hAPP(fun(U_829,bool),U_829,U_825,hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(fun(U_829,bool),fun(fun(U_829,bool),fun(U_829,bool)),minus_minus(fun(U_829,bool)),U_827),hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(U_829,fun(fun(U_829,bool),fun(U_829,bool)),insert(U_829),U_828),bot_bot(fun(U_829,bool))))))
    | hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(fun(U_829,bool),fun(fun(U_829,bool),fun(U_829,bool)),minus_minus(fun(U_829,bool)),U_827),hAPP(fun(U_829,bool),fun(U_829,bool),hAPP(U_829,fun(fun(U_829,bool),fun(U_829,bool)),insert(U_829),U_828),bot_bot(fun(U_829,bool)))) = bot_bot(fun(U_829,bool))
    | ~ sP40(U_825,U_826,U_827,U_828,U_829) ),
    inference(clausify,[status(thm)],[f_227_3]) ).

fof(f_228_1,plain,
    ! [X_b,X_1,A_3,F,F_2] :
      ( ( ( hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))
          | hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) )
        & ( hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = ti(X_b,X_1)
          | hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) ) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_175_folding__one_Oinsert__remove]) ).

fof(f_228_2,plain,
    ! [U_834,U_833,U_832,U_831,U_830] :
      ( ( ( hAPP(fun(U_834,bool),U_834,U_830,hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),U_832)) = hAPP(U_834,U_834,hAPP(U_834,fun(U_834,U_834),U_831,U_833),hAPP(fun(U_834,bool),U_834,U_830,hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(fun(U_834,bool),fun(fun(U_834,bool),fun(U_834,bool)),minus_minus(fun(U_834,bool)),U_832),hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),bot_bot(fun(U_834,bool))))))
          | hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(fun(U_834,bool),fun(fun(U_834,bool),fun(U_834,bool)),minus_minus(fun(U_834,bool)),U_832),hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),bot_bot(fun(U_834,bool)))) = bot_bot(fun(U_834,bool)) )
        & ( hAPP(fun(U_834,bool),U_834,U_830,hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),U_832)) = ti(U_834,U_833)
          | hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(fun(U_834,bool),fun(fun(U_834,bool),fun(U_834,bool)),minus_minus(fun(U_834,bool)),U_832),hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),bot_bot(fun(U_834,bool)))) != bot_bot(fun(U_834,bool)) ) )
      | ~ hBOOL(hAPP(fun(U_834,bool),bool,finite_finite(U_834),U_832))
      | ~ hBOOL(hAPP(fun(fun(U_834,bool),U_834),bool,hAPP(fun(U_834,fun(U_834,U_834)),fun(fun(fun(U_834,bool),U_834),bool),finite_folding_one(U_834),U_831),U_830)) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

fof(f_228_3,plain,
    ( ! [U_833,U_832,U_834,U_830,U_831] :
        ( hAPP(fun(U_834,bool),U_834,U_830,hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),U_832)) = hAPP(U_834,U_834,hAPP(U_834,fun(U_834,U_834),U_831,U_833),hAPP(fun(U_834,bool),U_834,U_830,hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(fun(U_834,bool),fun(fun(U_834,bool),fun(U_834,bool)),minus_minus(fun(U_834,bool)),U_832),hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),bot_bot(fun(U_834,bool))))))
        | hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(fun(U_834,bool),fun(fun(U_834,bool),fun(U_834,bool)),minus_minus(fun(U_834,bool)),U_832),hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),bot_bot(fun(U_834,bool)))) = bot_bot(fun(U_834,bool))
        | ~ sP41(U_833,U_832,U_834,U_830,U_831) )
    & ! [U_833,U_832,U_834,U_830,U_831] :
        ( hAPP(fun(U_834,bool),U_834,U_830,hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),U_832)) = ti(U_834,U_833)
        | hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(fun(U_834,bool),fun(fun(U_834,bool),fun(U_834,bool)),minus_minus(fun(U_834,bool)),U_832),hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),bot_bot(fun(U_834,bool)))) != bot_bot(fun(U_834,bool))
        | ~ sP41(U_833,U_832,U_834,U_830,U_831) )
    & ! [U_833,U_832,U_834,U_830,U_831] :
        ( sP41(U_833,U_832,U_834,U_830,U_831)
        | ~ hBOOL(hAPP(fun(U_834,bool),bool,finite_finite(U_834),U_832))
        | ~ hBOOL(hAPP(fun(fun(U_834,bool),U_834),bool,hAPP(fun(U_834,fun(U_834,U_834)),fun(fun(fun(U_834,bool),U_834),bool),finite_folding_one(U_834),U_831),U_830)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41])],[f_228_2]) ).

cnf(f_228_4,plain,
    ( sP41(U_833,U_832,U_834,U_830,U_831)
    | ~ hBOOL(hAPP(fun(U_834,bool),bool,finite_finite(U_834),U_832))
    | ~ hBOOL(hAPP(fun(fun(U_834,bool),U_834),bool,hAPP(fun(U_834,fun(U_834,U_834)),fun(fun(fun(U_834,bool),U_834),bool),finite_folding_one(U_834),U_831),U_830)) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_5,plain,
    ( hAPP(fun(U_834,bool),U_834,U_830,hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),U_832)) = ti(U_834,U_833)
    | hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(fun(U_834,bool),fun(fun(U_834,bool),fun(U_834,bool)),minus_minus(fun(U_834,bool)),U_832),hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),bot_bot(fun(U_834,bool)))) != bot_bot(fun(U_834,bool))
    | ~ sP41(U_833,U_832,U_834,U_830,U_831) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_6,plain,
    ( hAPP(fun(U_834,bool),U_834,U_830,hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),U_832)) = hAPP(U_834,U_834,hAPP(U_834,fun(U_834,U_834),U_831,U_833),hAPP(fun(U_834,bool),U_834,U_830,hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(fun(U_834,bool),fun(fun(U_834,bool),fun(U_834,bool)),minus_minus(fun(U_834,bool)),U_832),hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),bot_bot(fun(U_834,bool))))))
    | hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(fun(U_834,bool),fun(fun(U_834,bool),fun(U_834,bool)),minus_minus(fun(U_834,bool)),U_832),hAPP(fun(U_834,bool),fun(U_834,bool),hAPP(U_834,fun(fun(U_834,bool),fun(U_834,bool)),insert(U_834),U_833),bot_bot(fun(U_834,bool)))) = bot_bot(fun(U_834,bool))
    | ~ sP41(U_833,U_832,U_834,U_830,U_831) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

fof(f_229_1,plain,
    ! [X_b,A_3,A_2,B_2] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))),
    inference(fof_nnf,[status(thm)],[fact_176_Diff__insert]) ).

fof(f_229_2,plain,
    ! [U_838,U_837,U_836,U_835] : hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(fun(U_838,bool),fun(fun(U_838,bool),fun(U_838,bool)),minus_minus(fun(U_838,bool)),U_837),hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(U_838,fun(fun(U_838,bool),fun(U_838,bool)),insert(U_838),U_836),U_835)) = hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(fun(U_838,bool),fun(fun(U_838,bool),fun(U_838,bool)),minus_minus(fun(U_838,bool)),hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(fun(U_838,bool),fun(fun(U_838,bool),fun(U_838,bool)),minus_minus(fun(U_838,bool)),U_837),U_835)),hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(U_838,fun(fun(U_838,bool),fun(U_838,bool)),insert(U_838),U_836),bot_bot(fun(U_838,bool)))),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

fof(f_229_3,plain,
    ! [U_836,U_838,U_837,U_835] : hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(fun(U_838,bool),fun(fun(U_838,bool),fun(U_838,bool)),minus_minus(fun(U_838,bool)),U_837),hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(U_838,fun(fun(U_838,bool),fun(U_838,bool)),insert(U_838),U_836),U_835)) = hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(fun(U_838,bool),fun(fun(U_838,bool),fun(U_838,bool)),minus_minus(fun(U_838,bool)),hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(fun(U_838,bool),fun(fun(U_838,bool),fun(U_838,bool)),minus_minus(fun(U_838,bool)),U_837),U_835)),hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(U_838,fun(fun(U_838,bool),fun(U_838,bool)),insert(U_838),U_836),bot_bot(fun(U_838,bool)))),
    inference(definitional_conversion,[status(esa)],[f_229_2]) ).

cnf(f_229_4,plain,
    hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(fun(U_838,bool),fun(fun(U_838,bool),fun(U_838,bool)),minus_minus(fun(U_838,bool)),U_837),hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(U_838,fun(fun(U_838,bool),fun(U_838,bool)),insert(U_838),U_836),U_835)) = hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(fun(U_838,bool),fun(fun(U_838,bool),fun(U_838,bool)),minus_minus(fun(U_838,bool)),hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(fun(U_838,bool),fun(fun(U_838,bool),fun(U_838,bool)),minus_minus(fun(U_838,bool)),U_837),U_835)),hAPP(fun(U_838,bool),fun(U_838,bool),hAPP(U_838,fun(fun(U_838,bool),fun(U_838,bool)),insert(U_838),U_836),bot_bot(fun(U_838,bool)))),
    inference(clausify,[status(thm)],[f_229_3]) ).

fof(f_230_1,plain,
    ! [X_b,A_3,A_2,B_2] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),B_2),
    inference(fof_nnf,[status(thm)],[fact_177_Diff__insert2]) ).

fof(f_230_2,plain,
    ! [U_842,U_841,U_840,U_839] : hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(fun(U_842,bool),fun(fun(U_842,bool),fun(U_842,bool)),minus_minus(fun(U_842,bool)),U_841),hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(U_842,fun(fun(U_842,bool),fun(U_842,bool)),insert(U_842),U_840),U_839)) = hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(fun(U_842,bool),fun(fun(U_842,bool),fun(U_842,bool)),minus_minus(fun(U_842,bool)),hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(fun(U_842,bool),fun(fun(U_842,bool),fun(U_842,bool)),minus_minus(fun(U_842,bool)),U_841),hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(U_842,fun(fun(U_842,bool),fun(U_842,bool)),insert(U_842),U_840),bot_bot(fun(U_842,bool))))),U_839),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

fof(f_230_3,plain,
    ! [U_839,U_842,U_841,U_840] : hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(fun(U_842,bool),fun(fun(U_842,bool),fun(U_842,bool)),minus_minus(fun(U_842,bool)),U_841),hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(U_842,fun(fun(U_842,bool),fun(U_842,bool)),insert(U_842),U_840),U_839)) = hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(fun(U_842,bool),fun(fun(U_842,bool),fun(U_842,bool)),minus_minus(fun(U_842,bool)),hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(fun(U_842,bool),fun(fun(U_842,bool),fun(U_842,bool)),minus_minus(fun(U_842,bool)),U_841),hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(U_842,fun(fun(U_842,bool),fun(U_842,bool)),insert(U_842),U_840),bot_bot(fun(U_842,bool))))),U_839),
    inference(definitional_conversion,[status(esa)],[f_230_2]) ).

cnf(f_230_4,plain,
    hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(fun(U_842,bool),fun(fun(U_842,bool),fun(U_842,bool)),minus_minus(fun(U_842,bool)),U_841),hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(U_842,fun(fun(U_842,bool),fun(U_842,bool)),insert(U_842),U_840),U_839)) = hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(fun(U_842,bool),fun(fun(U_842,bool),fun(U_842,bool)),minus_minus(fun(U_842,bool)),hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(fun(U_842,bool),fun(fun(U_842,bool),fun(U_842,bool)),minus_minus(fun(U_842,bool)),U_841),hAPP(fun(U_842,bool),fun(U_842,bool),hAPP(U_842,fun(fun(U_842,bool),fun(U_842,bool)),insert(U_842),U_840),bot_bot(fun(U_842,bool))))),U_839),
    inference(clausify,[status(thm)],[f_230_3]) ).

fof(f_231_1,plain,
    ! [X_b,A_2,A_3] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3),
    inference(fof_nnf,[status(thm)],[fact_178_insert__Diff__single]) ).

fof(f_231_2,plain,
    ! [U_845,U_844,U_843] : hAPP(fun(U_845,bool),fun(U_845,bool),hAPP(U_845,fun(fun(U_845,bool),fun(U_845,bool)),insert(U_845),U_844),hAPP(fun(U_845,bool),fun(U_845,bool),hAPP(fun(U_845,bool),fun(fun(U_845,bool),fun(U_845,bool)),minus_minus(fun(U_845,bool)),U_843),hAPP(fun(U_845,bool),fun(U_845,bool),hAPP(U_845,fun(fun(U_845,bool),fun(U_845,bool)),insert(U_845),U_844),bot_bot(fun(U_845,bool))))) = hAPP(fun(U_845,bool),fun(U_845,bool),hAPP(U_845,fun(fun(U_845,bool),fun(U_845,bool)),insert(U_845),U_844),U_843),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

fof(f_231_3,plain,
    ! [U_845,U_843,U_844] : hAPP(fun(U_845,bool),fun(U_845,bool),hAPP(U_845,fun(fun(U_845,bool),fun(U_845,bool)),insert(U_845),U_844),hAPP(fun(U_845,bool),fun(U_845,bool),hAPP(fun(U_845,bool),fun(fun(U_845,bool),fun(U_845,bool)),minus_minus(fun(U_845,bool)),U_843),hAPP(fun(U_845,bool),fun(U_845,bool),hAPP(U_845,fun(fun(U_845,bool),fun(U_845,bool)),insert(U_845),U_844),bot_bot(fun(U_845,bool))))) = hAPP(fun(U_845,bool),fun(U_845,bool),hAPP(U_845,fun(fun(U_845,bool),fun(U_845,bool)),insert(U_845),U_844),U_843),
    inference(definitional_conversion,[status(esa)],[f_231_2]) ).

cnf(f_231_4,plain,
    hAPP(fun(U_845,bool),fun(U_845,bool),hAPP(U_845,fun(fun(U_845,bool),fun(U_845,bool)),insert(U_845),U_844),hAPP(fun(U_845,bool),fun(U_845,bool),hAPP(fun(U_845,bool),fun(fun(U_845,bool),fun(U_845,bool)),minus_minus(fun(U_845,bool)),U_843),hAPP(fun(U_845,bool),fun(U_845,bool),hAPP(U_845,fun(fun(U_845,bool),fun(U_845,bool)),insert(U_845),U_844),bot_bot(fun(U_845,bool))))) = hAPP(fun(U_845,bool),fun(U_845,bool),hAPP(U_845,fun(fun(U_845,bool),fun(U_845,bool)),insert(U_845),U_844),U_843),
    inference(clausify,[status(thm)],[f_231_3]) ).

fof(f_232_1,plain,
    ! [X_b,X_1,A_3] :
      ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(fun(X_b,bool),A_3)
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_179_Diff__insert__absorb]) ).

fof(f_232_2,plain,
    ! [U_848,U_847,U_846] :
      ( hAPP(fun(U_848,bool),fun(U_848,bool),hAPP(fun(U_848,bool),fun(fun(U_848,bool),fun(U_848,bool)),minus_minus(fun(U_848,bool)),hAPP(fun(U_848,bool),fun(U_848,bool),hAPP(U_848,fun(fun(U_848,bool),fun(U_848,bool)),insert(U_848),U_847),U_846)),hAPP(fun(U_848,bool),fun(U_848,bool),hAPP(U_848,fun(fun(U_848,bool),fun(U_848,bool)),insert(U_848),U_847),bot_bot(fun(U_848,bool)))) = ti(fun(U_848,bool),U_846)
      | hBOOL(hAPP(fun(U_848,bool),bool,hAPP(U_848,fun(fun(U_848,bool),bool),member(U_848),U_847),U_846)) ),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

fof(f_232_3,plain,
    ! [U_848,U_846,U_847] :
      ( hAPP(fun(U_848,bool),fun(U_848,bool),hAPP(fun(U_848,bool),fun(fun(U_848,bool),fun(U_848,bool)),minus_minus(fun(U_848,bool)),hAPP(fun(U_848,bool),fun(U_848,bool),hAPP(U_848,fun(fun(U_848,bool),fun(U_848,bool)),insert(U_848),U_847),U_846)),hAPP(fun(U_848,bool),fun(U_848,bool),hAPP(U_848,fun(fun(U_848,bool),fun(U_848,bool)),insert(U_848),U_847),bot_bot(fun(U_848,bool)))) = ti(fun(U_848,bool),U_846)
      | hBOOL(hAPP(fun(U_848,bool),bool,hAPP(U_848,fun(fun(U_848,bool),bool),member(U_848),U_847),U_846)) ),
    inference(definitional_conversion,[status(esa)],[f_232_2]) ).

cnf(f_232_4,plain,
    ( hAPP(fun(U_848,bool),fun(U_848,bool),hAPP(fun(U_848,bool),fun(fun(U_848,bool),fun(U_848,bool)),minus_minus(fun(U_848,bool)),hAPP(fun(U_848,bool),fun(U_848,bool),hAPP(U_848,fun(fun(U_848,bool),fun(U_848,bool)),insert(U_848),U_847),U_846)),hAPP(fun(U_848,bool),fun(U_848,bool),hAPP(U_848,fun(fun(U_848,bool),fun(U_848,bool)),insert(U_848),U_847),bot_bot(fun(U_848,bool)))) = ti(fun(U_848,bool),U_846)
    | hBOOL(hAPP(fun(U_848,bool),bool,hAPP(U_848,fun(fun(U_848,bool),bool),member(U_848),U_847),U_846)) ),
    inference(clausify,[status(thm)],[f_232_3]) ).

fof(f_233_1,plain,
    ! [X_b,A_2,A_3] :
      ( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = ti(fun(X_b,bool),A_3)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_180_insert__Diff]) ).

fof(f_233_2,plain,
    ! [U_851,U_850,U_849] :
      ( hAPP(fun(U_851,bool),fun(U_851,bool),hAPP(U_851,fun(fun(U_851,bool),fun(U_851,bool)),insert(U_851),U_850),hAPP(fun(U_851,bool),fun(U_851,bool),hAPP(fun(U_851,bool),fun(fun(U_851,bool),fun(U_851,bool)),minus_minus(fun(U_851,bool)),U_849),hAPP(fun(U_851,bool),fun(U_851,bool),hAPP(U_851,fun(fun(U_851,bool),fun(U_851,bool)),insert(U_851),U_850),bot_bot(fun(U_851,bool))))) = ti(fun(U_851,bool),U_849)
      | ~ hBOOL(hAPP(fun(U_851,bool),bool,hAPP(U_851,fun(fun(U_851,bool),bool),member(U_851),U_850),U_849)) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

fof(f_233_3,plain,
    ! [U_851,U_849,U_850] :
      ( hAPP(fun(U_851,bool),fun(U_851,bool),hAPP(U_851,fun(fun(U_851,bool),fun(U_851,bool)),insert(U_851),U_850),hAPP(fun(U_851,bool),fun(U_851,bool),hAPP(fun(U_851,bool),fun(fun(U_851,bool),fun(U_851,bool)),minus_minus(fun(U_851,bool)),U_849),hAPP(fun(U_851,bool),fun(U_851,bool),hAPP(U_851,fun(fun(U_851,bool),fun(U_851,bool)),insert(U_851),U_850),bot_bot(fun(U_851,bool))))) = ti(fun(U_851,bool),U_849)
      | ~ hBOOL(hAPP(fun(U_851,bool),bool,hAPP(U_851,fun(fun(U_851,bool),bool),member(U_851),U_850),U_849)) ),
    inference(definitional_conversion,[status(esa)],[f_233_2]) ).

cnf(f_233_4,plain,
    ( hAPP(fun(U_851,bool),fun(U_851,bool),hAPP(U_851,fun(fun(U_851,bool),fun(U_851,bool)),insert(U_851),U_850),hAPP(fun(U_851,bool),fun(U_851,bool),hAPP(fun(U_851,bool),fun(fun(U_851,bool),fun(U_851,bool)),minus_minus(fun(U_851,bool)),U_849),hAPP(fun(U_851,bool),fun(U_851,bool),hAPP(U_851,fun(fun(U_851,bool),fun(U_851,bool)),insert(U_851),U_850),bot_bot(fun(U_851,bool))))) = ti(fun(U_851,bool),U_849)
    | ~ hBOOL(hAPP(fun(U_851,bool),bool,hAPP(U_851,fun(fun(U_851,bool),bool),member(U_851),U_850),U_849)) ),
    inference(clausify,[status(thm)],[f_233_3]) ).

fof(f_234_1,plain,
    ! [X_b,A_3,A_2,B_2] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2))))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) )
      & ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_181_finite__Diff__insert]) ).

fof(f_234_2,plain,
    ! [U_855,U_854,U_853,U_852] :
      ( ( hBOOL(hAPP(fun(U_855,bool),bool,finite_finite(U_855),hAPP(fun(U_855,bool),fun(U_855,bool),hAPP(fun(U_855,bool),fun(fun(U_855,bool),fun(U_855,bool)),minus_minus(fun(U_855,bool)),U_854),hAPP(fun(U_855,bool),fun(U_855,bool),hAPP(U_855,fun(fun(U_855,bool),fun(U_855,bool)),insert(U_855),U_853),U_852))))
        | ~ hBOOL(hAPP(fun(U_855,bool),bool,finite_finite(U_855),hAPP(fun(U_855,bool),fun(U_855,bool),hAPP(fun(U_855,bool),fun(fun(U_855,bool),fun(U_855,bool)),minus_minus(fun(U_855,bool)),U_854),U_852))) )
      & ( hBOOL(hAPP(fun(U_855,bool),bool,finite_finite(U_855),hAPP(fun(U_855,bool),fun(U_855,bool),hAPP(fun(U_855,bool),fun(fun(U_855,bool),fun(U_855,bool)),minus_minus(fun(U_855,bool)),U_854),U_852)))
        | ~ hBOOL(hAPP(fun(U_855,bool),bool,finite_finite(U_855),hAPP(fun(U_855,bool),fun(U_855,bool),hAPP(fun(U_855,bool),fun(fun(U_855,bool),fun(U_855,bool)),minus_minus(fun(U_855,bool)),U_854),hAPP(fun(U_855,bool),fun(U_855,bool),hAPP(U_855,fun(fun(U_855,bool),fun(U_855,bool)),insert(U_855),U_853),U_852)))) ) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

fof(f_234_3,plain,
    ( ! [U_863,U_861,U_859,U_857] :
        ( hBOOL(hAPP(fun(U_863,bool),bool,finite_finite(U_863),hAPP(fun(U_863,bool),fun(U_863,bool),hAPP(fun(U_863,bool),fun(fun(U_863,bool),fun(U_863,bool)),minus_minus(fun(U_863,bool)),U_861),hAPP(fun(U_863,bool),fun(U_863,bool),hAPP(U_863,fun(fun(U_863,bool),fun(U_863,bool)),insert(U_863),U_859),U_857))))
        | ~ hBOOL(hAPP(fun(U_863,bool),bool,finite_finite(U_863),hAPP(fun(U_863,bool),fun(U_863,bool),hAPP(fun(U_863,bool),fun(fun(U_863,bool),fun(U_863,bool)),minus_minus(fun(U_863,bool)),U_861),U_857))) )
    & ! [U_862,U_860,U_858,U_856] :
        ( hBOOL(hAPP(fun(U_862,bool),bool,finite_finite(U_862),hAPP(fun(U_862,bool),fun(U_862,bool),hAPP(fun(U_862,bool),fun(fun(U_862,bool),fun(U_862,bool)),minus_minus(fun(U_862,bool)),U_860),U_856)))
        | ~ hBOOL(hAPP(fun(U_862,bool),bool,finite_finite(U_862),hAPP(fun(U_862,bool),fun(U_862,bool),hAPP(fun(U_862,bool),fun(fun(U_862,bool),fun(U_862,bool)),minus_minus(fun(U_862,bool)),U_860),hAPP(fun(U_862,bool),fun(U_862,bool),hAPP(U_862,fun(fun(U_862,bool),fun(U_862,bool)),insert(U_862),U_858),U_856)))) ) ),
    inference(miniscope,[status(thm)],[f_234_2]) ).

fof(f_234_4,plain,
    ( ! [U_863,U_857,U_859,U_861] :
        ( hBOOL(hAPP(fun(U_863,bool),bool,finite_finite(U_863),hAPP(fun(U_863,bool),fun(U_863,bool),hAPP(fun(U_863,bool),fun(fun(U_863,bool),fun(U_863,bool)),minus_minus(fun(U_863,bool)),U_861),hAPP(fun(U_863,bool),fun(U_863,bool),hAPP(U_863,fun(fun(U_863,bool),fun(U_863,bool)),insert(U_863),U_859),U_857))))
        | ~ hBOOL(hAPP(fun(U_863,bool),bool,finite_finite(U_863),hAPP(fun(U_863,bool),fun(U_863,bool),hAPP(fun(U_863,bool),fun(fun(U_863,bool),fun(U_863,bool)),minus_minus(fun(U_863,bool)),U_861),U_857))) )
    & ! [U_858,U_862,U_856,U_860] :
        ( hBOOL(hAPP(fun(U_862,bool),bool,finite_finite(U_862),hAPP(fun(U_862,bool),fun(U_862,bool),hAPP(fun(U_862,bool),fun(fun(U_862,bool),fun(U_862,bool)),minus_minus(fun(U_862,bool)),U_860),U_856)))
        | ~ hBOOL(hAPP(fun(U_862,bool),bool,finite_finite(U_862),hAPP(fun(U_862,bool),fun(U_862,bool),hAPP(fun(U_862,bool),fun(fun(U_862,bool),fun(U_862,bool)),minus_minus(fun(U_862,bool)),U_860),hAPP(fun(U_862,bool),fun(U_862,bool),hAPP(U_862,fun(fun(U_862,bool),fun(U_862,bool)),insert(U_862),U_858),U_856)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_234_3]) ).

cnf(f_234_5,plain,
    ( hBOOL(hAPP(fun(U_862,bool),bool,finite_finite(U_862),hAPP(fun(U_862,bool),fun(U_862,bool),hAPP(fun(U_862,bool),fun(fun(U_862,bool),fun(U_862,bool)),minus_minus(fun(U_862,bool)),U_860),U_856)))
    | ~ hBOOL(hAPP(fun(U_862,bool),bool,finite_finite(U_862),hAPP(fun(U_862,bool),fun(U_862,bool),hAPP(fun(U_862,bool),fun(fun(U_862,bool),fun(U_862,bool)),minus_minus(fun(U_862,bool)),U_860),hAPP(fun(U_862,bool),fun(U_862,bool),hAPP(U_862,fun(fun(U_862,bool),fun(U_862,bool)),insert(U_862),U_858),U_856)))) ),
    inference(clausify,[status(thm)],[f_234_4]) ).

cnf(f_234_6,plain,
    ( hBOOL(hAPP(fun(U_863,bool),bool,finite_finite(U_863),hAPP(fun(U_863,bool),fun(U_863,bool),hAPP(fun(U_863,bool),fun(fun(U_863,bool),fun(U_863,bool)),minus_minus(fun(U_863,bool)),U_861),hAPP(fun(U_863,bool),fun(U_863,bool),hAPP(U_863,fun(fun(U_863,bool),fun(U_863,bool)),insert(U_863),U_859),U_857))))
    | ~ hBOOL(hAPP(fun(U_863,bool),bool,finite_finite(U_863),hAPP(fun(U_863,bool),fun(U_863,bool),hAPP(fun(U_863,bool),fun(fun(U_863,bool),fun(U_863,bool)),minus_minus(fun(U_863,bool)),U_861),U_857))) ),
    inference(clausify,[status(thm)],[f_234_4]) ).

fof(f_235_1,plain,
    ! [X_b,X_c,F,A_3,B_2] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_2))),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),B_2)))),
    inference(fof_nnf,[status(thm)],[fact_182_image__diff__subset]) ).

fof(f_235_2,plain,
    ! [U_868,U_867,U_866,U_865,U_864] : hBOOL(hAPP(fun(U_868,bool),bool,hAPP(fun(U_868,bool),fun(fun(U_868,bool),bool),ord_less_eq(fun(U_868,bool)),hAPP(fun(U_868,bool),fun(U_868,bool),hAPP(fun(U_868,bool),fun(fun(U_868,bool),fun(U_868,bool)),minus_minus(fun(U_868,bool)),hAPP(fun(U_867,bool),fun(U_868,bool),hAPP(fun(U_867,U_868),fun(fun(U_867,bool),fun(U_868,bool)),image(U_867,U_868),U_866),U_865)),hAPP(fun(U_867,bool),fun(U_868,bool),hAPP(fun(U_867,U_868),fun(fun(U_867,bool),fun(U_868,bool)),image(U_867,U_868),U_866),U_864))),hAPP(fun(U_867,bool),fun(U_868,bool),hAPP(fun(U_867,U_868),fun(fun(U_867,bool),fun(U_868,bool)),image(U_867,U_868),U_866),hAPP(fun(U_867,bool),fun(U_867,bool),hAPP(fun(U_867,bool),fun(fun(U_867,bool),fun(U_867,bool)),minus_minus(fun(U_867,bool)),U_865),U_864)))),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

fof(f_235_3,plain,
    ! [U_864,U_865,U_868,U_866,U_867] : hBOOL(hAPP(fun(U_868,bool),bool,hAPP(fun(U_868,bool),fun(fun(U_868,bool),bool),ord_less_eq(fun(U_868,bool)),hAPP(fun(U_868,bool),fun(U_868,bool),hAPP(fun(U_868,bool),fun(fun(U_868,bool),fun(U_868,bool)),minus_minus(fun(U_868,bool)),hAPP(fun(U_867,bool),fun(U_868,bool),hAPP(fun(U_867,U_868),fun(fun(U_867,bool),fun(U_868,bool)),image(U_867,U_868),U_866),U_865)),hAPP(fun(U_867,bool),fun(U_868,bool),hAPP(fun(U_867,U_868),fun(fun(U_867,bool),fun(U_868,bool)),image(U_867,U_868),U_866),U_864))),hAPP(fun(U_867,bool),fun(U_868,bool),hAPP(fun(U_867,U_868),fun(fun(U_867,bool),fun(U_868,bool)),image(U_867,U_868),U_866),hAPP(fun(U_867,bool),fun(U_867,bool),hAPP(fun(U_867,bool),fun(fun(U_867,bool),fun(U_867,bool)),minus_minus(fun(U_867,bool)),U_865),U_864)))),
    inference(definitional_conversion,[status(esa)],[f_235_2]) ).

cnf(f_235_4,plain,
    hBOOL(hAPP(fun(U_868,bool),bool,hAPP(fun(U_868,bool),fun(fun(U_868,bool),bool),ord_less_eq(fun(U_868,bool)),hAPP(fun(U_868,bool),fun(U_868,bool),hAPP(fun(U_868,bool),fun(fun(U_868,bool),fun(U_868,bool)),minus_minus(fun(U_868,bool)),hAPP(fun(U_867,bool),fun(U_868,bool),hAPP(fun(U_867,U_868),fun(fun(U_867,bool),fun(U_868,bool)),image(U_867,U_868),U_866),U_865)),hAPP(fun(U_867,bool),fun(U_868,bool),hAPP(fun(U_867,U_868),fun(fun(U_867,bool),fun(U_868,bool)),image(U_867,U_868),U_866),U_864))),hAPP(fun(U_867,bool),fun(U_868,bool),hAPP(fun(U_867,U_868),fun(fun(U_867,bool),fun(U_868,bool)),image(U_867,U_868),U_866),hAPP(fun(U_867,bool),fun(U_867,bool),hAPP(fun(U_867,bool),fun(fun(U_867,bool),fun(U_867,bool)),minus_minus(fun(U_867,bool)),U_865),U_864)))),
    inference(clausify,[status(thm)],[f_235_3]) ).

fof(f_236_1,plain,
    ! [X_b,X_1,A_3,F,F_2] :
      ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3)) = hAPP(fun(X_b,bool),X_b,F_2,A_3)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_183_folding__one__idem_Oin__idem]) ).

fof(f_236_2,plain,
    ! [U_873,U_872,U_871,U_870,U_869] :
      ( hAPP(U_873,U_873,hAPP(U_873,fun(U_873,U_873),U_870,U_872),hAPP(fun(U_873,bool),U_873,U_869,U_871)) = hAPP(fun(U_873,bool),U_873,U_869,U_871)
      | ~ hBOOL(hAPP(fun(U_873,bool),bool,hAPP(U_873,fun(fun(U_873,bool),bool),member(U_873),U_872),U_871))
      | ~ hBOOL(hAPP(fun(U_873,bool),bool,finite_finite(U_873),U_871))
      | ~ hBOOL(hAPP(fun(fun(U_873,bool),U_873),bool,hAPP(fun(U_873,fun(U_873,U_873)),fun(fun(fun(U_873,bool),U_873),bool),finite2073411215e_idem(U_873),U_870),U_869)) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

fof(f_236_3,plain,
    ! [U_870,U_873,U_869,U_871,U_872] :
      ( hAPP(U_873,U_873,hAPP(U_873,fun(U_873,U_873),U_870,U_872),hAPP(fun(U_873,bool),U_873,U_869,U_871)) = hAPP(fun(U_873,bool),U_873,U_869,U_871)
      | ~ hBOOL(hAPP(fun(U_873,bool),bool,hAPP(U_873,fun(fun(U_873,bool),bool),member(U_873),U_872),U_871))
      | ~ hBOOL(hAPP(fun(U_873,bool),bool,finite_finite(U_873),U_871))
      | ~ hBOOL(hAPP(fun(fun(U_873,bool),U_873),bool,hAPP(fun(U_873,fun(U_873,U_873)),fun(fun(fun(U_873,bool),U_873),bool),finite2073411215e_idem(U_873),U_870),U_869)) ),
    inference(definitional_conversion,[status(esa)],[f_236_2]) ).

cnf(f_236_4,plain,
    ( hAPP(U_873,U_873,hAPP(U_873,fun(U_873,U_873),U_870,U_872),hAPP(fun(U_873,bool),U_873,U_869,U_871)) = hAPP(fun(U_873,bool),U_873,U_869,U_871)
    | ~ hBOOL(hAPP(fun(U_873,bool),bool,hAPP(U_873,fun(fun(U_873,bool),bool),member(U_873),U_872),U_871))
    | ~ hBOOL(hAPP(fun(U_873,bool),bool,finite_finite(U_873),U_871))
    | ~ hBOOL(hAPP(fun(fun(U_873,bool),U_873),bool,hAPP(fun(U_873,fun(U_873,U_873)),fun(fun(fun(U_873,bool),U_873),bool),finite2073411215e_idem(U_873),U_870),U_869)) ),
    inference(clausify,[status(thm)],[f_236_3]) ).

fof(f_237_1,plain,
    ! [X_b,A_3,X_1,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_184_diff__single__insert]) ).

fof(f_237_2,plain,
    ! [U_877,U_876,U_875,U_874] :
      ( hBOOL(hAPP(fun(U_877,bool),bool,hAPP(fun(U_877,bool),fun(fun(U_877,bool),bool),ord_less_eq(fun(U_877,bool)),U_876),hAPP(fun(U_877,bool),fun(U_877,bool),hAPP(U_877,fun(fun(U_877,bool),fun(U_877,bool)),insert(U_877),U_875),U_874)))
      | ~ hBOOL(hAPP(fun(U_877,bool),bool,hAPP(U_877,fun(fun(U_877,bool),bool),member(U_877),U_875),U_876))
      | ~ hBOOL(hAPP(fun(U_877,bool),bool,hAPP(fun(U_877,bool),fun(fun(U_877,bool),bool),ord_less_eq(fun(U_877,bool)),hAPP(fun(U_877,bool),fun(U_877,bool),hAPP(fun(U_877,bool),fun(fun(U_877,bool),fun(U_877,bool)),minus_minus(fun(U_877,bool)),U_876),hAPP(fun(U_877,bool),fun(U_877,bool),hAPP(U_877,fun(fun(U_877,bool),fun(U_877,bool)),insert(U_877),U_875),bot_bot(fun(U_877,bool))))),U_874)) ),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

fof(f_237_3,plain,
    ! [U_877,U_875,U_876,U_874] :
      ( hBOOL(hAPP(fun(U_877,bool),bool,hAPP(fun(U_877,bool),fun(fun(U_877,bool),bool),ord_less_eq(fun(U_877,bool)),U_876),hAPP(fun(U_877,bool),fun(U_877,bool),hAPP(U_877,fun(fun(U_877,bool),fun(U_877,bool)),insert(U_877),U_875),U_874)))
      | ~ hBOOL(hAPP(fun(U_877,bool),bool,hAPP(U_877,fun(fun(U_877,bool),bool),member(U_877),U_875),U_876))
      | ~ hBOOL(hAPP(fun(U_877,bool),bool,hAPP(fun(U_877,bool),fun(fun(U_877,bool),bool),ord_less_eq(fun(U_877,bool)),hAPP(fun(U_877,bool),fun(U_877,bool),hAPP(fun(U_877,bool),fun(fun(U_877,bool),fun(U_877,bool)),minus_minus(fun(U_877,bool)),U_876),hAPP(fun(U_877,bool),fun(U_877,bool),hAPP(U_877,fun(fun(U_877,bool),fun(U_877,bool)),insert(U_877),U_875),bot_bot(fun(U_877,bool))))),U_874)) ),
    inference(definitional_conversion,[status(esa)],[f_237_2]) ).

cnf(f_237_4,plain,
    ( hBOOL(hAPP(fun(U_877,bool),bool,hAPP(fun(U_877,bool),fun(fun(U_877,bool),bool),ord_less_eq(fun(U_877,bool)),U_876),hAPP(fun(U_877,bool),fun(U_877,bool),hAPP(U_877,fun(fun(U_877,bool),fun(U_877,bool)),insert(U_877),U_875),U_874)))
    | ~ hBOOL(hAPP(fun(U_877,bool),bool,hAPP(U_877,fun(fun(U_877,bool),bool),member(U_877),U_875),U_876))
    | ~ hBOOL(hAPP(fun(U_877,bool),bool,hAPP(fun(U_877,bool),fun(fun(U_877,bool),bool),ord_less_eq(fun(U_877,bool)),hAPP(fun(U_877,bool),fun(U_877,bool),hAPP(fun(U_877,bool),fun(fun(U_877,bool),fun(U_877,bool)),minus_minus(fun(U_877,bool)),U_876),hAPP(fun(U_877,bool),fun(U_877,bool),hAPP(U_877,fun(fun(U_877,bool),fun(U_877,bool)),insert(U_877),U_875),bot_bot(fun(U_877,bool))))),U_874)) ),
    inference(clausify,[status(thm)],[f_237_3]) ).

fof(f_238_1,plain,
    ! [X_b,A_3,X_1,B_2] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2)))
        | ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
          & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) )
        | ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_2))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ) )
      & ( ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
            | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) )
          & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_2))
            | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ) )
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_185_subset__insert__iff]) ).

fof(f_238_2,plain,
    ! [U_881,U_880,U_879,U_878] :
      ( ( hBOOL(hAPP(fun(U_881,bool),bool,hAPP(fun(U_881,bool),fun(fun(U_881,bool),bool),ord_less_eq(fun(U_881,bool)),U_880),hAPP(fun(U_881,bool),fun(U_881,bool),hAPP(U_881,fun(fun(U_881,bool),fun(U_881,bool)),insert(U_881),U_879),U_878)))
        | ( ~ hBOOL(hAPP(fun(U_881,bool),bool,hAPP(fun(U_881,bool),fun(fun(U_881,bool),bool),ord_less_eq(fun(U_881,bool)),U_880),U_878))
          & ~ hBOOL(hAPP(fun(U_881,bool),bool,hAPP(U_881,fun(fun(U_881,bool),bool),member(U_881),U_879),U_880)) )
        | ( ~ hBOOL(hAPP(fun(U_881,bool),bool,hAPP(fun(U_881,bool),fun(fun(U_881,bool),bool),ord_less_eq(fun(U_881,bool)),hAPP(fun(U_881,bool),fun(U_881,bool),hAPP(fun(U_881,bool),fun(fun(U_881,bool),fun(U_881,bool)),minus_minus(fun(U_881,bool)),U_880),hAPP(fun(U_881,bool),fun(U_881,bool),hAPP(U_881,fun(fun(U_881,bool),fun(U_881,bool)),insert(U_881),U_879),bot_bot(fun(U_881,bool))))),U_878))
          & hBOOL(hAPP(fun(U_881,bool),bool,hAPP(U_881,fun(fun(U_881,bool),bool),member(U_881),U_879),U_880)) ) )
      & ( ( ( hBOOL(hAPP(fun(U_881,bool),bool,hAPP(fun(U_881,bool),fun(fun(U_881,bool),bool),ord_less_eq(fun(U_881,bool)),U_880),U_878))
            | hBOOL(hAPP(fun(U_881,bool),bool,hAPP(U_881,fun(fun(U_881,bool),bool),member(U_881),U_879),U_880)) )
          & ( hBOOL(hAPP(fun(U_881,bool),bool,hAPP(fun(U_881,bool),fun(fun(U_881,bool),bool),ord_less_eq(fun(U_881,bool)),hAPP(fun(U_881,bool),fun(U_881,bool),hAPP(fun(U_881,bool),fun(fun(U_881,bool),fun(U_881,bool)),minus_minus(fun(U_881,bool)),U_880),hAPP(fun(U_881,bool),fun(U_881,bool),hAPP(U_881,fun(fun(U_881,bool),fun(U_881,bool)),insert(U_881),U_879),bot_bot(fun(U_881,bool))))),U_878))
            | ~ hBOOL(hAPP(fun(U_881,bool),bool,hAPP(U_881,fun(fun(U_881,bool),bool),member(U_881),U_879),U_880)) ) )
        | ~ hBOOL(hAPP(fun(U_881,bool),bool,hAPP(fun(U_881,bool),fun(fun(U_881,bool),bool),ord_less_eq(fun(U_881,bool)),U_880),hAPP(fun(U_881,bool),fun(U_881,bool),hAPP(U_881,fun(fun(U_881,bool),fun(U_881,bool)),insert(U_881),U_879),U_878))) ) ),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

fof(f_238_3,plain,
    ( ! [U_889,U_887,U_885,U_883] :
        ( hBOOL(hAPP(fun(U_889,bool),bool,hAPP(fun(U_889,bool),fun(fun(U_889,bool),bool),ord_less_eq(fun(U_889,bool)),U_887),hAPP(fun(U_889,bool),fun(U_889,bool),hAPP(U_889,fun(fun(U_889,bool),fun(U_889,bool)),insert(U_889),U_885),U_883)))
        | ( ~ hBOOL(hAPP(fun(U_889,bool),bool,hAPP(fun(U_889,bool),fun(fun(U_889,bool),bool),ord_less_eq(fun(U_889,bool)),U_887),U_883))
          & ~ hBOOL(hAPP(fun(U_889,bool),bool,hAPP(U_889,fun(fun(U_889,bool),bool),member(U_889),U_885),U_887)) )
        | ( ~ hBOOL(hAPP(fun(U_889,bool),bool,hAPP(fun(U_889,bool),fun(fun(U_889,bool),bool),ord_less_eq(fun(U_889,bool)),hAPP(fun(U_889,bool),fun(U_889,bool),hAPP(fun(U_889,bool),fun(fun(U_889,bool),fun(U_889,bool)),minus_minus(fun(U_889,bool)),U_887),hAPP(fun(U_889,bool),fun(U_889,bool),hAPP(U_889,fun(fun(U_889,bool),fun(U_889,bool)),insert(U_889),U_885),bot_bot(fun(U_889,bool))))),U_883))
          & hBOOL(hAPP(fun(U_889,bool),bool,hAPP(U_889,fun(fun(U_889,bool),bool),member(U_889),U_885),U_887)) ) )
    & ! [U_888,U_886,U_884,U_882] :
        ( ( ( hBOOL(hAPP(fun(U_888,bool),bool,hAPP(fun(U_888,bool),fun(fun(U_888,bool),bool),ord_less_eq(fun(U_888,bool)),U_886),U_882))
            | hBOOL(hAPP(fun(U_888,bool),bool,hAPP(U_888,fun(fun(U_888,bool),bool),member(U_888),U_884),U_886)) )
          & ( hBOOL(hAPP(fun(U_888,bool),bool,hAPP(fun(U_888,bool),fun(fun(U_888,bool),bool),ord_less_eq(fun(U_888,bool)),hAPP(fun(U_888,bool),fun(U_888,bool),hAPP(fun(U_888,bool),fun(fun(U_888,bool),fun(U_888,bool)),minus_minus(fun(U_888,bool)),U_886),hAPP(fun(U_888,bool),fun(U_888,bool),hAPP(U_888,fun(fun(U_888,bool),fun(U_888,bool)),insert(U_888),U_884),bot_bot(fun(U_888,bool))))),U_882))
            | ~ hBOOL(hAPP(fun(U_888,bool),bool,hAPP(U_888,fun(fun(U_888,bool),bool),member(U_888),U_884),U_886)) ) )
        | ~ hBOOL(hAPP(fun(U_888,bool),bool,hAPP(fun(U_888,bool),fun(fun(U_888,bool),bool),ord_less_eq(fun(U_888,bool)),U_886),hAPP(fun(U_888,bool),fun(U_888,bool),hAPP(U_888,fun(fun(U_888,bool),fun(U_888,bool)),insert(U_888),U_884),U_882))) ) ),
    inference(miniscope,[status(thm)],[f_238_2]) ).

fof(f_238_4,plain,
    ( ! [U_885,U_887,U_883,U_889] :
        ( ~ hBOOL(hAPP(fun(U_889,bool),bool,hAPP(fun(U_889,bool),fun(fun(U_889,bool),bool),ord_less_eq(fun(U_889,bool)),U_887),U_883))
        | ~ sP44(U_885,U_887,U_883,U_889) )
    & ! [U_885,U_887,U_883,U_889] :
        ( ~ hBOOL(hAPP(fun(U_889,bool),bool,hAPP(U_889,fun(fun(U_889,bool),bool),member(U_889),U_885),U_887))
        | ~ sP44(U_885,U_887,U_883,U_889) )
    & ! [U_885,U_887,U_883,U_889] :
        ( ~ hBOOL(hAPP(fun(U_889,bool),bool,hAPP(fun(U_889,bool),fun(fun(U_889,bool),bool),ord_less_eq(fun(U_889,bool)),hAPP(fun(U_889,bool),fun(U_889,bool),hAPP(fun(U_889,bool),fun(fun(U_889,bool),fun(U_889,bool)),minus_minus(fun(U_889,bool)),U_887),hAPP(fun(U_889,bool),fun(U_889,bool),hAPP(U_889,fun(fun(U_889,bool),fun(U_889,bool)),insert(U_889),U_885),bot_bot(fun(U_889,bool))))),U_883))
        | ~ sP43(U_885,U_887,U_883,U_889) )
    & ! [U_885,U_887,U_883,U_889] :
        ( hBOOL(hAPP(fun(U_889,bool),bool,hAPP(U_889,fun(fun(U_889,bool),bool),member(U_889),U_885),U_887))
        | ~ sP43(U_885,U_887,U_883,U_889) )
    & ! [U_886,U_888,U_882,U_884] :
        ( hBOOL(hAPP(fun(U_888,bool),bool,hAPP(fun(U_888,bool),fun(fun(U_888,bool),bool),ord_less_eq(fun(U_888,bool)),U_886),U_882))
        | hBOOL(hAPP(fun(U_888,bool),bool,hAPP(U_888,fun(fun(U_888,bool),bool),member(U_888),U_884),U_886))
        | ~ sP42(U_886,U_888,U_882,U_884) )
    & ! [U_886,U_888,U_882,U_884] :
        ( hBOOL(hAPP(fun(U_888,bool),bool,hAPP(fun(U_888,bool),fun(fun(U_888,bool),bool),ord_less_eq(fun(U_888,bool)),hAPP(fun(U_888,bool),fun(U_888,bool),hAPP(fun(U_888,bool),fun(fun(U_888,bool),fun(U_888,bool)),minus_minus(fun(U_888,bool)),U_886),hAPP(fun(U_888,bool),fun(U_888,bool),hAPP(U_888,fun(fun(U_888,bool),fun(U_888,bool)),insert(U_888),U_884),bot_bot(fun(U_888,bool))))),U_882))
        | ~ hBOOL(hAPP(fun(U_888,bool),bool,hAPP(U_888,fun(fun(U_888,bool),bool),member(U_888),U_884),U_886))
        | ~ sP42(U_886,U_888,U_882,U_884) )
    & ! [U_885,U_887,U_883,U_889] :
        ( hBOOL(hAPP(fun(U_889,bool),bool,hAPP(fun(U_889,bool),fun(fun(U_889,bool),bool),ord_less_eq(fun(U_889,bool)),U_887),hAPP(fun(U_889,bool),fun(U_889,bool),hAPP(U_889,fun(fun(U_889,bool),fun(U_889,bool)),insert(U_889),U_885),U_883)))
        | sP44(U_885,U_887,U_883,U_889)
        | sP43(U_885,U_887,U_883,U_889) )
    & ! [U_886,U_888,U_882,U_884] :
        ( sP42(U_886,U_888,U_882,U_884)
        | ~ hBOOL(hAPP(fun(U_888,bool),bool,hAPP(fun(U_888,bool),fun(fun(U_888,bool),bool),ord_less_eq(fun(U_888,bool)),U_886),hAPP(fun(U_888,bool),fun(U_888,bool),hAPP(U_888,fun(fun(U_888,bool),fun(U_888,bool)),insert(U_888),U_884),U_882))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42,sP43,sP44])],[f_238_3]) ).

cnf(f_238_5,plain,
    ( sP42(U_886,U_888,U_882,U_884)
    | ~ hBOOL(hAPP(fun(U_888,bool),bool,hAPP(fun(U_888,bool),fun(fun(U_888,bool),bool),ord_less_eq(fun(U_888,bool)),U_886),hAPP(fun(U_888,bool),fun(U_888,bool),hAPP(U_888,fun(fun(U_888,bool),fun(U_888,bool)),insert(U_888),U_884),U_882))) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_6,plain,
    ( hBOOL(hAPP(fun(U_889,bool),bool,hAPP(fun(U_889,bool),fun(fun(U_889,bool),bool),ord_less_eq(fun(U_889,bool)),U_887),hAPP(fun(U_889,bool),fun(U_889,bool),hAPP(U_889,fun(fun(U_889,bool),fun(U_889,bool)),insert(U_889),U_885),U_883)))
    | sP44(U_885,U_887,U_883,U_889)
    | sP43(U_885,U_887,U_883,U_889) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_7,plain,
    ( hBOOL(hAPP(fun(U_888,bool),bool,hAPP(fun(U_888,bool),fun(fun(U_888,bool),bool),ord_less_eq(fun(U_888,bool)),hAPP(fun(U_888,bool),fun(U_888,bool),hAPP(fun(U_888,bool),fun(fun(U_888,bool),fun(U_888,bool)),minus_minus(fun(U_888,bool)),U_886),hAPP(fun(U_888,bool),fun(U_888,bool),hAPP(U_888,fun(fun(U_888,bool),fun(U_888,bool)),insert(U_888),U_884),bot_bot(fun(U_888,bool))))),U_882))
    | ~ hBOOL(hAPP(fun(U_888,bool),bool,hAPP(U_888,fun(fun(U_888,bool),bool),member(U_888),U_884),U_886))
    | ~ sP42(U_886,U_888,U_882,U_884) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_8,plain,
    ( hBOOL(hAPP(fun(U_888,bool),bool,hAPP(fun(U_888,bool),fun(fun(U_888,bool),bool),ord_less_eq(fun(U_888,bool)),U_886),U_882))
    | hBOOL(hAPP(fun(U_888,bool),bool,hAPP(U_888,fun(fun(U_888,bool),bool),member(U_888),U_884),U_886))
    | ~ sP42(U_886,U_888,U_882,U_884) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_9,plain,
    ( hBOOL(hAPP(fun(U_889,bool),bool,hAPP(U_889,fun(fun(U_889,bool),bool),member(U_889),U_885),U_887))
    | ~ sP43(U_885,U_887,U_883,U_889) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_10,plain,
    ( ~ hBOOL(hAPP(fun(U_889,bool),bool,hAPP(fun(U_889,bool),fun(fun(U_889,bool),bool),ord_less_eq(fun(U_889,bool)),hAPP(fun(U_889,bool),fun(U_889,bool),hAPP(fun(U_889,bool),fun(fun(U_889,bool),fun(U_889,bool)),minus_minus(fun(U_889,bool)),U_887),hAPP(fun(U_889,bool),fun(U_889,bool),hAPP(U_889,fun(fun(U_889,bool),fun(U_889,bool)),insert(U_889),U_885),bot_bot(fun(U_889,bool))))),U_883))
    | ~ sP43(U_885,U_887,U_883,U_889) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_11,plain,
    ( ~ hBOOL(hAPP(fun(U_889,bool),bool,hAPP(U_889,fun(fun(U_889,bool),bool),member(U_889),U_885),U_887))
    | ~ sP44(U_885,U_887,U_883,U_889) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

cnf(f_238_12,plain,
    ( ~ hBOOL(hAPP(fun(U_889,bool),bool,hAPP(fun(U_889,bool),fun(fun(U_889,bool),bool),ord_less_eq(fun(U_889,bool)),U_887),U_883))
    | ~ sP44(U_885,U_887,U_883,U_889) ),
    inference(clausify,[status(thm)],[f_238_4]) ).

fof(f_239_1,plain,
    ! [X_b] :
      ( ! [A_2,B,C_1,D_1] :
          ( ( ( ti(X_b,A_2) = ti(X_b,B)
              | ti(X_b,C_1) != ti(X_b,D_1) )
            & ( ti(X_b,C_1) = ti(X_b,D_1)
              | ti(X_b,A_2) != ti(X_b,B) ) )
          | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1) )
      | ~ ab_group_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_186_diff__eq__diff__eq]) ).

fof(f_239_2,plain,
    ! [U_894] :
      ( ! [U_893,U_892,U_891,U_890] :
          ( ( ( ti(U_894,U_893) = ti(U_894,U_892)
              | ti(U_894,U_891) != ti(U_894,U_890) )
            & ( ti(U_894,U_891) = ti(U_894,U_890)
              | ti(U_894,U_893) != ti(U_894,U_892) ) )
          | hAPP(U_894,U_894,hAPP(U_894,fun(U_894,U_894),minus_minus(U_894),U_893),U_892) != hAPP(U_894,U_894,hAPP(U_894,fun(U_894,U_894),minus_minus(U_894),U_891),U_890) )
      | ~ ab_group_add(U_894) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

fof(f_239_3,plain,
    ( ! [U_892,U_894,U_891,U_890,U_893] :
        ( ti(U_894,U_893) = ti(U_894,U_892)
        | ti(U_894,U_891) != ti(U_894,U_890)
        | ~ sP45(U_892,U_894,U_891,U_890,U_893) )
    & ! [U_892,U_894,U_891,U_890,U_893] :
        ( ti(U_894,U_891) = ti(U_894,U_890)
        | ti(U_894,U_893) != ti(U_894,U_892)
        | ~ sP45(U_892,U_894,U_891,U_890,U_893) )
    & ! [U_892,U_894,U_891,U_890,U_893] :
        ( sP45(U_892,U_894,U_891,U_890,U_893)
        | hAPP(U_894,U_894,hAPP(U_894,fun(U_894,U_894),minus_minus(U_894),U_893),U_892) != hAPP(U_894,U_894,hAPP(U_894,fun(U_894,U_894),minus_minus(U_894),U_891),U_890)
        | ~ ab_group_add(U_894) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45])],[f_239_2]) ).

cnf(f_239_4,plain,
    ( sP45(U_892,U_894,U_891,U_890,U_893)
    | hAPP(U_894,U_894,hAPP(U_894,fun(U_894,U_894),minus_minus(U_894),U_893),U_892) != hAPP(U_894,U_894,hAPP(U_894,fun(U_894,U_894),minus_minus(U_894),U_891),U_890)
    | ~ ab_group_add(U_894) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

cnf(f_239_5,plain,
    ( ti(U_894,U_891) = ti(U_894,U_890)
    | ti(U_894,U_893) != ti(U_894,U_892)
    | ~ sP45(U_892,U_894,U_891,U_890,U_893) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

cnf(f_239_6,plain,
    ( ti(U_894,U_893) = ti(U_894,U_892)
    | ti(U_894,U_891) != ti(U_894,U_890)
    | ~ sP45(U_892,U_894,U_891,U_890,U_893) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

fof(f_240_1,plain,
    ! [X_b,X_1,F,F_2] :
      ( hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_187_folding__one_Osingleton]) ).

fof(f_240_2,plain,
    ! [U_898,U_897,U_896,U_895] :
      ( hAPP(fun(U_898,bool),U_898,U_895,hAPP(fun(U_898,bool),fun(U_898,bool),hAPP(U_898,fun(fun(U_898,bool),fun(U_898,bool)),insert(U_898),U_897),bot_bot(fun(U_898,bool)))) = ti(U_898,U_897)
      | ~ hBOOL(hAPP(fun(fun(U_898,bool),U_898),bool,hAPP(fun(U_898,fun(U_898,U_898)),fun(fun(fun(U_898,bool),U_898),bool),finite_folding_one(U_898),U_896),U_895)) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

fof(f_240_3,plain,
    ! [U_896,U_895,U_897,U_898] :
      ( hAPP(fun(U_898,bool),U_898,U_895,hAPP(fun(U_898,bool),fun(U_898,bool),hAPP(U_898,fun(fun(U_898,bool),fun(U_898,bool)),insert(U_898),U_897),bot_bot(fun(U_898,bool)))) = ti(U_898,U_897)
      | ~ hBOOL(hAPP(fun(fun(U_898,bool),U_898),bool,hAPP(fun(U_898,fun(U_898,U_898)),fun(fun(fun(U_898,bool),U_898),bool),finite_folding_one(U_898),U_896),U_895)) ),
    inference(definitional_conversion,[status(esa)],[f_240_2]) ).

cnf(f_240_4,plain,
    ( hAPP(fun(U_898,bool),U_898,U_895,hAPP(fun(U_898,bool),fun(U_898,bool),hAPP(U_898,fun(fun(U_898,bool),fun(U_898,bool)),insert(U_898),U_897),bot_bot(fun(U_898,bool)))) = ti(U_898,U_897)
    | ~ hBOOL(hAPP(fun(fun(U_898,bool),U_898),bool,hAPP(fun(U_898,fun(U_898,U_898)),fun(fun(fun(U_898,bool),U_898),bool),finite_folding_one(U_898),U_896),U_895)) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

fof(f_241_1,plain,
    ! [X_b,A_3,B_2] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_188_card__Diff__subset]) ).

fof(f_241_2,plain,
    ! [U_901,U_900,U_899] :
      ( hAPP(fun(U_901,bool),nat,finite_card(U_901),hAPP(fun(U_901,bool),fun(U_901,bool),hAPP(fun(U_901,bool),fun(fun(U_901,bool),fun(U_901,bool)),minus_minus(fun(U_901,bool)),U_900),U_899)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_901,bool),nat,finite_card(U_901),U_900)),hAPP(fun(U_901,bool),nat,finite_card(U_901),U_899))
      | ~ hBOOL(hAPP(fun(U_901,bool),bool,hAPP(fun(U_901,bool),fun(fun(U_901,bool),bool),ord_less_eq(fun(U_901,bool)),U_899),U_900))
      | ~ hBOOL(hAPP(fun(U_901,bool),bool,finite_finite(U_901),U_899)) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

fof(f_241_3,plain,
    ! [U_899,U_900,U_901] :
      ( hAPP(fun(U_901,bool),nat,finite_card(U_901),hAPP(fun(U_901,bool),fun(U_901,bool),hAPP(fun(U_901,bool),fun(fun(U_901,bool),fun(U_901,bool)),minus_minus(fun(U_901,bool)),U_900),U_899)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_901,bool),nat,finite_card(U_901),U_900)),hAPP(fun(U_901,bool),nat,finite_card(U_901),U_899))
      | ~ hBOOL(hAPP(fun(U_901,bool),bool,hAPP(fun(U_901,bool),fun(fun(U_901,bool),bool),ord_less_eq(fun(U_901,bool)),U_899),U_900))
      | ~ hBOOL(hAPP(fun(U_901,bool),bool,finite_finite(U_901),U_899)) ),
    inference(definitional_conversion,[status(esa)],[f_241_2]) ).

cnf(f_241_4,plain,
    ( hAPP(fun(U_901,bool),nat,finite_card(U_901),hAPP(fun(U_901,bool),fun(U_901,bool),hAPP(fun(U_901,bool),fun(fun(U_901,bool),fun(U_901,bool)),minus_minus(fun(U_901,bool)),U_900),U_899)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_901,bool),nat,finite_card(U_901),U_900)),hAPP(fun(U_901,bool),nat,finite_card(U_901),U_899))
    | ~ hBOOL(hAPP(fun(U_901,bool),bool,hAPP(fun(U_901,bool),fun(fun(U_901,bool),bool),ord_less_eq(fun(U_901,bool)),U_899),U_900))
    | ~ hBOOL(hAPP(fun(U_901,bool),bool,finite_finite(U_901),U_899)) ),
    inference(clausify,[status(thm)],[f_241_3]) ).

fof(f_242_1,plain,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_189_diff__card__le__card__Diff]) ).

fof(f_242_2,plain,
    ! [U_904,U_903,U_902] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_904,bool),nat,finite_card(U_904),U_903)),hAPP(fun(U_904,bool),nat,finite_card(U_904),U_902))),hAPP(fun(U_904,bool),nat,finite_card(U_904),hAPP(fun(U_904,bool),fun(U_904,bool),hAPP(fun(U_904,bool),fun(fun(U_904,bool),fun(U_904,bool)),minus_minus(fun(U_904,bool)),U_903),U_902))))
      | ~ hBOOL(hAPP(fun(U_904,bool),bool,finite_finite(U_904),U_902)) ),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

fof(f_242_3,plain,
    ! [U_902,U_904,U_903] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_904,bool),nat,finite_card(U_904),U_903)),hAPP(fun(U_904,bool),nat,finite_card(U_904),U_902))),hAPP(fun(U_904,bool),nat,finite_card(U_904),hAPP(fun(U_904,bool),fun(U_904,bool),hAPP(fun(U_904,bool),fun(fun(U_904,bool),fun(U_904,bool)),minus_minus(fun(U_904,bool)),U_903),U_902))))
      | ~ hBOOL(hAPP(fun(U_904,bool),bool,finite_finite(U_904),U_902)) ),
    inference(definitional_conversion,[status(esa)],[f_242_2]) ).

cnf(f_242_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_904,bool),nat,finite_card(U_904),U_903)),hAPP(fun(U_904,bool),nat,finite_card(U_904),U_902))),hAPP(fun(U_904,bool),nat,finite_card(U_904),hAPP(fun(U_904,bool),fun(U_904,bool),hAPP(fun(U_904,bool),fun(fun(U_904,bool),fun(U_904,bool)),minus_minus(fun(U_904,bool)),U_903),U_902))))
    | ~ hBOOL(hAPP(fun(U_904,bool),bool,finite_finite(U_904),U_902)) ),
    inference(clausify,[status(thm)],[f_242_3]) ).

fof(f_243_1,plain,
    ! [X_b,X_1,A_3] :
      ( hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_190_card__Suc__Diff1]) ).

fof(f_243_2,plain,
    ! [U_907,U_906,U_905] :
      ( hAPP(nat,nat,suc,hAPP(fun(U_907,bool),nat,finite_card(U_907),hAPP(fun(U_907,bool),fun(U_907,bool),hAPP(fun(U_907,bool),fun(fun(U_907,bool),fun(U_907,bool)),minus_minus(fun(U_907,bool)),U_905),hAPP(fun(U_907,bool),fun(U_907,bool),hAPP(U_907,fun(fun(U_907,bool),fun(U_907,bool)),insert(U_907),U_906),bot_bot(fun(U_907,bool)))))) = hAPP(fun(U_907,bool),nat,finite_card(U_907),U_905)
      | ~ hBOOL(hAPP(fun(U_907,bool),bool,hAPP(U_907,fun(fun(U_907,bool),bool),member(U_907),U_906),U_905))
      | ~ hBOOL(hAPP(fun(U_907,bool),bool,finite_finite(U_907),U_905)) ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

fof(f_243_3,plain,
    ! [U_906,U_905,U_907] :
      ( hAPP(nat,nat,suc,hAPP(fun(U_907,bool),nat,finite_card(U_907),hAPP(fun(U_907,bool),fun(U_907,bool),hAPP(fun(U_907,bool),fun(fun(U_907,bool),fun(U_907,bool)),minus_minus(fun(U_907,bool)),U_905),hAPP(fun(U_907,bool),fun(U_907,bool),hAPP(U_907,fun(fun(U_907,bool),fun(U_907,bool)),insert(U_907),U_906),bot_bot(fun(U_907,bool)))))) = hAPP(fun(U_907,bool),nat,finite_card(U_907),U_905)
      | ~ hBOOL(hAPP(fun(U_907,bool),bool,hAPP(U_907,fun(fun(U_907,bool),bool),member(U_907),U_906),U_905))
      | ~ hBOOL(hAPP(fun(U_907,bool),bool,finite_finite(U_907),U_905)) ),
    inference(definitional_conversion,[status(esa)],[f_243_2]) ).

cnf(f_243_4,plain,
    ( hAPP(nat,nat,suc,hAPP(fun(U_907,bool),nat,finite_card(U_907),hAPP(fun(U_907,bool),fun(U_907,bool),hAPP(fun(U_907,bool),fun(fun(U_907,bool),fun(U_907,bool)),minus_minus(fun(U_907,bool)),U_905),hAPP(fun(U_907,bool),fun(U_907,bool),hAPP(U_907,fun(fun(U_907,bool),fun(U_907,bool)),insert(U_907),U_906),bot_bot(fun(U_907,bool)))))) = hAPP(fun(U_907,bool),nat,finite_card(U_907),U_905)
    | ~ hBOOL(hAPP(fun(U_907,bool),bool,hAPP(U_907,fun(fun(U_907,bool),bool),member(U_907),U_906),U_905))
    | ~ hBOOL(hAPP(fun(U_907,bool),bool,finite_finite(U_907),U_905)) ),
    inference(clausify,[status(thm)],[f_243_3]) ).

fof(f_244_1,plain,
    ! [X_b,X_1,A_3] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_191_card__insert]) ).

fof(f_244_2,plain,
    ! [U_910,U_909,U_908] :
      ( hAPP(fun(U_910,bool),nat,finite_card(U_910),hAPP(fun(U_910,bool),fun(U_910,bool),hAPP(U_910,fun(fun(U_910,bool),fun(U_910,bool)),insert(U_910),U_909),U_908)) = hAPP(nat,nat,suc,hAPP(fun(U_910,bool),nat,finite_card(U_910),hAPP(fun(U_910,bool),fun(U_910,bool),hAPP(fun(U_910,bool),fun(fun(U_910,bool),fun(U_910,bool)),minus_minus(fun(U_910,bool)),U_908),hAPP(fun(U_910,bool),fun(U_910,bool),hAPP(U_910,fun(fun(U_910,bool),fun(U_910,bool)),insert(U_910),U_909),bot_bot(fun(U_910,bool))))))
      | ~ hBOOL(hAPP(fun(U_910,bool),bool,finite_finite(U_910),U_908)) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

fof(f_244_3,plain,
    ! [U_909,U_908,U_910] :
      ( hAPP(fun(U_910,bool),nat,finite_card(U_910),hAPP(fun(U_910,bool),fun(U_910,bool),hAPP(U_910,fun(fun(U_910,bool),fun(U_910,bool)),insert(U_910),U_909),U_908)) = hAPP(nat,nat,suc,hAPP(fun(U_910,bool),nat,finite_card(U_910),hAPP(fun(U_910,bool),fun(U_910,bool),hAPP(fun(U_910,bool),fun(fun(U_910,bool),fun(U_910,bool)),minus_minus(fun(U_910,bool)),U_908),hAPP(fun(U_910,bool),fun(U_910,bool),hAPP(U_910,fun(fun(U_910,bool),fun(U_910,bool)),insert(U_910),U_909),bot_bot(fun(U_910,bool))))))
      | ~ hBOOL(hAPP(fun(U_910,bool),bool,finite_finite(U_910),U_908)) ),
    inference(definitional_conversion,[status(esa)],[f_244_2]) ).

cnf(f_244_4,plain,
    ( hAPP(fun(U_910,bool),nat,finite_card(U_910),hAPP(fun(U_910,bool),fun(U_910,bool),hAPP(U_910,fun(fun(U_910,bool),fun(U_910,bool)),insert(U_910),U_909),U_908)) = hAPP(nat,nat,suc,hAPP(fun(U_910,bool),nat,finite_card(U_910),hAPP(fun(U_910,bool),fun(U_910,bool),hAPP(fun(U_910,bool),fun(fun(U_910,bool),fun(U_910,bool)),minus_minus(fun(U_910,bool)),U_908),hAPP(fun(U_910,bool),fun(U_910,bool),hAPP(U_910,fun(fun(U_910,bool),fun(U_910,bool)),insert(U_910),U_909),bot_bot(fun(U_910,bool))))))
    | ~ hBOOL(hAPP(fun(U_910,bool),bool,finite_finite(U_910),U_908)) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

fof(f_245_1,plain,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_192_card__Diff1__le]) ).

fof(f_245_2,plain,
    ! [U_913,U_912,U_911] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_913,bool),nat,finite_card(U_913),hAPP(fun(U_913,bool),fun(U_913,bool),hAPP(fun(U_913,bool),fun(fun(U_913,bool),fun(U_913,bool)),minus_minus(fun(U_913,bool)),U_911),hAPP(fun(U_913,bool),fun(U_913,bool),hAPP(U_913,fun(fun(U_913,bool),fun(U_913,bool)),insert(U_913),U_912),bot_bot(fun(U_913,bool)))))),hAPP(fun(U_913,bool),nat,finite_card(U_913),U_911)))
      | ~ hBOOL(hAPP(fun(U_913,bool),bool,finite_finite(U_913),U_911)) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ! [U_913,U_911,U_912] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_913,bool),nat,finite_card(U_913),hAPP(fun(U_913,bool),fun(U_913,bool),hAPP(fun(U_913,bool),fun(fun(U_913,bool),fun(U_913,bool)),minus_minus(fun(U_913,bool)),U_911),hAPP(fun(U_913,bool),fun(U_913,bool),hAPP(U_913,fun(fun(U_913,bool),fun(U_913,bool)),insert(U_913),U_912),bot_bot(fun(U_913,bool)))))),hAPP(fun(U_913,bool),nat,finite_card(U_913),U_911)))
      | ~ hBOOL(hAPP(fun(U_913,bool),bool,finite_finite(U_913),U_911)) ),
    inference(definitional_conversion,[status(esa)],[f_245_2]) ).

cnf(f_245_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(U_913,bool),nat,finite_card(U_913),hAPP(fun(U_913,bool),fun(U_913,bool),hAPP(fun(U_913,bool),fun(fun(U_913,bool),fun(U_913,bool)),minus_minus(fun(U_913,bool)),U_911),hAPP(fun(U_913,bool),fun(U_913,bool),hAPP(U_913,fun(fun(U_913,bool),fun(U_913,bool)),insert(U_913),U_912),bot_bot(fun(U_913,bool)))))),hAPP(fun(U_913,bool),nat,finite_card(U_913),U_911)))
    | ~ hBOOL(hAPP(fun(U_913,bool),bool,finite_finite(U_913),U_911)) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

fof(f_246_1,plain,
    ! [X_b,N_1,H,F,F_2] :
      ( hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_2,N_1)) = hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_1))
      | ti(fun(X_b,bool),N_1) = bot_bot(fun(X_b,bool))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),N_1))
      | ? [X_2,Y_2] : hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_2)) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_2))
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_193_folding__one__idem_Ohom__commute]) ).

fof(f_246_2,plain,
    ! [U_920,U_919,U_918,U_917,U_916] :
      ( hAPP(U_920,U_920,U_918,hAPP(fun(U_920,bool),U_920,U_916,U_919)) = hAPP(fun(U_920,bool),U_920,U_916,hAPP(fun(U_920,bool),fun(U_920,bool),hAPP(fun(U_920,U_920),fun(fun(U_920,bool),fun(U_920,bool)),image(U_920,U_920),U_918),U_919))
      | ti(fun(U_920,bool),U_919) = bot_bot(fun(U_920,bool))
      | ~ hBOOL(hAPP(fun(U_920,bool),bool,finite_finite(U_920),U_919))
      | ? [U_915,U_914] : hAPP(U_920,U_920,U_918,hAPP(U_920,U_920,hAPP(U_920,fun(U_920,U_920),U_917,U_915),U_914)) != hAPP(U_920,U_920,hAPP(U_920,fun(U_920,U_920),U_917,hAPP(U_920,U_920,U_918,U_915)),hAPP(U_920,U_920,U_918,U_914))
      | ~ hBOOL(hAPP(fun(fun(U_920,bool),U_920),bool,hAPP(fun(U_920,fun(U_920,U_920)),fun(fun(fun(U_920,bool),U_920),bool),finite2073411215e_idem(U_920),U_917),U_916)) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

fof(f_246_3,plain,
    ! [U_920,U_919,U_918,U_917,U_916] :
      ( hAPP(U_920,U_920,U_918,hAPP(fun(U_920,bool),U_920,U_916,U_919)) = hAPP(fun(U_920,bool),U_920,U_916,hAPP(fun(U_920,bool),fun(U_920,bool),hAPP(fun(U_920,U_920),fun(fun(U_920,bool),fun(U_920,bool)),image(U_920,U_920),U_918),U_919))
      | ti(fun(U_920,bool),U_919) = bot_bot(fun(U_920,bool))
      | ~ hBOOL(hAPP(fun(U_920,bool),bool,finite_finite(U_920),U_919))
      | ? [U_914] : hAPP(U_920,U_920,U_918,hAPP(U_920,U_920,hAPP(U_920,fun(U_920,U_920),U_917,sK33(U_920,U_919,U_918,U_917,U_916)),U_914)) != hAPP(U_920,U_920,hAPP(U_920,fun(U_920,U_920),U_917,hAPP(U_920,U_920,U_918,sK33(U_920,U_919,U_918,U_917,U_916))),hAPP(U_920,U_920,U_918,U_914))
      | ~ hBOOL(hAPP(fun(fun(U_920,bool),U_920),bool,hAPP(fun(U_920,fun(U_920,U_920)),fun(fun(fun(U_920,bool),U_920),bool),finite2073411215e_idem(U_920),U_917),U_916)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_915,sK33(U_920,U_919,U_918,U_917,U_916))],[f_246_2]) ).

fof(f_246_4,plain,
    ! [U_920,U_919,U_918,U_917,U_916] :
      ( hAPP(U_920,U_920,U_918,hAPP(fun(U_920,bool),U_920,U_916,U_919)) = hAPP(fun(U_920,bool),U_920,U_916,hAPP(fun(U_920,bool),fun(U_920,bool),hAPP(fun(U_920,U_920),fun(fun(U_920,bool),fun(U_920,bool)),image(U_920,U_920),U_918),U_919))
      | ti(fun(U_920,bool),U_919) = bot_bot(fun(U_920,bool))
      | ~ hBOOL(hAPP(fun(U_920,bool),bool,finite_finite(U_920),U_919))
      | hAPP(U_920,U_920,U_918,hAPP(U_920,U_920,hAPP(U_920,fun(U_920,U_920),U_917,sK33(U_920,U_919,U_918,U_917,U_916)),sK34(U_920,U_919,U_918,U_917,U_916))) != hAPP(U_920,U_920,hAPP(U_920,fun(U_920,U_920),U_917,hAPP(U_920,U_920,U_918,sK33(U_920,U_919,U_918,U_917,U_916))),hAPP(U_920,U_920,U_918,sK34(U_920,U_919,U_918,U_917,U_916)))
      | ~ hBOOL(hAPP(fun(fun(U_920,bool),U_920),bool,hAPP(fun(U_920,fun(U_920,U_920)),fun(fun(fun(U_920,bool),U_920),bool),finite2073411215e_idem(U_920),U_917),U_916)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_914,sK34(U_920,U_919,U_918,U_917,U_916))],[f_246_3]) ).

fof(f_246_5,plain,
    ! [U_916,U_918,U_917,U_919,U_920] :
      ( hAPP(U_920,U_920,U_918,hAPP(fun(U_920,bool),U_920,U_916,U_919)) = hAPP(fun(U_920,bool),U_920,U_916,hAPP(fun(U_920,bool),fun(U_920,bool),hAPP(fun(U_920,U_920),fun(fun(U_920,bool),fun(U_920,bool)),image(U_920,U_920),U_918),U_919))
      | ti(fun(U_920,bool),U_919) = bot_bot(fun(U_920,bool))
      | ~ hBOOL(hAPP(fun(U_920,bool),bool,finite_finite(U_920),U_919))
      | hAPP(U_920,U_920,U_918,hAPP(U_920,U_920,hAPP(U_920,fun(U_920,U_920),U_917,sK33(U_920,U_919,U_918,U_917,U_916)),sK34(U_920,U_919,U_918,U_917,U_916))) != hAPP(U_920,U_920,hAPP(U_920,fun(U_920,U_920),U_917,hAPP(U_920,U_920,U_918,sK33(U_920,U_919,U_918,U_917,U_916))),hAPP(U_920,U_920,U_918,sK34(U_920,U_919,U_918,U_917,U_916)))
      | ~ hBOOL(hAPP(fun(fun(U_920,bool),U_920),bool,hAPP(fun(U_920,fun(U_920,U_920)),fun(fun(fun(U_920,bool),U_920),bool),finite2073411215e_idem(U_920),U_917),U_916)) ),
    inference(definitional_conversion,[status(esa)],[f_246_4]) ).

cnf(f_246_6,plain,
    ( hAPP(U_920,U_920,U_918,hAPP(fun(U_920,bool),U_920,U_916,U_919)) = hAPP(fun(U_920,bool),U_920,U_916,hAPP(fun(U_920,bool),fun(U_920,bool),hAPP(fun(U_920,U_920),fun(fun(U_920,bool),fun(U_920,bool)),image(U_920,U_920),U_918),U_919))
    | ti(fun(U_920,bool),U_919) = bot_bot(fun(U_920,bool))
    | ~ hBOOL(hAPP(fun(U_920,bool),bool,finite_finite(U_920),U_919))
    | hAPP(U_920,U_920,U_918,hAPP(U_920,U_920,hAPP(U_920,fun(U_920,U_920),U_917,sK33(U_920,U_919,U_918,U_917,U_916)),sK34(U_920,U_919,U_918,U_917,U_916))) != hAPP(U_920,U_920,hAPP(U_920,fun(U_920,U_920),U_917,hAPP(U_920,U_920,U_918,sK33(U_920,U_919,U_918,U_917,U_916))),hAPP(U_920,U_920,U_918,sK34(U_920,U_919,U_918,U_917,U_916)))
    | ~ hBOOL(hAPP(fun(fun(U_920,bool),U_920),bool,hAPP(fun(U_920,fun(U_920,U_920)),fun(fun(fun(U_920,bool),U_920),bool),finite2073411215e_idem(U_920),U_917),U_916)) ),
    inference(clausify,[status(thm)],[f_246_5]) ).

fof(f_247_1,plain,
    ! [X_b,A_3,F,F_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,F_2,A_3)),A_3))
      | ? [X_2,Y_2] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool))))))
      | ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ~ hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_194_folding__one_Oclosed]) ).

fof(f_247_2,plain,
    ! [U_926,U_925,U_924,U_923] :
      ( hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),hAPP(fun(U_926,bool),U_926,U_923,U_925)),U_925))
      | ? [U_922,U_921] : ~ hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),hAPP(U_926,U_926,hAPP(U_926,fun(U_926,U_926),U_924,U_922),U_921)),hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),U_922),hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),U_921),bot_bot(fun(U_926,bool))))))
      | ti(fun(U_926,bool),U_925) = bot_bot(fun(U_926,bool))
      | ~ hBOOL(hAPP(fun(U_926,bool),bool,finite_finite(U_926),U_925))
      | ~ hBOOL(hAPP(fun(fun(U_926,bool),U_926),bool,hAPP(fun(U_926,fun(U_926,U_926)),fun(fun(fun(U_926,bool),U_926),bool),finite_folding_one(U_926),U_924),U_923)) ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

fof(f_247_3,plain,
    ! [U_926,U_925,U_924,U_923] :
      ( hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),hAPP(fun(U_926,bool),U_926,U_923,U_925)),U_925))
      | ? [U_921] : ~ hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),hAPP(U_926,U_926,hAPP(U_926,fun(U_926,U_926),U_924,sK35(U_926,U_925,U_924,U_923)),U_921)),hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),sK35(U_926,U_925,U_924,U_923)),hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),U_921),bot_bot(fun(U_926,bool))))))
      | ti(fun(U_926,bool),U_925) = bot_bot(fun(U_926,bool))
      | ~ hBOOL(hAPP(fun(U_926,bool),bool,finite_finite(U_926),U_925))
      | ~ hBOOL(hAPP(fun(fun(U_926,bool),U_926),bool,hAPP(fun(U_926,fun(U_926,U_926)),fun(fun(fun(U_926,bool),U_926),bool),finite_folding_one(U_926),U_924),U_923)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_922,sK35(U_926,U_925,U_924,U_923))],[f_247_2]) ).

fof(f_247_4,plain,
    ! [U_926,U_925,U_924,U_923] :
      ( hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),hAPP(fun(U_926,bool),U_926,U_923,U_925)),U_925))
      | ~ hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),hAPP(U_926,U_926,hAPP(U_926,fun(U_926,U_926),U_924,sK35(U_926,U_925,U_924,U_923)),sK36(U_926,U_925,U_924,U_923))),hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),sK35(U_926,U_925,U_924,U_923)),hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),sK36(U_926,U_925,U_924,U_923)),bot_bot(fun(U_926,bool))))))
      | ti(fun(U_926,bool),U_925) = bot_bot(fun(U_926,bool))
      | ~ hBOOL(hAPP(fun(U_926,bool),bool,finite_finite(U_926),U_925))
      | ~ hBOOL(hAPP(fun(fun(U_926,bool),U_926),bool,hAPP(fun(U_926,fun(U_926,U_926)),fun(fun(fun(U_926,bool),U_926),bool),finite_folding_one(U_926),U_924),U_923)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_921,sK36(U_926,U_925,U_924,U_923))],[f_247_3]) ).

fof(f_247_5,plain,
    ! [U_923,U_924,U_925,U_926] :
      ( hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),hAPP(fun(U_926,bool),U_926,U_923,U_925)),U_925))
      | ~ hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),hAPP(U_926,U_926,hAPP(U_926,fun(U_926,U_926),U_924,sK35(U_926,U_925,U_924,U_923)),sK36(U_926,U_925,U_924,U_923))),hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),sK35(U_926,U_925,U_924,U_923)),hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),sK36(U_926,U_925,U_924,U_923)),bot_bot(fun(U_926,bool))))))
      | ti(fun(U_926,bool),U_925) = bot_bot(fun(U_926,bool))
      | ~ hBOOL(hAPP(fun(U_926,bool),bool,finite_finite(U_926),U_925))
      | ~ hBOOL(hAPP(fun(fun(U_926,bool),U_926),bool,hAPP(fun(U_926,fun(U_926,U_926)),fun(fun(fun(U_926,bool),U_926),bool),finite_folding_one(U_926),U_924),U_923)) ),
    inference(definitional_conversion,[status(esa)],[f_247_4]) ).

cnf(f_247_6,plain,
    ( hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),hAPP(fun(U_926,bool),U_926,U_923,U_925)),U_925))
    | ~ hBOOL(hAPP(fun(U_926,bool),bool,hAPP(U_926,fun(fun(U_926,bool),bool),member(U_926),hAPP(U_926,U_926,hAPP(U_926,fun(U_926,U_926),U_924,sK35(U_926,U_925,U_924,U_923)),sK36(U_926,U_925,U_924,U_923))),hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),sK35(U_926,U_925,U_924,U_923)),hAPP(fun(U_926,bool),fun(U_926,bool),hAPP(U_926,fun(fun(U_926,bool),fun(U_926,bool)),insert(U_926),sK36(U_926,U_925,U_924,U_923)),bot_bot(fun(U_926,bool))))))
    | ti(fun(U_926,bool),U_925) = bot_bot(fun(U_926,bool))
    | ~ hBOOL(hAPP(fun(U_926,bool),bool,finite_finite(U_926),U_925))
    | ~ hBOOL(hAPP(fun(fun(U_926,bool),U_926),bool,hAPP(fun(U_926,fun(U_926,U_926)),fun(fun(fun(U_926,bool),U_926),bool),finite_folding_one(U_926),U_924),U_923)) ),
    inference(clausify,[status(thm)],[f_247_5]) ).

fof(f_248_1,plain,
    ! [X_b,Pa,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool))))
      | ? [A_5,A_4] :
          ( ~ hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_4),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_5),bot_bot(fun(X_b,bool))))))
          & hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_4))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_4))
          & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_4)) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_195_finite__empty__induct]) ).

fof(f_248_2,plain,
    ! [U_931,U_930,U_929] :
      ( hBOOL(hAPP(fun(U_931,bool),bool,U_930,bot_bot(fun(U_931,bool))))
      | ? [U_928,U_927] :
          ( ~ hBOOL(hAPP(fun(U_931,bool),bool,U_930,hAPP(fun(U_931,bool),fun(U_931,bool),hAPP(fun(U_931,bool),fun(fun(U_931,bool),fun(U_931,bool)),minus_minus(fun(U_931,bool)),U_927),hAPP(fun(U_931,bool),fun(U_931,bool),hAPP(U_931,fun(fun(U_931,bool),fun(U_931,bool)),insert(U_931),U_928),bot_bot(fun(U_931,bool))))))
          & hBOOL(hAPP(fun(U_931,bool),bool,U_930,U_927))
          & hBOOL(hAPP(fun(U_931,bool),bool,hAPP(U_931,fun(fun(U_931,bool),bool),member(U_931),U_928),U_927))
          & hBOOL(hAPP(fun(U_931,bool),bool,finite_finite(U_931),U_927)) )
      | ~ hBOOL(hAPP(fun(U_931,bool),bool,U_930,U_929))
      | ~ hBOOL(hAPP(fun(U_931,bool),bool,finite_finite(U_931),U_929)) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

fof(f_248_3,plain,
    ! [U_931,U_930,U_929] :
      ( hBOOL(hAPP(fun(U_931,bool),bool,U_930,bot_bot(fun(U_931,bool))))
      | ? [U_927] :
          ( ~ hBOOL(hAPP(fun(U_931,bool),bool,U_930,hAPP(fun(U_931,bool),fun(U_931,bool),hAPP(fun(U_931,bool),fun(fun(U_931,bool),fun(U_931,bool)),minus_minus(fun(U_931,bool)),U_927),hAPP(fun(U_931,bool),fun(U_931,bool),hAPP(U_931,fun(fun(U_931,bool),fun(U_931,bool)),insert(U_931),sK37(U_931,U_930,U_929)),bot_bot(fun(U_931,bool))))))
          & hBOOL(hAPP(fun(U_931,bool),bool,U_930,U_927))
          & hBOOL(hAPP(fun(U_931,bool),bool,hAPP(U_931,fun(fun(U_931,bool),bool),member(U_931),sK37(U_931,U_930,U_929)),U_927))
          & hBOOL(hAPP(fun(U_931,bool),bool,finite_finite(U_931),U_927)) )
      | ~ hBOOL(hAPP(fun(U_931,bool),bool,U_930,U_929))
      | ~ hBOOL(hAPP(fun(U_931,bool),bool,finite_finite(U_931),U_929)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_928,sK37(U_931,U_930,U_929))],[f_248_2]) ).

fof(f_248_4,plain,
    ! [U_931,U_930,U_929] :
      ( hBOOL(hAPP(fun(U_931,bool),bool,U_930,bot_bot(fun(U_931,bool))))
      | ( ~ hBOOL(hAPP(fun(U_931,bool),bool,U_930,hAPP(fun(U_931,bool),fun(U_931,bool),hAPP(fun(U_931,bool),fun(fun(U_931,bool),fun(U_931,bool)),minus_minus(fun(U_931,bool)),sK38(U_931,U_930,U_929)),hAPP(fun(U_931,bool),fun(U_931,bool),hAPP(U_931,fun(fun(U_931,bool),fun(U_931,bool)),insert(U_931),sK37(U_931,U_930,U_929)),bot_bot(fun(U_931,bool))))))
        & hBOOL(hAPP(fun(U_931,bool),bool,U_930,sK38(U_931,U_930,U_929)))
        & hBOOL(hAPP(fun(U_931,bool),bool,hAPP(U_931,fun(fun(U_931,bool),bool),member(U_931),sK37(U_931,U_930,U_929)),sK38(U_931,U_930,U_929)))
        & hBOOL(hAPP(fun(U_931,bool),bool,finite_finite(U_931),sK38(U_931,U_930,U_929))) )
      | ~ hBOOL(hAPP(fun(U_931,bool),bool,U_930,U_929))
      | ~ hBOOL(hAPP(fun(U_931,bool),bool,finite_finite(U_931),U_929)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_927,sK38(U_931,U_930,U_929))],[f_248_3]) ).

fof(f_248_5,plain,
    ( ! [U_930,U_929,U_931] :
        ( ~ hBOOL(hAPP(fun(U_931,bool),bool,U_930,hAPP(fun(U_931,bool),fun(U_931,bool),hAPP(fun(U_931,bool),fun(fun(U_931,bool),fun(U_931,bool)),minus_minus(fun(U_931,bool)),sK38(U_931,U_930,U_929)),hAPP(fun(U_931,bool),fun(U_931,bool),hAPP(U_931,fun(fun(U_931,bool),fun(U_931,bool)),insert(U_931),sK37(U_931,U_930,U_929)),bot_bot(fun(U_931,bool))))))
        | ~ sP46(U_930,U_929,U_931) )
    & ! [U_930,U_929,U_931] :
        ( hBOOL(hAPP(fun(U_931,bool),bool,U_930,sK38(U_931,U_930,U_929)))
        | ~ sP46(U_930,U_929,U_931) )
    & ! [U_930,U_929,U_931] :
        ( hBOOL(hAPP(fun(U_931,bool),bool,hAPP(U_931,fun(fun(U_931,bool),bool),member(U_931),sK37(U_931,U_930,U_929)),sK38(U_931,U_930,U_929)))
        | ~ sP46(U_930,U_929,U_931) )
    & ! [U_930,U_929,U_931] :
        ( hBOOL(hAPP(fun(U_931,bool),bool,finite_finite(U_931),sK38(U_931,U_930,U_929)))
        | ~ sP46(U_930,U_929,U_931) )
    & ! [U_930,U_929,U_931] :
        ( hBOOL(hAPP(fun(U_931,bool),bool,U_930,bot_bot(fun(U_931,bool))))
        | sP46(U_930,U_929,U_931)
        | ~ hBOOL(hAPP(fun(U_931,bool),bool,U_930,U_929))
        | ~ hBOOL(hAPP(fun(U_931,bool),bool,finite_finite(U_931),U_929)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_248_4]) ).

cnf(f_248_6,plain,
    ( hBOOL(hAPP(fun(U_931,bool),bool,U_930,bot_bot(fun(U_931,bool))))
    | sP46(U_930,U_929,U_931)
    | ~ hBOOL(hAPP(fun(U_931,bool),bool,U_930,U_929))
    | ~ hBOOL(hAPP(fun(U_931,bool),bool,finite_finite(U_931),U_929)) ),
    inference(clausify,[status(thm)],[f_248_5]) ).

cnf(f_248_7,plain,
    ( hBOOL(hAPP(fun(U_931,bool),bool,finite_finite(U_931),sK38(U_931,U_930,U_929)))
    | ~ sP46(U_930,U_929,U_931) ),
    inference(clausify,[status(thm)],[f_248_5]) ).

cnf(f_248_8,plain,
    ( hBOOL(hAPP(fun(U_931,bool),bool,hAPP(U_931,fun(fun(U_931,bool),bool),member(U_931),sK37(U_931,U_930,U_929)),sK38(U_931,U_930,U_929)))
    | ~ sP46(U_930,U_929,U_931) ),
    inference(clausify,[status(thm)],[f_248_5]) ).

cnf(f_248_9,plain,
    ( hBOOL(hAPP(fun(U_931,bool),bool,U_930,sK38(U_931,U_930,U_929)))
    | ~ sP46(U_930,U_929,U_931) ),
    inference(clausify,[status(thm)],[f_248_5]) ).

cnf(f_248_10,plain,
    ( ~ hBOOL(hAPP(fun(U_931,bool),bool,U_930,hAPP(fun(U_931,bool),fun(U_931,bool),hAPP(fun(U_931,bool),fun(fun(U_931,bool),fun(U_931,bool)),minus_minus(fun(U_931,bool)),sK38(U_931,U_930,U_929)),hAPP(fun(U_931,bool),fun(U_931,bool),hAPP(U_931,fun(fun(U_931,bool),fun(U_931,bool)),insert(U_931),sK37(U_931,U_930,U_929)),bot_bot(fun(U_931,bool))))))
    | ~ sP46(U_930,U_929,U_931) ),
    inference(clausify,[status(thm)],[f_248_5]) ).

fof(f_249_1,plain,
    ! [X_c,X_b,X_1,A_3,F,Z_1,G,F_2] :
      ( hAPP(fun(X_c,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool))))))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))
      | ~ hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_196_folding__image__simple_Oremove]) ).

fof(f_249_2,plain,
    ! [U_939,U_938,U_937,U_936,U_935,U_934,U_933,U_932] :
      ( hAPP(fun(U_939,bool),U_938,U_932,U_936) = hAPP(U_938,U_938,hAPP(U_938,fun(U_938,U_938),U_935,hAPP(U_939,U_938,U_933,U_937)),hAPP(fun(U_939,bool),U_938,U_932,hAPP(fun(U_939,bool),fun(U_939,bool),hAPP(fun(U_939,bool),fun(fun(U_939,bool),fun(U_939,bool)),minus_minus(fun(U_939,bool)),U_936),hAPP(fun(U_939,bool),fun(U_939,bool),hAPP(U_939,fun(fun(U_939,bool),fun(U_939,bool)),insert(U_939),U_937),bot_bot(fun(U_939,bool))))))
      | ~ hBOOL(hAPP(fun(U_939,bool),bool,hAPP(U_939,fun(fun(U_939,bool),bool),member(U_939),U_937),U_936))
      | ~ hBOOL(hAPP(fun(U_939,bool),bool,finite_finite(U_939),U_936))
      | ~ hBOOL(hAPP(fun(fun(U_939,bool),U_938),bool,hAPP(fun(U_939,U_938),fun(fun(fun(U_939,bool),U_938),bool),hAPP(U_938,fun(fun(U_939,U_938),fun(fun(fun(U_939,bool),U_938),bool)),hAPP(fun(U_938,fun(U_938,U_938)),fun(U_938,fun(fun(U_939,U_938),fun(fun(fun(U_939,bool),U_938),bool))),finite1357897459simple(U_938,U_939),U_935),U_934),U_933),U_932)) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

fof(f_249_3,plain,
    ! [U_935,U_933,U_936,U_934,U_937,U_932,U_938,U_939] :
      ( hAPP(fun(U_939,bool),U_938,U_932,U_936) = hAPP(U_938,U_938,hAPP(U_938,fun(U_938,U_938),U_935,hAPP(U_939,U_938,U_933,U_937)),hAPP(fun(U_939,bool),U_938,U_932,hAPP(fun(U_939,bool),fun(U_939,bool),hAPP(fun(U_939,bool),fun(fun(U_939,bool),fun(U_939,bool)),minus_minus(fun(U_939,bool)),U_936),hAPP(fun(U_939,bool),fun(U_939,bool),hAPP(U_939,fun(fun(U_939,bool),fun(U_939,bool)),insert(U_939),U_937),bot_bot(fun(U_939,bool))))))
      | ~ hBOOL(hAPP(fun(U_939,bool),bool,hAPP(U_939,fun(fun(U_939,bool),bool),member(U_939),U_937),U_936))
      | ~ hBOOL(hAPP(fun(U_939,bool),bool,finite_finite(U_939),U_936))
      | ~ hBOOL(hAPP(fun(fun(U_939,bool),U_938),bool,hAPP(fun(U_939,U_938),fun(fun(fun(U_939,bool),U_938),bool),hAPP(U_938,fun(fun(U_939,U_938),fun(fun(fun(U_939,bool),U_938),bool)),hAPP(fun(U_938,fun(U_938,U_938)),fun(U_938,fun(fun(U_939,U_938),fun(fun(fun(U_939,bool),U_938),bool))),finite1357897459simple(U_938,U_939),U_935),U_934),U_933),U_932)) ),
    inference(definitional_conversion,[status(esa)],[f_249_2]) ).

cnf(f_249_4,plain,
    ( hAPP(fun(U_939,bool),U_938,U_932,U_936) = hAPP(U_938,U_938,hAPP(U_938,fun(U_938,U_938),U_935,hAPP(U_939,U_938,U_933,U_937)),hAPP(fun(U_939,bool),U_938,U_932,hAPP(fun(U_939,bool),fun(U_939,bool),hAPP(fun(U_939,bool),fun(fun(U_939,bool),fun(U_939,bool)),minus_minus(fun(U_939,bool)),U_936),hAPP(fun(U_939,bool),fun(U_939,bool),hAPP(U_939,fun(fun(U_939,bool),fun(U_939,bool)),insert(U_939),U_937),bot_bot(fun(U_939,bool))))))
    | ~ hBOOL(hAPP(fun(U_939,bool),bool,hAPP(U_939,fun(fun(U_939,bool),bool),member(U_939),U_937),U_936))
    | ~ hBOOL(hAPP(fun(U_939,bool),bool,finite_finite(U_939),U_936))
    | ~ hBOOL(hAPP(fun(fun(U_939,bool),U_938),bool,hAPP(fun(U_939,U_938),fun(fun(fun(U_939,bool),U_938),bool),hAPP(U_938,fun(fun(U_939,U_938),fun(fun(fun(U_939,bool),U_938),bool)),hAPP(fun(U_938,fun(U_938,U_938)),fun(U_938,fun(fun(U_939,U_938),fun(fun(fun(U_939,bool),U_938),bool))),finite1357897459simple(U_938,U_939),U_935),U_934),U_933),U_932)) ),
    inference(clausify,[status(thm)],[f_249_3]) ).

fof(f_250_1,plain,
    ! [X_c,X_b,X_1,A_3,F,Z_1,G,F_2] :
      ( hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool))))))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))
      | ~ hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_197_folding__image__simple_Oinsert__remove]) ).

fof(f_250_2,plain,
    ! [U_947,U_946,U_945,U_944,U_943,U_942,U_941,U_940] :
      ( hAPP(fun(U_947,bool),U_946,U_940,hAPP(fun(U_947,bool),fun(U_947,bool),hAPP(U_947,fun(fun(U_947,bool),fun(U_947,bool)),insert(U_947),U_945),U_944)) = hAPP(U_946,U_946,hAPP(U_946,fun(U_946,U_946),U_943,hAPP(U_947,U_946,U_941,U_945)),hAPP(fun(U_947,bool),U_946,U_940,hAPP(fun(U_947,bool),fun(U_947,bool),hAPP(fun(U_947,bool),fun(fun(U_947,bool),fun(U_947,bool)),minus_minus(fun(U_947,bool)),U_944),hAPP(fun(U_947,bool),fun(U_947,bool),hAPP(U_947,fun(fun(U_947,bool),fun(U_947,bool)),insert(U_947),U_945),bot_bot(fun(U_947,bool))))))
      | ~ hBOOL(hAPP(fun(U_947,bool),bool,finite_finite(U_947),U_944))
      | ~ hBOOL(hAPP(fun(fun(U_947,bool),U_946),bool,hAPP(fun(U_947,U_946),fun(fun(fun(U_947,bool),U_946),bool),hAPP(U_946,fun(fun(U_947,U_946),fun(fun(fun(U_947,bool),U_946),bool)),hAPP(fun(U_946,fun(U_946,U_946)),fun(U_946,fun(fun(U_947,U_946),fun(fun(fun(U_947,bool),U_946),bool))),finite1357897459simple(U_946,U_947),U_943),U_942),U_941),U_940)) ),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

fof(f_250_3,plain,
    ! [U_944,U_941,U_942,U_945,U_947,U_946,U_940,U_943] :
      ( hAPP(fun(U_947,bool),U_946,U_940,hAPP(fun(U_947,bool),fun(U_947,bool),hAPP(U_947,fun(fun(U_947,bool),fun(U_947,bool)),insert(U_947),U_945),U_944)) = hAPP(U_946,U_946,hAPP(U_946,fun(U_946,U_946),U_943,hAPP(U_947,U_946,U_941,U_945)),hAPP(fun(U_947,bool),U_946,U_940,hAPP(fun(U_947,bool),fun(U_947,bool),hAPP(fun(U_947,bool),fun(fun(U_947,bool),fun(U_947,bool)),minus_minus(fun(U_947,bool)),U_944),hAPP(fun(U_947,bool),fun(U_947,bool),hAPP(U_947,fun(fun(U_947,bool),fun(U_947,bool)),insert(U_947),U_945),bot_bot(fun(U_947,bool))))))
      | ~ hBOOL(hAPP(fun(U_947,bool),bool,finite_finite(U_947),U_944))
      | ~ hBOOL(hAPP(fun(fun(U_947,bool),U_946),bool,hAPP(fun(U_947,U_946),fun(fun(fun(U_947,bool),U_946),bool),hAPP(U_946,fun(fun(U_947,U_946),fun(fun(fun(U_947,bool),U_946),bool)),hAPP(fun(U_946,fun(U_946,U_946)),fun(U_946,fun(fun(U_947,U_946),fun(fun(fun(U_947,bool),U_946),bool))),finite1357897459simple(U_946,U_947),U_943),U_942),U_941),U_940)) ),
    inference(definitional_conversion,[status(esa)],[f_250_2]) ).

cnf(f_250_4,plain,
    ( hAPP(fun(U_947,bool),U_946,U_940,hAPP(fun(U_947,bool),fun(U_947,bool),hAPP(U_947,fun(fun(U_947,bool),fun(U_947,bool)),insert(U_947),U_945),U_944)) = hAPP(U_946,U_946,hAPP(U_946,fun(U_946,U_946),U_943,hAPP(U_947,U_946,U_941,U_945)),hAPP(fun(U_947,bool),U_946,U_940,hAPP(fun(U_947,bool),fun(U_947,bool),hAPP(fun(U_947,bool),fun(fun(U_947,bool),fun(U_947,bool)),minus_minus(fun(U_947,bool)),U_944),hAPP(fun(U_947,bool),fun(U_947,bool),hAPP(U_947,fun(fun(U_947,bool),fun(U_947,bool)),insert(U_947),U_945),bot_bot(fun(U_947,bool))))))
    | ~ hBOOL(hAPP(fun(U_947,bool),bool,finite_finite(U_947),U_944))
    | ~ hBOOL(hAPP(fun(fun(U_947,bool),U_946),bool,hAPP(fun(U_947,U_946),fun(fun(fun(U_947,bool),U_946),bool),hAPP(U_946,fun(fun(U_947,U_946),fun(fun(fun(U_947,bool),U_946),bool)),hAPP(fun(U_946,fun(U_946,U_946)),fun(U_946,fun(fun(U_947,U_946),fun(fun(fun(U_947,bool),U_946),bool))),finite1357897459simple(U_946,U_947),U_943),U_942),U_941),U_940)) ),
    inference(clausify,[status(thm)],[f_250_3]) ).

fof(f_251_1,plain,
    ! [X_b,X_1] : hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_1)) = ti(X_b,X_1),
    inference(fof_nnf,[status(thm)],[fact_198_the__sym__eq__trivial]) ).

fof(f_251_2,plain,
    ! [U_949,U_948] : hAPP(fun(U_949,bool),U_949,the(U_949),hAPP(U_949,fun(U_949,bool),fequal(U_949),U_948)) = ti(U_949,U_948),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

fof(f_251_3,plain,
    ! [U_948,U_949] : hAPP(fun(U_949,bool),U_949,the(U_949),hAPP(U_949,fun(U_949,bool),fequal(U_949),U_948)) = ti(U_949,U_948),
    inference(definitional_conversion,[status(esa)],[f_251_2]) ).

cnf(f_251_4,plain,
    hAPP(fun(U_949,bool),U_949,the(U_949),hAPP(U_949,fun(U_949,bool),fequal(U_949),U_948)) = ti(U_949,U_948),
    inference(clausify,[status(thm)],[f_251_3]) ).

fof(f_252_1,plain,
    ! [X_b,C_1,A_3,B_2] :
      ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))
        & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_199_DiffE]) ).

fof(f_252_2,plain,
    ! [U_953,U_952,U_951,U_950] :
      ( ( ~ hBOOL(hAPP(fun(U_953,bool),bool,hAPP(U_953,fun(fun(U_953,bool),bool),member(U_953),U_952),U_950))
        & hBOOL(hAPP(fun(U_953,bool),bool,hAPP(U_953,fun(fun(U_953,bool),bool),member(U_953),U_952),U_951)) )
      | ~ hBOOL(hAPP(fun(U_953,bool),bool,hAPP(U_953,fun(fun(U_953,bool),bool),member(U_953),U_952),hAPP(fun(U_953,bool),fun(U_953,bool),hAPP(fun(U_953,bool),fun(fun(U_953,bool),fun(U_953,bool)),minus_minus(fun(U_953,bool)),U_951),U_950))) ),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

fof(f_252_3,plain,
    ( ! [U_952,U_953,U_950,U_951] :
        ( ~ hBOOL(hAPP(fun(U_953,bool),bool,hAPP(U_953,fun(fun(U_953,bool),bool),member(U_953),U_952),U_950))
        | ~ sP47(U_952,U_953,U_950,U_951) )
    & ! [U_952,U_953,U_950,U_951] :
        ( hBOOL(hAPP(fun(U_953,bool),bool,hAPP(U_953,fun(fun(U_953,bool),bool),member(U_953),U_952),U_951))
        | ~ sP47(U_952,U_953,U_950,U_951) )
    & ! [U_952,U_953,U_950,U_951] :
        ( sP47(U_952,U_953,U_950,U_951)
        | ~ hBOOL(hAPP(fun(U_953,bool),bool,hAPP(U_953,fun(fun(U_953,bool),bool),member(U_953),U_952),hAPP(fun(U_953,bool),fun(U_953,bool),hAPP(fun(U_953,bool),fun(fun(U_953,bool),fun(U_953,bool)),minus_minus(fun(U_953,bool)),U_951),U_950))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_252_2]) ).

cnf(f_252_4,plain,
    ( sP47(U_952,U_953,U_950,U_951)
    | ~ hBOOL(hAPP(fun(U_953,bool),bool,hAPP(U_953,fun(fun(U_953,bool),bool),member(U_953),U_952),hAPP(fun(U_953,bool),fun(U_953,bool),hAPP(fun(U_953,bool),fun(fun(U_953,bool),fun(U_953,bool)),minus_minus(fun(U_953,bool)),U_951),U_950))) ),
    inference(clausify,[status(thm)],[f_252_3]) ).

cnf(f_252_5,plain,
    ( hBOOL(hAPP(fun(U_953,bool),bool,hAPP(U_953,fun(fun(U_953,bool),bool),member(U_953),U_952),U_951))
    | ~ sP47(U_952,U_953,U_950,U_951) ),
    inference(clausify,[status(thm)],[f_252_3]) ).

cnf(f_252_6,plain,
    ( ~ hBOOL(hAPP(fun(U_953,bool),bool,hAPP(U_953,fun(fun(U_953,bool),bool),member(U_953),U_952),U_950))
    | ~ sP47(U_952,U_953,U_950,U_951) ),
    inference(clausify,[status(thm)],[f_252_3]) ).

fof(f_253_1,plain,
    ! [X_b,B_2,C_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_200_DiffI]) ).

fof(f_253_2,plain,
    ! [U_957,U_956,U_955,U_954] :
      ( hBOOL(hAPP(fun(U_957,bool),bool,hAPP(U_957,fun(fun(U_957,bool),bool),member(U_957),U_955),hAPP(fun(U_957,bool),fun(U_957,bool),hAPP(fun(U_957,bool),fun(fun(U_957,bool),fun(U_957,bool)),minus_minus(fun(U_957,bool)),U_954),U_956)))
      | hBOOL(hAPP(fun(U_957,bool),bool,hAPP(U_957,fun(fun(U_957,bool),bool),member(U_957),U_955),U_956))
      | ~ hBOOL(hAPP(fun(U_957,bool),bool,hAPP(U_957,fun(fun(U_957,bool),bool),member(U_957),U_955),U_954)) ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

fof(f_253_3,plain,
    ! [U_956,U_954,U_957,U_955] :
      ( hBOOL(hAPP(fun(U_957,bool),bool,hAPP(U_957,fun(fun(U_957,bool),bool),member(U_957),U_955),hAPP(fun(U_957,bool),fun(U_957,bool),hAPP(fun(U_957,bool),fun(fun(U_957,bool),fun(U_957,bool)),minus_minus(fun(U_957,bool)),U_954),U_956)))
      | hBOOL(hAPP(fun(U_957,bool),bool,hAPP(U_957,fun(fun(U_957,bool),bool),member(U_957),U_955),U_956))
      | ~ hBOOL(hAPP(fun(U_957,bool),bool,hAPP(U_957,fun(fun(U_957,bool),bool),member(U_957),U_955),U_954)) ),
    inference(definitional_conversion,[status(esa)],[f_253_2]) ).

cnf(f_253_4,plain,
    ( hBOOL(hAPP(fun(U_957,bool),bool,hAPP(U_957,fun(fun(U_957,bool),bool),member(U_957),U_955),hAPP(fun(U_957,bool),fun(U_957,bool),hAPP(fun(U_957,bool),fun(fun(U_957,bool),fun(U_957,bool)),minus_minus(fun(U_957,bool)),U_954),U_956)))
    | hBOOL(hAPP(fun(U_957,bool),bool,hAPP(U_957,fun(fun(U_957,bool),bool),member(U_957),U_955),U_956))
    | ~ hBOOL(hAPP(fun(U_957,bool),bool,hAPP(U_957,fun(fun(U_957,bool),bool),member(U_957),U_955),U_954)) ),
    inference(clausify,[status(thm)],[f_253_3]) ).

fof(f_254_1,plain,
    ! [X_b,C_1,A_3,B_2] :
      ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_201_DiffD2]) ).

fof(f_254_2,plain,
    ! [U_961,U_960,U_959,U_958] :
      ( ~ hBOOL(hAPP(fun(U_961,bool),bool,hAPP(U_961,fun(fun(U_961,bool),bool),member(U_961),U_960),U_958))
      | ~ hBOOL(hAPP(fun(U_961,bool),bool,hAPP(U_961,fun(fun(U_961,bool),bool),member(U_961),U_960),hAPP(fun(U_961,bool),fun(U_961,bool),hAPP(fun(U_961,bool),fun(fun(U_961,bool),fun(U_961,bool)),minus_minus(fun(U_961,bool)),U_959),U_958))) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

fof(f_254_3,plain,
    ! [U_958,U_961,U_960,U_959] :
      ( ~ hBOOL(hAPP(fun(U_961,bool),bool,hAPP(U_961,fun(fun(U_961,bool),bool),member(U_961),U_960),U_958))
      | ~ hBOOL(hAPP(fun(U_961,bool),bool,hAPP(U_961,fun(fun(U_961,bool),bool),member(U_961),U_960),hAPP(fun(U_961,bool),fun(U_961,bool),hAPP(fun(U_961,bool),fun(fun(U_961,bool),fun(U_961,bool)),minus_minus(fun(U_961,bool)),U_959),U_958))) ),
    inference(definitional_conversion,[status(esa)],[f_254_2]) ).

cnf(f_254_4,plain,
    ( ~ hBOOL(hAPP(fun(U_961,bool),bool,hAPP(U_961,fun(fun(U_961,bool),bool),member(U_961),U_960),U_958))
    | ~ hBOOL(hAPP(fun(U_961,bool),bool,hAPP(U_961,fun(fun(U_961,bool),bool),member(U_961),U_960),hAPP(fun(U_961,bool),fun(U_961,bool),hAPP(fun(U_961,bool),fun(fun(U_961,bool),fun(U_961,bool)),minus_minus(fun(U_961,bool)),U_959),U_958))) ),
    inference(clausify,[status(thm)],[f_254_3]) ).

fof(f_255_1,plain,
    ! [X_b,C_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_202_DiffD1]) ).

fof(f_255_2,plain,
    ! [U_965,U_964,U_963,U_962] :
      ( hBOOL(hAPP(fun(U_965,bool),bool,hAPP(U_965,fun(fun(U_965,bool),bool),member(U_965),U_964),U_963))
      | ~ hBOOL(hAPP(fun(U_965,bool),bool,hAPP(U_965,fun(fun(U_965,bool),bool),member(U_965),U_964),hAPP(fun(U_965,bool),fun(U_965,bool),hAPP(fun(U_965,bool),fun(fun(U_965,bool),fun(U_965,bool)),minus_minus(fun(U_965,bool)),U_963),U_962))) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

fof(f_255_3,plain,
    ! [U_965,U_964,U_963] :
      ( ! [U_962] : ~ hBOOL(hAPP(fun(U_965,bool),bool,hAPP(U_965,fun(fun(U_965,bool),bool),member(U_965),U_964),hAPP(fun(U_965,bool),fun(U_965,bool),hAPP(fun(U_965,bool),fun(fun(U_965,bool),fun(U_965,bool)),minus_minus(fun(U_965,bool)),U_963),U_962)))
      | hBOOL(hAPP(fun(U_965,bool),bool,hAPP(U_965,fun(fun(U_965,bool),bool),member(U_965),U_964),U_963)) ),
    inference(miniscope,[status(thm)],[f_255_2]) ).

fof(f_255_4,plain,
    ! [U_964,U_965,U_962,U_963] :
      ( ~ hBOOL(hAPP(fun(U_965,bool),bool,hAPP(U_965,fun(fun(U_965,bool),bool),member(U_965),U_964),hAPP(fun(U_965,bool),fun(U_965,bool),hAPP(fun(U_965,bool),fun(fun(U_965,bool),fun(U_965,bool)),minus_minus(fun(U_965,bool)),U_963),U_962)))
      | hBOOL(hAPP(fun(U_965,bool),bool,hAPP(U_965,fun(fun(U_965,bool),bool),member(U_965),U_964),U_963)) ),
    inference(definitional_conversion,[status(esa)],[f_255_3]) ).

cnf(f_255_5,plain,
    ( ~ hBOOL(hAPP(fun(U_965,bool),bool,hAPP(U_965,fun(fun(U_965,bool),bool),member(U_965),U_964),hAPP(fun(U_965,bool),fun(U_965,bool),hAPP(fun(U_965,bool),fun(fun(U_965,bool),fun(U_965,bool)),minus_minus(fun(U_965,bool)),U_963),U_962)))
    | hBOOL(hAPP(fun(U_965,bool),bool,hAPP(U_965,fun(fun(U_965,bool),bool),member(U_965),U_964),U_963)) ),
    inference(clausify,[status(thm)],[f_255_4]) ).

fof(f_256_1,plain,
    ! [X_b,A_3,B_2] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2),
    inference(fof_nnf,[status(thm)],[fact_203_Diff__idemp]) ).

fof(f_256_2,plain,
    ! [U_968,U_967,U_966] : hAPP(fun(U_968,bool),fun(U_968,bool),hAPP(fun(U_968,bool),fun(fun(U_968,bool),fun(U_968,bool)),minus_minus(fun(U_968,bool)),hAPP(fun(U_968,bool),fun(U_968,bool),hAPP(fun(U_968,bool),fun(fun(U_968,bool),fun(U_968,bool)),minus_minus(fun(U_968,bool)),U_967),U_966)),U_966) = hAPP(fun(U_968,bool),fun(U_968,bool),hAPP(fun(U_968,bool),fun(fun(U_968,bool),fun(U_968,bool)),minus_minus(fun(U_968,bool)),U_967),U_966),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

fof(f_256_3,plain,
    ! [U_966,U_968,U_967] : hAPP(fun(U_968,bool),fun(U_968,bool),hAPP(fun(U_968,bool),fun(fun(U_968,bool),fun(U_968,bool)),minus_minus(fun(U_968,bool)),hAPP(fun(U_968,bool),fun(U_968,bool),hAPP(fun(U_968,bool),fun(fun(U_968,bool),fun(U_968,bool)),minus_minus(fun(U_968,bool)),U_967),U_966)),U_966) = hAPP(fun(U_968,bool),fun(U_968,bool),hAPP(fun(U_968,bool),fun(fun(U_968,bool),fun(U_968,bool)),minus_minus(fun(U_968,bool)),U_967),U_966),
    inference(definitional_conversion,[status(esa)],[f_256_2]) ).

cnf(f_256_4,plain,
    hAPP(fun(U_968,bool),fun(U_968,bool),hAPP(fun(U_968,bool),fun(fun(U_968,bool),fun(U_968,bool)),minus_minus(fun(U_968,bool)),hAPP(fun(U_968,bool),fun(U_968,bool),hAPP(fun(U_968,bool),fun(fun(U_968,bool),fun(U_968,bool)),minus_minus(fun(U_968,bool)),U_967),U_966)),U_966) = hAPP(fun(U_968,bool),fun(U_968,bool),hAPP(fun(U_968,bool),fun(fun(U_968,bool),fun(U_968,bool)),minus_minus(fun(U_968,bool)),U_967),U_966),
    inference(clausify,[status(thm)],[f_256_3]) ).

fof(f_257_1,plain,
    ! [X_b,C_1,A_3,B_2] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))
        | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) )
      & ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3)) )
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_204_Diff__iff]) ).

fof(f_257_2,plain,
    ! [U_972,U_971,U_970,U_969] :
      ( ( hBOOL(hAPP(fun(U_972,bool),bool,hAPP(U_972,fun(fun(U_972,bool),bool),member(U_972),U_971),hAPP(fun(U_972,bool),fun(U_972,bool),hAPP(fun(U_972,bool),fun(fun(U_972,bool),fun(U_972,bool)),minus_minus(fun(U_972,bool)),U_970),U_969)))
        | hBOOL(hAPP(fun(U_972,bool),bool,hAPP(U_972,fun(fun(U_972,bool),bool),member(U_972),U_971),U_969))
        | ~ hBOOL(hAPP(fun(U_972,bool),bool,hAPP(U_972,fun(fun(U_972,bool),bool),member(U_972),U_971),U_970)) )
      & ( ( ~ hBOOL(hAPP(fun(U_972,bool),bool,hAPP(U_972,fun(fun(U_972,bool),bool),member(U_972),U_971),U_969))
          & hBOOL(hAPP(fun(U_972,bool),bool,hAPP(U_972,fun(fun(U_972,bool),bool),member(U_972),U_971),U_970)) )
        | ~ hBOOL(hAPP(fun(U_972,bool),bool,hAPP(U_972,fun(fun(U_972,bool),bool),member(U_972),U_971),hAPP(fun(U_972,bool),fun(U_972,bool),hAPP(fun(U_972,bool),fun(fun(U_972,bool),fun(U_972,bool)),minus_minus(fun(U_972,bool)),U_970),U_969))) ) ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

fof(f_257_3,plain,
    ( ! [U_980,U_978,U_976,U_974] :
        ( hBOOL(hAPP(fun(U_980,bool),bool,hAPP(U_980,fun(fun(U_980,bool),bool),member(U_980),U_978),hAPP(fun(U_980,bool),fun(U_980,bool),hAPP(fun(U_980,bool),fun(fun(U_980,bool),fun(U_980,bool)),minus_minus(fun(U_980,bool)),U_976),U_974)))
        | hBOOL(hAPP(fun(U_980,bool),bool,hAPP(U_980,fun(fun(U_980,bool),bool),member(U_980),U_978),U_974))
        | ~ hBOOL(hAPP(fun(U_980,bool),bool,hAPP(U_980,fun(fun(U_980,bool),bool),member(U_980),U_978),U_976)) )
    & ! [U_979,U_977,U_975,U_973] :
        ( ( ~ hBOOL(hAPP(fun(U_979,bool),bool,hAPP(U_979,fun(fun(U_979,bool),bool),member(U_979),U_977),U_973))
          & hBOOL(hAPP(fun(U_979,bool),bool,hAPP(U_979,fun(fun(U_979,bool),bool),member(U_979),U_977),U_975)) )
        | ~ hBOOL(hAPP(fun(U_979,bool),bool,hAPP(U_979,fun(fun(U_979,bool),bool),member(U_979),U_977),hAPP(fun(U_979,bool),fun(U_979,bool),hAPP(fun(U_979,bool),fun(fun(U_979,bool),fun(U_979,bool)),minus_minus(fun(U_979,bool)),U_975),U_973))) ) ),
    inference(miniscope,[status(thm)],[f_257_2]) ).

fof(f_257_4,plain,
    ( ! [U_975,U_979,U_973,U_977] :
        ( ~ hBOOL(hAPP(fun(U_979,bool),bool,hAPP(U_979,fun(fun(U_979,bool),bool),member(U_979),U_977),U_973))
        | ~ sP48(U_975,U_979,U_973,U_977) )
    & ! [U_975,U_979,U_973,U_977] :
        ( hBOOL(hAPP(fun(U_979,bool),bool,hAPP(U_979,fun(fun(U_979,bool),bool),member(U_979),U_977),U_975))
        | ~ sP48(U_975,U_979,U_973,U_977) )
    & ! [U_978,U_974,U_976,U_980] :
        ( hBOOL(hAPP(fun(U_980,bool),bool,hAPP(U_980,fun(fun(U_980,bool),bool),member(U_980),U_978),hAPP(fun(U_980,bool),fun(U_980,bool),hAPP(fun(U_980,bool),fun(fun(U_980,bool),fun(U_980,bool)),minus_minus(fun(U_980,bool)),U_976),U_974)))
        | hBOOL(hAPP(fun(U_980,bool),bool,hAPP(U_980,fun(fun(U_980,bool),bool),member(U_980),U_978),U_974))
        | ~ hBOOL(hAPP(fun(U_980,bool),bool,hAPP(U_980,fun(fun(U_980,bool),bool),member(U_980),U_978),U_976)) )
    & ! [U_975,U_979,U_973,U_977] :
        ( sP48(U_975,U_979,U_973,U_977)
        | ~ hBOOL(hAPP(fun(U_979,bool),bool,hAPP(U_979,fun(fun(U_979,bool),bool),member(U_979),U_977),hAPP(fun(U_979,bool),fun(U_979,bool),hAPP(fun(U_979,bool),fun(fun(U_979,bool),fun(U_979,bool)),minus_minus(fun(U_979,bool)),U_975),U_973))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_257_3]) ).

cnf(f_257_5,plain,
    ( sP48(U_975,U_979,U_973,U_977)
    | ~ hBOOL(hAPP(fun(U_979,bool),bool,hAPP(U_979,fun(fun(U_979,bool),bool),member(U_979),U_977),hAPP(fun(U_979,bool),fun(U_979,bool),hAPP(fun(U_979,bool),fun(fun(U_979,bool),fun(U_979,bool)),minus_minus(fun(U_979,bool)),U_975),U_973))) ),
    inference(clausify,[status(thm)],[f_257_4]) ).

cnf(f_257_6,plain,
    ( hBOOL(hAPP(fun(U_980,bool),bool,hAPP(U_980,fun(fun(U_980,bool),bool),member(U_980),U_978),hAPP(fun(U_980,bool),fun(U_980,bool),hAPP(fun(U_980,bool),fun(fun(U_980,bool),fun(U_980,bool)),minus_minus(fun(U_980,bool)),U_976),U_974)))
    | hBOOL(hAPP(fun(U_980,bool),bool,hAPP(U_980,fun(fun(U_980,bool),bool),member(U_980),U_978),U_974))
    | ~ hBOOL(hAPP(fun(U_980,bool),bool,hAPP(U_980,fun(fun(U_980,bool),bool),member(U_980),U_978),U_976)) ),
    inference(clausify,[status(thm)],[f_257_4]) ).

cnf(f_257_7,plain,
    ( hBOOL(hAPP(fun(U_979,bool),bool,hAPP(U_979,fun(fun(U_979,bool),bool),member(U_979),U_977),U_975))
    | ~ sP48(U_975,U_979,U_973,U_977) ),
    inference(clausify,[status(thm)],[f_257_4]) ).

cnf(f_257_8,plain,
    ( ~ hBOOL(hAPP(fun(U_979,bool),bool,hAPP(U_979,fun(fun(U_979,bool),bool),member(U_979),U_977),U_973))
    | ~ sP48(U_975,U_979,U_973,U_977) ),
    inference(clausify,[status(thm)],[f_257_4]) ).

fof(f_258_1,plain,
    ! [X_b,A_3,B_2] : hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_3))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2)))),
    inference(fof_nnf,[status(thm)],[fact_205_set__diff__eq]) ).

fof(f_258_2,plain,
    ! [U_983,U_982,U_981] : hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,bool),fun(fun(U_983,bool),fun(U_983,bool)),minus_minus(fun(U_983,bool)),U_982),U_981) = hAPP(fun(U_983,bool),fun(U_983,bool),collect(U_983),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(bool,bool)),fun(fun(U_983,bool),fun(U_983,bool)),combs(U_983,bool,bool),hAPP(fun(U_983,bool),fun(U_983,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_983,bool),fun(U_983,fun(bool,bool))),combb(bool,fun(bool,bool),U_983),fconj),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(fun(U_983,bool),bool)),fun(fun(U_983,bool),fun(U_983,bool)),combc(U_983,fun(U_983,bool),bool),member(U_983)),U_982))),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(bool,bool),fun(fun(U_983,bool),fun(U_983,bool)),combb(bool,bool,U_983),fNot),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(fun(U_983,bool),bool)),fun(fun(U_983,bool),fun(U_983,bool)),combc(U_983,fun(U_983,bool),bool),member(U_983)),U_981)))),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

fof(f_258_3,plain,
    ! [U_981,U_982,U_983] : hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,bool),fun(fun(U_983,bool),fun(U_983,bool)),minus_minus(fun(U_983,bool)),U_982),U_981) = hAPP(fun(U_983,bool),fun(U_983,bool),collect(U_983),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(bool,bool)),fun(fun(U_983,bool),fun(U_983,bool)),combs(U_983,bool,bool),hAPP(fun(U_983,bool),fun(U_983,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_983,bool),fun(U_983,fun(bool,bool))),combb(bool,fun(bool,bool),U_983),fconj),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(fun(U_983,bool),bool)),fun(fun(U_983,bool),fun(U_983,bool)),combc(U_983,fun(U_983,bool),bool),member(U_983)),U_982))),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(bool,bool),fun(fun(U_983,bool),fun(U_983,bool)),combb(bool,bool,U_983),fNot),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(fun(U_983,bool),bool)),fun(fun(U_983,bool),fun(U_983,bool)),combc(U_983,fun(U_983,bool),bool),member(U_983)),U_981)))),
    inference(definitional_conversion,[status(esa)],[f_258_2]) ).

cnf(f_258_4,plain,
    hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,bool),fun(fun(U_983,bool),fun(U_983,bool)),minus_minus(fun(U_983,bool)),U_982),U_981) = hAPP(fun(U_983,bool),fun(U_983,bool),collect(U_983),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(bool,bool)),fun(fun(U_983,bool),fun(U_983,bool)),combs(U_983,bool,bool),hAPP(fun(U_983,bool),fun(U_983,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_983,bool),fun(U_983,fun(bool,bool))),combb(bool,fun(bool,bool),U_983),fconj),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(fun(U_983,bool),bool)),fun(fun(U_983,bool),fun(U_983,bool)),combc(U_983,fun(U_983,bool),bool),member(U_983)),U_982))),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(bool,bool),fun(fun(U_983,bool),fun(U_983,bool)),combb(bool,bool,U_983),fNot),hAPP(fun(U_983,bool),fun(U_983,bool),hAPP(fun(U_983,fun(fun(U_983,bool),bool)),fun(fun(U_983,bool),fun(U_983,bool)),combc(U_983,fun(U_983,bool),bool),member(U_983)),U_981)))),
    inference(clausify,[status(thm)],[f_258_3]) ).

fof(f_259_1,plain,
    ! [X_c,X_b,F,Z_1,G,F_2] :
      ( hAPP(fun(X_c,bool),X_b,F_2,bot_bot(fun(X_c,bool))) = ti(X_b,Z_1)
      | ~ hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_206_folding__image__simple_Oempty]) ).

fof(f_259_2,plain,
    ! [U_989,U_988,U_987,U_986,U_985,U_984] :
      ( hAPP(fun(U_989,bool),U_988,U_984,bot_bot(fun(U_989,bool))) = ti(U_988,U_986)
      | ~ hBOOL(hAPP(fun(fun(U_989,bool),U_988),bool,hAPP(fun(U_989,U_988),fun(fun(fun(U_989,bool),U_988),bool),hAPP(U_988,fun(fun(U_989,U_988),fun(fun(fun(U_989,bool),U_988),bool)),hAPP(fun(U_988,fun(U_988,U_988)),fun(U_988,fun(fun(U_989,U_988),fun(fun(fun(U_989,bool),U_988),bool))),finite1357897459simple(U_988,U_989),U_987),U_986),U_985),U_984)) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

fof(f_259_3,plain,
    ! [U_984,U_987,U_985,U_986,U_988,U_989] :
      ( hAPP(fun(U_989,bool),U_988,U_984,bot_bot(fun(U_989,bool))) = ti(U_988,U_986)
      | ~ hBOOL(hAPP(fun(fun(U_989,bool),U_988),bool,hAPP(fun(U_989,U_988),fun(fun(fun(U_989,bool),U_988),bool),hAPP(U_988,fun(fun(U_989,U_988),fun(fun(fun(U_989,bool),U_988),bool)),hAPP(fun(U_988,fun(U_988,U_988)),fun(U_988,fun(fun(U_989,U_988),fun(fun(fun(U_989,bool),U_988),bool))),finite1357897459simple(U_988,U_989),U_987),U_986),U_985),U_984)) ),
    inference(definitional_conversion,[status(esa)],[f_259_2]) ).

cnf(f_259_4,plain,
    ( hAPP(fun(U_989,bool),U_988,U_984,bot_bot(fun(U_989,bool))) = ti(U_988,U_986)
    | ~ hBOOL(hAPP(fun(fun(U_989,bool),U_988),bool,hAPP(fun(U_989,U_988),fun(fun(fun(U_989,bool),U_988),bool),hAPP(U_988,fun(fun(U_989,U_988),fun(fun(fun(U_989,bool),U_988),bool)),hAPP(fun(U_988,fun(U_988,U_988)),fun(U_988,fun(fun(U_989,U_988),fun(fun(fun(U_989,bool),U_988),bool))),finite1357897459simple(U_988,U_989),U_987),U_986),U_985),U_984)) ),
    inference(clausify,[status(thm)],[f_259_3]) ).

fof(f_260_1,plain,
    ! [X_c,X_b,X_1,A_3,F,Z_1,G,F_2] :
      ( hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,A_3))
      | hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))
      | ~ hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_207_folding__image__simple_Oinsert]) ).

fof(f_260_2,plain,
    ! [U_997,U_996,U_995,U_994,U_993,U_992,U_991,U_990] :
      ( hAPP(fun(U_997,bool),U_996,U_990,hAPP(fun(U_997,bool),fun(U_997,bool),hAPP(U_997,fun(fun(U_997,bool),fun(U_997,bool)),insert(U_997),U_995),U_994)) = hAPP(U_996,U_996,hAPP(U_996,fun(U_996,U_996),U_993,hAPP(U_997,U_996,U_991,U_995)),hAPP(fun(U_997,bool),U_996,U_990,U_994))
      | hBOOL(hAPP(fun(U_997,bool),bool,hAPP(U_997,fun(fun(U_997,bool),bool),member(U_997),U_995),U_994))
      | ~ hBOOL(hAPP(fun(U_997,bool),bool,finite_finite(U_997),U_994))
      | ~ hBOOL(hAPP(fun(fun(U_997,bool),U_996),bool,hAPP(fun(U_997,U_996),fun(fun(fun(U_997,bool),U_996),bool),hAPP(U_996,fun(fun(U_997,U_996),fun(fun(fun(U_997,bool),U_996),bool)),hAPP(fun(U_996,fun(U_996,U_996)),fun(U_996,fun(fun(U_997,U_996),fun(fun(fun(U_997,bool),U_996),bool))),finite1357897459simple(U_996,U_997),U_993),U_992),U_991),U_990)) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

fof(f_260_3,plain,
    ! [U_996,U_991,U_990,U_992,U_993,U_994,U_995,U_997] :
      ( hAPP(fun(U_997,bool),U_996,U_990,hAPP(fun(U_997,bool),fun(U_997,bool),hAPP(U_997,fun(fun(U_997,bool),fun(U_997,bool)),insert(U_997),U_995),U_994)) = hAPP(U_996,U_996,hAPP(U_996,fun(U_996,U_996),U_993,hAPP(U_997,U_996,U_991,U_995)),hAPP(fun(U_997,bool),U_996,U_990,U_994))
      | hBOOL(hAPP(fun(U_997,bool),bool,hAPP(U_997,fun(fun(U_997,bool),bool),member(U_997),U_995),U_994))
      | ~ hBOOL(hAPP(fun(U_997,bool),bool,finite_finite(U_997),U_994))
      | ~ hBOOL(hAPP(fun(fun(U_997,bool),U_996),bool,hAPP(fun(U_997,U_996),fun(fun(fun(U_997,bool),U_996),bool),hAPP(U_996,fun(fun(U_997,U_996),fun(fun(fun(U_997,bool),U_996),bool)),hAPP(fun(U_996,fun(U_996,U_996)),fun(U_996,fun(fun(U_997,U_996),fun(fun(fun(U_997,bool),U_996),bool))),finite1357897459simple(U_996,U_997),U_993),U_992),U_991),U_990)) ),
    inference(definitional_conversion,[status(esa)],[f_260_2]) ).

cnf(f_260_4,plain,
    ( hAPP(fun(U_997,bool),U_996,U_990,hAPP(fun(U_997,bool),fun(U_997,bool),hAPP(U_997,fun(fun(U_997,bool),fun(U_997,bool)),insert(U_997),U_995),U_994)) = hAPP(U_996,U_996,hAPP(U_996,fun(U_996,U_996),U_993,hAPP(U_997,U_996,U_991,U_995)),hAPP(fun(U_997,bool),U_996,U_990,U_994))
    | hBOOL(hAPP(fun(U_997,bool),bool,hAPP(U_997,fun(fun(U_997,bool),bool),member(U_997),U_995),U_994))
    | ~ hBOOL(hAPP(fun(U_997,bool),bool,finite_finite(U_997),U_994))
    | ~ hBOOL(hAPP(fun(fun(U_997,bool),U_996),bool,hAPP(fun(U_997,U_996),fun(fun(fun(U_997,bool),U_996),bool),hAPP(U_996,fun(fun(U_997,U_996),fun(fun(fun(U_997,bool),U_996),bool)),hAPP(fun(U_996,fun(U_996,U_996)),fun(U_996,fun(fun(U_997,U_996),fun(fun(fun(U_997,bool),U_996),bool))),finite1357897459simple(U_996,U_997),U_993),U_992),U_991),U_990)) ),
    inference(clausify,[status(thm)],[f_260_3]) ).

fof(f_261_1,plain,
    ! [X_b,X_1,Y_1,Pa] :
      ( ( ti(X_b,Y_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_1))))
        | hBOOL(Pa) )
      & ( ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_1))))
        | ~ hBOOL(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_208_If__def]) ).

fof(f_261_2,plain,
    ! [U_1001,U_1000,U_999,U_998] :
      ( ( ti(U_1001,U_999) = hAPP(fun(U_1001,bool),U_1001,the(U_1001),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(fun(U_1001,fun(bool,bool)),fun(fun(U_1001,bool),fun(U_1001,bool)),combs(U_1001,bool,bool),hAPP(fun(U_1001,bool),fun(U_1001,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1001,bool),fun(U_1001,fun(bool,bool))),combb(bool,fun(bool,bool),U_1001),fconj),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(fun(bool,bool),fun(fun(U_1001,bool),fun(U_1001,bool)),combb(bool,bool,U_1001),hAPP(bool,fun(bool,bool),fimplies,U_998)),hAPP(U_1001,fun(U_1001,bool),hAPP(fun(U_1001,fun(U_1001,bool)),fun(U_1001,fun(U_1001,bool)),combc(U_1001,U_1001,bool),fequal(U_1001)),U_1000)))),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(fun(bool,bool),fun(fun(U_1001,bool),fun(U_1001,bool)),combb(bool,bool,U_1001),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_998))),hAPP(U_1001,fun(U_1001,bool),hAPP(fun(U_1001,fun(U_1001,bool)),fun(U_1001,fun(U_1001,bool)),combc(U_1001,U_1001,bool),fequal(U_1001)),U_999))))
        | hBOOL(U_998) )
      & ( ti(U_1001,U_1000) = hAPP(fun(U_1001,bool),U_1001,the(U_1001),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(fun(U_1001,fun(bool,bool)),fun(fun(U_1001,bool),fun(U_1001,bool)),combs(U_1001,bool,bool),hAPP(fun(U_1001,bool),fun(U_1001,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1001,bool),fun(U_1001,fun(bool,bool))),combb(bool,fun(bool,bool),U_1001),fconj),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(fun(bool,bool),fun(fun(U_1001,bool),fun(U_1001,bool)),combb(bool,bool,U_1001),hAPP(bool,fun(bool,bool),fimplies,U_998)),hAPP(U_1001,fun(U_1001,bool),hAPP(fun(U_1001,fun(U_1001,bool)),fun(U_1001,fun(U_1001,bool)),combc(U_1001,U_1001,bool),fequal(U_1001)),U_1000)))),hAPP(fun(U_1001,bool),fun(U_1001,bool),hAPP(fun(bool,bool),fun(fun(U_1001,bool),fun(U_1001,bool)),combb(bool,bool,U_1001),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_998))),hAPP(U_1001,fun(U_1001,bool),hAPP(fun(U_1001,fun(U_1001,bool)),fun(U_1001,fun(U_1001,bool)),combc(U_1001,U_1001,bool),fequal(U_1001)),U_999))))
        | ~ hBOOL(U_998) ) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

fof(f_261_3,plain,
    ( ! [U_1009,U_1007,U_1005,U_1003] :
        ( ti(U_1009,U_1005) = hAPP(fun(U_1009,bool),U_1009,the(U_1009),hAPP(fun(U_1009,bool),fun(U_1009,bool),hAPP(fun(U_1009,fun(bool,bool)),fun(fun(U_1009,bool),fun(U_1009,bool)),combs(U_1009,bool,bool),hAPP(fun(U_1009,bool),fun(U_1009,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1009,bool),fun(U_1009,fun(bool,bool))),combb(bool,fun(bool,bool),U_1009),fconj),hAPP(fun(U_1009,bool),fun(U_1009,bool),hAPP(fun(bool,bool),fun(fun(U_1009,bool),fun(U_1009,bool)),combb(bool,bool,U_1009),hAPP(bool,fun(bool,bool),fimplies,U_1003)),hAPP(U_1009,fun(U_1009,bool),hAPP(fun(U_1009,fun(U_1009,bool)),fun(U_1009,fun(U_1009,bool)),combc(U_1009,U_1009,bool),fequal(U_1009)),U_1007)))),hAPP(fun(U_1009,bool),fun(U_1009,bool),hAPP(fun(bool,bool),fun(fun(U_1009,bool),fun(U_1009,bool)),combb(bool,bool,U_1009),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1003))),hAPP(U_1009,fun(U_1009,bool),hAPP(fun(U_1009,fun(U_1009,bool)),fun(U_1009,fun(U_1009,bool)),combc(U_1009,U_1009,bool),fequal(U_1009)),U_1005))))
        | hBOOL(U_1003) )
    & ! [U_1008,U_1006,U_1004,U_1002] :
        ( ti(U_1008,U_1006) = hAPP(fun(U_1008,bool),U_1008,the(U_1008),hAPP(fun(U_1008,bool),fun(U_1008,bool),hAPP(fun(U_1008,fun(bool,bool)),fun(fun(U_1008,bool),fun(U_1008,bool)),combs(U_1008,bool,bool),hAPP(fun(U_1008,bool),fun(U_1008,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1008,bool),fun(U_1008,fun(bool,bool))),combb(bool,fun(bool,bool),U_1008),fconj),hAPP(fun(U_1008,bool),fun(U_1008,bool),hAPP(fun(bool,bool),fun(fun(U_1008,bool),fun(U_1008,bool)),combb(bool,bool,U_1008),hAPP(bool,fun(bool,bool),fimplies,U_1002)),hAPP(U_1008,fun(U_1008,bool),hAPP(fun(U_1008,fun(U_1008,bool)),fun(U_1008,fun(U_1008,bool)),combc(U_1008,U_1008,bool),fequal(U_1008)),U_1006)))),hAPP(fun(U_1008,bool),fun(U_1008,bool),hAPP(fun(bool,bool),fun(fun(U_1008,bool),fun(U_1008,bool)),combb(bool,bool,U_1008),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1002))),hAPP(U_1008,fun(U_1008,bool),hAPP(fun(U_1008,fun(U_1008,bool)),fun(U_1008,fun(U_1008,bool)),combc(U_1008,U_1008,bool),fequal(U_1008)),U_1004))))
        | ~ hBOOL(U_1002) ) ),
    inference(miniscope,[status(thm)],[f_261_2]) ).

fof(f_261_4,plain,
    ( ! [U_1009,U_1003,U_1005,U_1007] :
        ( ti(U_1009,U_1005) = hAPP(fun(U_1009,bool),U_1009,the(U_1009),hAPP(fun(U_1009,bool),fun(U_1009,bool),hAPP(fun(U_1009,fun(bool,bool)),fun(fun(U_1009,bool),fun(U_1009,bool)),combs(U_1009,bool,bool),hAPP(fun(U_1009,bool),fun(U_1009,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1009,bool),fun(U_1009,fun(bool,bool))),combb(bool,fun(bool,bool),U_1009),fconj),hAPP(fun(U_1009,bool),fun(U_1009,bool),hAPP(fun(bool,bool),fun(fun(U_1009,bool),fun(U_1009,bool)),combb(bool,bool,U_1009),hAPP(bool,fun(bool,bool),fimplies,U_1003)),hAPP(U_1009,fun(U_1009,bool),hAPP(fun(U_1009,fun(U_1009,bool)),fun(U_1009,fun(U_1009,bool)),combc(U_1009,U_1009,bool),fequal(U_1009)),U_1007)))),hAPP(fun(U_1009,bool),fun(U_1009,bool),hAPP(fun(bool,bool),fun(fun(U_1009,bool),fun(U_1009,bool)),combb(bool,bool,U_1009),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1003))),hAPP(U_1009,fun(U_1009,bool),hAPP(fun(U_1009,fun(U_1009,bool)),fun(U_1009,fun(U_1009,bool)),combc(U_1009,U_1009,bool),fequal(U_1009)),U_1005))))
        | hBOOL(U_1003) )
    & ! [U_1004,U_1002,U_1008,U_1006] :
        ( ti(U_1008,U_1006) = hAPP(fun(U_1008,bool),U_1008,the(U_1008),hAPP(fun(U_1008,bool),fun(U_1008,bool),hAPP(fun(U_1008,fun(bool,bool)),fun(fun(U_1008,bool),fun(U_1008,bool)),combs(U_1008,bool,bool),hAPP(fun(U_1008,bool),fun(U_1008,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1008,bool),fun(U_1008,fun(bool,bool))),combb(bool,fun(bool,bool),U_1008),fconj),hAPP(fun(U_1008,bool),fun(U_1008,bool),hAPP(fun(bool,bool),fun(fun(U_1008,bool),fun(U_1008,bool)),combb(bool,bool,U_1008),hAPP(bool,fun(bool,bool),fimplies,U_1002)),hAPP(U_1008,fun(U_1008,bool),hAPP(fun(U_1008,fun(U_1008,bool)),fun(U_1008,fun(U_1008,bool)),combc(U_1008,U_1008,bool),fequal(U_1008)),U_1006)))),hAPP(fun(U_1008,bool),fun(U_1008,bool),hAPP(fun(bool,bool),fun(fun(U_1008,bool),fun(U_1008,bool)),combb(bool,bool,U_1008),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1002))),hAPP(U_1008,fun(U_1008,bool),hAPP(fun(U_1008,fun(U_1008,bool)),fun(U_1008,fun(U_1008,bool)),combc(U_1008,U_1008,bool),fequal(U_1008)),U_1004))))
        | ~ hBOOL(U_1002) ) ),
    inference(definitional_conversion,[status(esa)],[f_261_3]) ).

cnf(f_261_5,plain,
    ( ti(U_1008,U_1006) = hAPP(fun(U_1008,bool),U_1008,the(U_1008),hAPP(fun(U_1008,bool),fun(U_1008,bool),hAPP(fun(U_1008,fun(bool,bool)),fun(fun(U_1008,bool),fun(U_1008,bool)),combs(U_1008,bool,bool),hAPP(fun(U_1008,bool),fun(U_1008,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1008,bool),fun(U_1008,fun(bool,bool))),combb(bool,fun(bool,bool),U_1008),fconj),hAPP(fun(U_1008,bool),fun(U_1008,bool),hAPP(fun(bool,bool),fun(fun(U_1008,bool),fun(U_1008,bool)),combb(bool,bool,U_1008),hAPP(bool,fun(bool,bool),fimplies,U_1002)),hAPP(U_1008,fun(U_1008,bool),hAPP(fun(U_1008,fun(U_1008,bool)),fun(U_1008,fun(U_1008,bool)),combc(U_1008,U_1008,bool),fequal(U_1008)),U_1006)))),hAPP(fun(U_1008,bool),fun(U_1008,bool),hAPP(fun(bool,bool),fun(fun(U_1008,bool),fun(U_1008,bool)),combb(bool,bool,U_1008),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1002))),hAPP(U_1008,fun(U_1008,bool),hAPP(fun(U_1008,fun(U_1008,bool)),fun(U_1008,fun(U_1008,bool)),combc(U_1008,U_1008,bool),fequal(U_1008)),U_1004))))
    | ~ hBOOL(U_1002) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_6,plain,
    ( ti(U_1009,U_1005) = hAPP(fun(U_1009,bool),U_1009,the(U_1009),hAPP(fun(U_1009,bool),fun(U_1009,bool),hAPP(fun(U_1009,fun(bool,bool)),fun(fun(U_1009,bool),fun(U_1009,bool)),combs(U_1009,bool,bool),hAPP(fun(U_1009,bool),fun(U_1009,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_1009,bool),fun(U_1009,fun(bool,bool))),combb(bool,fun(bool,bool),U_1009),fconj),hAPP(fun(U_1009,bool),fun(U_1009,bool),hAPP(fun(bool,bool),fun(fun(U_1009,bool),fun(U_1009,bool)),combb(bool,bool,U_1009),hAPP(bool,fun(bool,bool),fimplies,U_1003)),hAPP(U_1009,fun(U_1009,bool),hAPP(fun(U_1009,fun(U_1009,bool)),fun(U_1009,fun(U_1009,bool)),combc(U_1009,U_1009,bool),fequal(U_1009)),U_1007)))),hAPP(fun(U_1009,bool),fun(U_1009,bool),hAPP(fun(bool,bool),fun(fun(U_1009,bool),fun(U_1009,bool)),combb(bool,bool,U_1009),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,U_1003))),hAPP(U_1009,fun(U_1009,bool),hAPP(fun(U_1009,fun(U_1009,bool)),fun(U_1009,fun(U_1009,bool)),combc(U_1009,U_1009,bool),fequal(U_1009)),U_1005))))
    | hBOOL(U_1003) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

fof(f_262_1,plain,
    ! [X_b,A_2] : hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = ti(X_b,A_2),
    inference(fof_nnf,[status(thm)],[fact_209_the__eq__trivial]) ).

fof(f_262_2,plain,
    ! [U_1011,U_1010] : hAPP(fun(U_1011,bool),U_1011,the(U_1011),hAPP(U_1011,fun(U_1011,bool),hAPP(fun(U_1011,fun(U_1011,bool)),fun(U_1011,fun(U_1011,bool)),combc(U_1011,U_1011,bool),fequal(U_1011)),U_1010)) = ti(U_1011,U_1010),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

fof(f_262_3,plain,
    ! [U_1011,U_1010] : hAPP(fun(U_1011,bool),U_1011,the(U_1011),hAPP(U_1011,fun(U_1011,bool),hAPP(fun(U_1011,fun(U_1011,bool)),fun(U_1011,fun(U_1011,bool)),combc(U_1011,U_1011,bool),fequal(U_1011)),U_1010)) = ti(U_1011,U_1010),
    inference(definitional_conversion,[status(esa)],[f_262_2]) ).

cnf(f_262_4,plain,
    hAPP(fun(U_1011,bool),U_1011,the(U_1011),hAPP(U_1011,fun(U_1011,bool),hAPP(fun(U_1011,fun(U_1011,bool)),fun(U_1011,fun(U_1011,bool)),combc(U_1011,U_1011,bool),fequal(U_1011)),U_1010)) = ti(U_1011,U_1010),
    inference(clausify,[status(thm)],[f_262_3]) ).

fof(f_263_1,plain,
    ! [X_b,Pa,A_2] :
      ( hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_2)
      | ? [X_2] :
          ( ti(X_b,X_2) != ti(X_b,A_2)
          & hBOOL(hAPP(X_b,bool,Pa,X_2)) )
      | ~ hBOOL(hAPP(X_b,bool,Pa,A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_210_the__equality]) ).

fof(f_263_2,plain,
    ! [U_1015,U_1014,U_1013] :
      ( hAPP(fun(U_1015,bool),U_1015,the(U_1015),U_1014) = ti(U_1015,U_1013)
      | ? [U_1012] :
          ( ti(U_1015,U_1012) != ti(U_1015,U_1013)
          & hBOOL(hAPP(U_1015,bool,U_1014,U_1012)) )
      | ~ hBOOL(hAPP(U_1015,bool,U_1014,U_1013)) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

fof(f_263_3,plain,
    ! [U_1015,U_1014,U_1013] :
      ( hAPP(fun(U_1015,bool),U_1015,the(U_1015),U_1014) = ti(U_1015,U_1013)
      | ( ti(U_1015,sK39(U_1015,U_1014,U_1013)) != ti(U_1015,U_1013)
        & hBOOL(hAPP(U_1015,bool,U_1014,sK39(U_1015,U_1014,U_1013))) )
      | ~ hBOOL(hAPP(U_1015,bool,U_1014,U_1013)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_1012,sK39(U_1015,U_1014,U_1013))],[f_263_2]) ).

fof(f_263_4,plain,
    ( ! [U_1013,U_1014,U_1015] :
        ( ti(U_1015,sK39(U_1015,U_1014,U_1013)) != ti(U_1015,U_1013)
        | ~ sP49(U_1013,U_1014,U_1015) )
    & ! [U_1013,U_1014,U_1015] :
        ( hBOOL(hAPP(U_1015,bool,U_1014,sK39(U_1015,U_1014,U_1013)))
        | ~ sP49(U_1013,U_1014,U_1015) )
    & ! [U_1013,U_1014,U_1015] :
        ( hAPP(fun(U_1015,bool),U_1015,the(U_1015),U_1014) = ti(U_1015,U_1013)
        | sP49(U_1013,U_1014,U_1015)
        | ~ hBOOL(hAPP(U_1015,bool,U_1014,U_1013)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_263_3]) ).

cnf(f_263_5,plain,
    ( hAPP(fun(U_1015,bool),U_1015,the(U_1015),U_1014) = ti(U_1015,U_1013)
    | sP49(U_1013,U_1014,U_1015)
    | ~ hBOOL(hAPP(U_1015,bool,U_1014,U_1013)) ),
    inference(clausify,[status(thm)],[f_263_4]) ).

cnf(f_263_6,plain,
    ( hBOOL(hAPP(U_1015,bool,U_1014,sK39(U_1015,U_1014,U_1013)))
    | ~ sP49(U_1013,U_1014,U_1015) ),
    inference(clausify,[status(thm)],[f_263_4]) ).

cnf(f_263_7,plain,
    ( ti(U_1015,sK39(U_1015,U_1014,U_1013)) != ti(U_1015,U_1013)
    | ~ sP49(U_1013,U_1014,U_1015) ),
    inference(clausify,[status(thm)],[f_263_4]) ).

fof(f_264_1,plain,
    ! [X_c,X_b,A_3,F,Z_1,G,F_2] :
      ( hAPP(fun(X_c,bool),X_b,F_2,A_3) = ti(X_b,Z_1)
      | ? [X_2] :
          ( hAPP(X_c,X_b,G,X_2) != ti(X_b,Z_1)
          & hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) )
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),A_3))
      | ~ hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_1),G),F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_211_folding__image__simple_Oneutral]) ).

fof(f_264_2,plain,
    ! [U_1023,U_1022,U_1021,U_1020,U_1019,U_1018,U_1017] :
      ( hAPP(fun(U_1023,bool),U_1022,U_1017,U_1021) = ti(U_1022,U_1019)
      | ? [U_1016] :
          ( hAPP(U_1023,U_1022,U_1018,U_1016) != ti(U_1022,U_1019)
          & hBOOL(hAPP(fun(U_1023,bool),bool,hAPP(U_1023,fun(fun(U_1023,bool),bool),member(U_1023),U_1016),U_1021)) )
      | ~ hBOOL(hAPP(fun(U_1023,bool),bool,finite_finite(U_1023),U_1021))
      | ~ hBOOL(hAPP(fun(fun(U_1023,bool),U_1022),bool,hAPP(fun(U_1023,U_1022),fun(fun(fun(U_1023,bool),U_1022),bool),hAPP(U_1022,fun(fun(U_1023,U_1022),fun(fun(fun(U_1023,bool),U_1022),bool)),hAPP(fun(U_1022,fun(U_1022,U_1022)),fun(U_1022,fun(fun(U_1023,U_1022),fun(fun(fun(U_1023,bool),U_1022),bool))),finite1357897459simple(U_1022,U_1023),U_1020),U_1019),U_1018),U_1017)) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

fof(f_264_3,plain,
    ! [U_1023,U_1022,U_1021,U_1020,U_1019,U_1018,U_1017] :
      ( hAPP(fun(U_1023,bool),U_1022,U_1017,U_1021) = ti(U_1022,U_1019)
      | ( hAPP(U_1023,U_1022,U_1018,sK40(U_1023,U_1022,U_1021,U_1020,U_1019,U_1018,U_1017)) != ti(U_1022,U_1019)
        & hBOOL(hAPP(fun(U_1023,bool),bool,hAPP(U_1023,fun(fun(U_1023,bool),bool),member(U_1023),sK40(U_1023,U_1022,U_1021,U_1020,U_1019,U_1018,U_1017)),U_1021)) )
      | ~ hBOOL(hAPP(fun(U_1023,bool),bool,finite_finite(U_1023),U_1021))
      | ~ hBOOL(hAPP(fun(fun(U_1023,bool),U_1022),bool,hAPP(fun(U_1023,U_1022),fun(fun(fun(U_1023,bool),U_1022),bool),hAPP(U_1022,fun(fun(U_1023,U_1022),fun(fun(fun(U_1023,bool),U_1022),bool)),hAPP(fun(U_1022,fun(U_1022,U_1022)),fun(U_1022,fun(fun(U_1023,U_1022),fun(fun(fun(U_1023,bool),U_1022),bool))),finite1357897459simple(U_1022,U_1023),U_1020),U_1019),U_1018),U_1017)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_1016,sK40(U_1023,U_1022,U_1021,U_1020,U_1019,U_1018,U_1017))],[f_264_2]) ).

fof(f_264_4,plain,
    ( ! [U_1018,U_1017,U_1019,U_1022,U_1020,U_1021,U_1023] :
        ( hAPP(U_1023,U_1022,U_1018,sK40(U_1023,U_1022,U_1021,U_1020,U_1019,U_1018,U_1017)) != ti(U_1022,U_1019)
        | ~ sP50(U_1018,U_1017,U_1019,U_1022,U_1020,U_1021,U_1023) )
    & ! [U_1018,U_1017,U_1019,U_1022,U_1020,U_1021,U_1023] :
        ( hBOOL(hAPP(fun(U_1023,bool),bool,hAPP(U_1023,fun(fun(U_1023,bool),bool),member(U_1023),sK40(U_1023,U_1022,U_1021,U_1020,U_1019,U_1018,U_1017)),U_1021))
        | ~ sP50(U_1018,U_1017,U_1019,U_1022,U_1020,U_1021,U_1023) )
    & ! [U_1018,U_1017,U_1019,U_1022,U_1020,U_1021,U_1023] :
        ( hAPP(fun(U_1023,bool),U_1022,U_1017,U_1021) = ti(U_1022,U_1019)
        | sP50(U_1018,U_1017,U_1019,U_1022,U_1020,U_1021,U_1023)
        | ~ hBOOL(hAPP(fun(U_1023,bool),bool,finite_finite(U_1023),U_1021))
        | ~ hBOOL(hAPP(fun(fun(U_1023,bool),U_1022),bool,hAPP(fun(U_1023,U_1022),fun(fun(fun(U_1023,bool),U_1022),bool),hAPP(U_1022,fun(fun(U_1023,U_1022),fun(fun(fun(U_1023,bool),U_1022),bool)),hAPP(fun(U_1022,fun(U_1022,U_1022)),fun(U_1022,fun(fun(U_1023,U_1022),fun(fun(fun(U_1023,bool),U_1022),bool))),finite1357897459simple(U_1022,U_1023),U_1020),U_1019),U_1018),U_1017)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50])],[f_264_3]) ).

cnf(f_264_5,plain,
    ( hAPP(fun(U_1023,bool),U_1022,U_1017,U_1021) = ti(U_1022,U_1019)
    | sP50(U_1018,U_1017,U_1019,U_1022,U_1020,U_1021,U_1023)
    | ~ hBOOL(hAPP(fun(U_1023,bool),bool,finite_finite(U_1023),U_1021))
    | ~ hBOOL(hAPP(fun(fun(U_1023,bool),U_1022),bool,hAPP(fun(U_1023,U_1022),fun(fun(fun(U_1023,bool),U_1022),bool),hAPP(U_1022,fun(fun(U_1023,U_1022),fun(fun(fun(U_1023,bool),U_1022),bool)),hAPP(fun(U_1022,fun(U_1022,U_1022)),fun(U_1022,fun(fun(U_1023,U_1022),fun(fun(fun(U_1023,bool),U_1022),bool))),finite1357897459simple(U_1022,U_1023),U_1020),U_1019),U_1018),U_1017)) ),
    inference(clausify,[status(thm)],[f_264_4]) ).

cnf(f_264_6,plain,
    ( hBOOL(hAPP(fun(U_1023,bool),bool,hAPP(U_1023,fun(fun(U_1023,bool),bool),member(U_1023),sK40(U_1023,U_1022,U_1021,U_1020,U_1019,U_1018,U_1017)),U_1021))
    | ~ sP50(U_1018,U_1017,U_1019,U_1022,U_1020,U_1021,U_1023) ),
    inference(clausify,[status(thm)],[f_264_4]) ).

cnf(f_264_7,plain,
    ( hAPP(U_1023,U_1022,U_1018,sK40(U_1023,U_1022,U_1021,U_1020,U_1019,U_1018,U_1017)) != ti(U_1022,U_1019)
    | ~ sP50(U_1018,U_1017,U_1019,U_1022,U_1020,U_1021,U_1023) ),
    inference(clausify,[status(thm)],[f_264_4]) ).

fof(f_265_1,plain,
    ! [X_b,X_c] :
      ( ! [A_3,B_2,X_2] : hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),minus_minus(fun(X_b,X_c)),A_3),B_2),X_2) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,A_3,X_2)),hAPP(X_b,X_c,B_2,X_2))
      | ~ minus(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_212_fun__diff__def]) ).

fof(f_265_2,plain,
    ! [U_1028,U_1027] :
      ( ! [U_1026,U_1025,U_1024] : hAPP(U_1028,U_1027,hAPP(fun(U_1028,U_1027),fun(U_1028,U_1027),hAPP(fun(U_1028,U_1027),fun(fun(U_1028,U_1027),fun(U_1028,U_1027)),minus_minus(fun(U_1028,U_1027)),U_1026),U_1025),U_1024) = hAPP(U_1027,U_1027,hAPP(U_1027,fun(U_1027,U_1027),minus_minus(U_1027),hAPP(U_1028,U_1027,U_1026,U_1024)),hAPP(U_1028,U_1027,U_1025,U_1024))
      | ~ minus(U_1027) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

fof(f_265_3,plain,
    ! [U_1025,U_1026,U_1028,U_1024,U_1027] :
      ( hAPP(U_1028,U_1027,hAPP(fun(U_1028,U_1027),fun(U_1028,U_1027),hAPP(fun(U_1028,U_1027),fun(fun(U_1028,U_1027),fun(U_1028,U_1027)),minus_minus(fun(U_1028,U_1027)),U_1026),U_1025),U_1024) = hAPP(U_1027,U_1027,hAPP(U_1027,fun(U_1027,U_1027),minus_minus(U_1027),hAPP(U_1028,U_1027,U_1026,U_1024)),hAPP(U_1028,U_1027,U_1025,U_1024))
      | ~ minus(U_1027) ),
    inference(definitional_conversion,[status(esa)],[f_265_2]) ).

cnf(f_265_4,plain,
    ( hAPP(U_1028,U_1027,hAPP(fun(U_1028,U_1027),fun(U_1028,U_1027),hAPP(fun(U_1028,U_1027),fun(fun(U_1028,U_1027),fun(U_1028,U_1027)),minus_minus(fun(U_1028,U_1027)),U_1026),U_1025),U_1024) = hAPP(U_1027,U_1027,hAPP(U_1027,fun(U_1027,U_1027),minus_minus(U_1027),hAPP(U_1028,U_1027,U_1026,U_1024)),hAPP(U_1028,U_1027,U_1025,U_1024))
    | ~ minus(U_1027) ),
    inference(clausify,[status(thm)],[f_265_3]) ).

fof(f_266_1,plain,
    ! [X_c,X_b] :
      ( ! [A_3,B_2,X_1] : hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),minus_minus(fun(X_c,X_b)),A_3),B_2),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_c,X_b,A_3,X_1)),hAPP(X_c,X_b,B_2,X_1))
      | ~ minus(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_213_minus__apply]) ).

fof(f_266_2,plain,
    ! [U_1033,U_1032] :
      ( ! [U_1031,U_1030,U_1029] : hAPP(U_1033,U_1032,hAPP(fun(U_1033,U_1032),fun(U_1033,U_1032),hAPP(fun(U_1033,U_1032),fun(fun(U_1033,U_1032),fun(U_1033,U_1032)),minus_minus(fun(U_1033,U_1032)),U_1031),U_1030),U_1029) = hAPP(U_1032,U_1032,hAPP(U_1032,fun(U_1032,U_1032),minus_minus(U_1032),hAPP(U_1033,U_1032,U_1031,U_1029)),hAPP(U_1033,U_1032,U_1030,U_1029))
      | ~ minus(U_1032) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

fof(f_266_3,plain,
    ! [U_1029,U_1030,U_1032,U_1031,U_1033] :
      ( hAPP(U_1033,U_1032,hAPP(fun(U_1033,U_1032),fun(U_1033,U_1032),hAPP(fun(U_1033,U_1032),fun(fun(U_1033,U_1032),fun(U_1033,U_1032)),minus_minus(fun(U_1033,U_1032)),U_1031),U_1030),U_1029) = hAPP(U_1032,U_1032,hAPP(U_1032,fun(U_1032,U_1032),minus_minus(U_1032),hAPP(U_1033,U_1032,U_1031,U_1029)),hAPP(U_1033,U_1032,U_1030,U_1029))
      | ~ minus(U_1032) ),
    inference(definitional_conversion,[status(esa)],[f_266_2]) ).

cnf(f_266_4,plain,
    ( hAPP(U_1033,U_1032,hAPP(fun(U_1033,U_1032),fun(U_1033,U_1032),hAPP(fun(U_1033,U_1032),fun(fun(U_1033,U_1032),fun(U_1033,U_1032)),minus_minus(fun(U_1033,U_1032)),U_1031),U_1030),U_1029) = hAPP(U_1032,U_1032,hAPP(U_1032,fun(U_1032,U_1032),minus_minus(U_1032),hAPP(U_1033,U_1032,U_1031,U_1029)),hAPP(U_1033,U_1032,U_1030,U_1029))
    | ~ minus(U_1032) ),
    inference(clausify,[status(thm)],[f_266_3]) ).

fof(f_267_1,plain,
    ! [X_b,Pa,A_2] :
      ( hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))
      | ? [X_2] :
          ( ti(X_b,X_2) != ti(X_b,A_2)
          & hBOOL(hAPP(X_b,bool,Pa,X_2)) )
      | ~ hBOOL(hAPP(X_b,bool,Pa,A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_214_theI]) ).

fof(f_267_2,plain,
    ! [U_1037,U_1036,U_1035] :
      ( hBOOL(hAPP(U_1037,bool,U_1036,hAPP(fun(U_1037,bool),U_1037,the(U_1037),U_1036)))
      | ? [U_1034] :
          ( ti(U_1037,U_1034) != ti(U_1037,U_1035)
          & hBOOL(hAPP(U_1037,bool,U_1036,U_1034)) )
      | ~ hBOOL(hAPP(U_1037,bool,U_1036,U_1035)) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

fof(f_267_3,plain,
    ! [U_1037,U_1036,U_1035] :
      ( hBOOL(hAPP(U_1037,bool,U_1036,hAPP(fun(U_1037,bool),U_1037,the(U_1037),U_1036)))
      | ( ti(U_1037,sK41(U_1037,U_1036,U_1035)) != ti(U_1037,U_1035)
        & hBOOL(hAPP(U_1037,bool,U_1036,sK41(U_1037,U_1036,U_1035))) )
      | ~ hBOOL(hAPP(U_1037,bool,U_1036,U_1035)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_1034,sK41(U_1037,U_1036,U_1035))],[f_267_2]) ).

fof(f_267_4,plain,
    ( ! [U_1036,U_1035,U_1037] :
        ( ti(U_1037,sK41(U_1037,U_1036,U_1035)) != ti(U_1037,U_1035)
        | ~ sP51(U_1036,U_1035,U_1037) )
    & ! [U_1036,U_1035,U_1037] :
        ( hBOOL(hAPP(U_1037,bool,U_1036,sK41(U_1037,U_1036,U_1035)))
        | ~ sP51(U_1036,U_1035,U_1037) )
    & ! [U_1036,U_1035,U_1037] :
        ( hBOOL(hAPP(U_1037,bool,U_1036,hAPP(fun(U_1037,bool),U_1037,the(U_1037),U_1036)))
        | sP51(U_1036,U_1035,U_1037)
        | ~ hBOOL(hAPP(U_1037,bool,U_1036,U_1035)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_267_3]) ).

cnf(f_267_5,plain,
    ( hBOOL(hAPP(U_1037,bool,U_1036,hAPP(fun(U_1037,bool),U_1037,the(U_1037),U_1036)))
    | sP51(U_1036,U_1035,U_1037)
    | ~ hBOOL(hAPP(U_1037,bool,U_1036,U_1035)) ),
    inference(clausify,[status(thm)],[f_267_4]) ).

cnf(f_267_6,plain,
    ( hBOOL(hAPP(U_1037,bool,U_1036,sK41(U_1037,U_1036,U_1035)))
    | ~ sP51(U_1036,U_1035,U_1037) ),
    inference(clausify,[status(thm)],[f_267_4]) ).

cnf(f_267_7,plain,
    ( ti(U_1037,sK41(U_1037,U_1036,U_1035)) != ti(U_1037,U_1035)
    | ~ sP51(U_1036,U_1035,U_1037) ),
    inference(clausify,[status(thm)],[f_267_4]) ).

fof(f_268_1,plain,
    ! [X_b,Pa] :
      ( hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))
      | ! [X_2] :
          ( ? [Y_2] :
              ( ti(X_b,Y_2) != ti(X_b,X_2)
              & hBOOL(hAPP(X_b,bool,Pa,Y_2)) )
          | ~ hBOOL(hAPP(X_b,bool,Pa,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_215_theI_H]) ).

fof(f_268_2,plain,
    ! [U_1041,U_1040] :
      ( hBOOL(hAPP(U_1041,bool,U_1040,hAPP(fun(U_1041,bool),U_1041,the(U_1041),U_1040)))
      | ! [U_1039] :
          ( ? [U_1038] :
              ( ti(U_1041,U_1038) != ti(U_1041,U_1039)
              & hBOOL(hAPP(U_1041,bool,U_1040,U_1038)) )
          | ~ hBOOL(hAPP(U_1041,bool,U_1040,U_1039)) ) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

fof(f_268_3,plain,
    ! [U_1041,U_1040] :
      ( hBOOL(hAPP(U_1041,bool,U_1040,hAPP(fun(U_1041,bool),U_1041,the(U_1041),U_1040)))
      | ! [U_1039] :
          ( ( ti(U_1041,sK42(U_1041,U_1040,U_1039)) != ti(U_1041,U_1039)
            & hBOOL(hAPP(U_1041,bool,U_1040,sK42(U_1041,U_1040,U_1039))) )
          | ~ hBOOL(hAPP(U_1041,bool,U_1040,U_1039)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_1038,sK42(U_1041,U_1040,U_1039))],[f_268_2]) ).

fof(f_268_4,plain,
    ( ! [U_1040,U_1039,U_1041] :
        ( ti(U_1041,sK42(U_1041,U_1040,U_1039)) != ti(U_1041,U_1039)
        | ~ sP52(U_1040,U_1039,U_1041) )
    & ! [U_1040,U_1039,U_1041] :
        ( hBOOL(hAPP(U_1041,bool,U_1040,sK42(U_1041,U_1040,U_1039)))
        | ~ sP52(U_1040,U_1039,U_1041) )
    & ! [U_1040,U_1039,U_1041] :
        ( hBOOL(hAPP(U_1041,bool,U_1040,hAPP(fun(U_1041,bool),U_1041,the(U_1041),U_1040)))
        | sP52(U_1040,U_1039,U_1041)
        | ~ hBOOL(hAPP(U_1041,bool,U_1040,U_1039)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52])],[f_268_3]) ).

cnf(f_268_5,plain,
    ( hBOOL(hAPP(U_1041,bool,U_1040,hAPP(fun(U_1041,bool),U_1041,the(U_1041),U_1040)))
    | sP52(U_1040,U_1039,U_1041)
    | ~ hBOOL(hAPP(U_1041,bool,U_1040,U_1039)) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

cnf(f_268_6,plain,
    ( hBOOL(hAPP(U_1041,bool,U_1040,sK42(U_1041,U_1040,U_1039)))
    | ~ sP52(U_1040,U_1039,U_1041) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

cnf(f_268_7,plain,
    ( ti(U_1041,sK42(U_1041,U_1040,U_1039)) != ti(U_1041,U_1039)
    | ~ sP52(U_1040,U_1039,U_1041) ),
    inference(clausify,[status(thm)],[f_268_4]) ).

fof(f_269_1,plain,
    ! [X_b,A_2,Pa] :
      ( hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_2)
      | ~ hBOOL(hAPP(X_b,bool,Pa,A_2))
      | ! [X_2] :
          ( ? [Y_2] :
              ( ti(X_b,Y_2) != ti(X_b,X_2)
              & hBOOL(hAPP(X_b,bool,Pa,Y_2)) )
          | ~ hBOOL(hAPP(X_b,bool,Pa,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_216_the1__equality]) ).

fof(f_269_2,plain,
    ! [U_1046,U_1045,U_1044] :
      ( hAPP(fun(U_1046,bool),U_1046,the(U_1046),U_1044) = ti(U_1046,U_1045)
      | ~ hBOOL(hAPP(U_1046,bool,U_1044,U_1045))
      | ! [U_1043] :
          ( ? [U_1042] :
              ( ti(U_1046,U_1042) != ti(U_1046,U_1043)
              & hBOOL(hAPP(U_1046,bool,U_1044,U_1042)) )
          | ~ hBOOL(hAPP(U_1046,bool,U_1044,U_1043)) ) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

fof(f_269_3,plain,
    ! [U_1046,U_1045,U_1044] :
      ( hAPP(fun(U_1046,bool),U_1046,the(U_1046),U_1044) = ti(U_1046,U_1045)
      | ~ hBOOL(hAPP(U_1046,bool,U_1044,U_1045))
      | ! [U_1043] :
          ( ( ti(U_1046,sK43(U_1046,U_1045,U_1044,U_1043)) != ti(U_1046,U_1043)
            & hBOOL(hAPP(U_1046,bool,U_1044,sK43(U_1046,U_1045,U_1044,U_1043))) )
          | ~ hBOOL(hAPP(U_1046,bool,U_1044,U_1043)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_1042,sK43(U_1046,U_1045,U_1044,U_1043))],[f_269_2]) ).

fof(f_269_4,plain,
    ( ! [U_1044,U_1043,U_1045,U_1046] :
        ( ti(U_1046,sK43(U_1046,U_1045,U_1044,U_1043)) != ti(U_1046,U_1043)
        | ~ sP53(U_1044,U_1043,U_1045,U_1046) )
    & ! [U_1044,U_1043,U_1045,U_1046] :
        ( hBOOL(hAPP(U_1046,bool,U_1044,sK43(U_1046,U_1045,U_1044,U_1043)))
        | ~ sP53(U_1044,U_1043,U_1045,U_1046) )
    & ! [U_1044,U_1043,U_1045,U_1046] :
        ( hAPP(fun(U_1046,bool),U_1046,the(U_1046),U_1044) = ti(U_1046,U_1045)
        | ~ hBOOL(hAPP(U_1046,bool,U_1044,U_1045))
        | sP53(U_1044,U_1043,U_1045,U_1046)
        | ~ hBOOL(hAPP(U_1046,bool,U_1044,U_1043)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53])],[f_269_3]) ).

cnf(f_269_5,plain,
    ( hAPP(fun(U_1046,bool),U_1046,the(U_1046),U_1044) = ti(U_1046,U_1045)
    | ~ hBOOL(hAPP(U_1046,bool,U_1044,U_1045))
    | sP53(U_1044,U_1043,U_1045,U_1046)
    | ~ hBOOL(hAPP(U_1046,bool,U_1044,U_1043)) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

cnf(f_269_6,plain,
    ( hBOOL(hAPP(U_1046,bool,U_1044,sK43(U_1046,U_1045,U_1044,U_1043)))
    | ~ sP53(U_1044,U_1043,U_1045,U_1046) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

cnf(f_269_7,plain,
    ( ti(U_1046,sK43(U_1046,U_1045,U_1044,U_1043)) != ti(U_1046,U_1043)
    | ~ sP53(U_1044,U_1043,U_1045,U_1046) ),
    inference(clausify,[status(thm)],[f_269_4]) ).

fof(f_270_1,plain,
    ! [X_b,A_3,B] :
      ( ( hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B),A_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool))))))
        | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool))))) )
      & ( hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),B),A_3) = ti(X_b,B)
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_217_flat__lub__def]) ).

fof(f_270_2,plain,
    ! [U_1049,U_1048,U_1047] :
      ( ( hAPP(fun(U_1049,bool),U_1049,hAPP(U_1049,fun(fun(U_1049,bool),U_1049),partial_flat_lub(U_1049),U_1047),U_1048) = hAPP(fun(U_1049,bool),U_1049,the(U_1049),hAPP(fun(U_1049,bool),fun(U_1049,bool),hAPP(fun(U_1049,fun(fun(U_1049,bool),bool)),fun(fun(U_1049,bool),fun(U_1049,bool)),combc(U_1049,fun(U_1049,bool),bool),member(U_1049)),hAPP(fun(U_1049,bool),fun(U_1049,bool),hAPP(fun(U_1049,bool),fun(fun(U_1049,bool),fun(U_1049,bool)),minus_minus(fun(U_1049,bool)),U_1048),hAPP(fun(U_1049,bool),fun(U_1049,bool),hAPP(U_1049,fun(fun(U_1049,bool),fun(U_1049,bool)),insert(U_1049),U_1047),bot_bot(fun(U_1049,bool))))))
        | hBOOL(hAPP(fun(U_1049,bool),bool,hAPP(fun(U_1049,bool),fun(fun(U_1049,bool),bool),ord_less_eq(fun(U_1049,bool)),U_1048),hAPP(fun(U_1049,bool),fun(U_1049,bool),hAPP(U_1049,fun(fun(U_1049,bool),fun(U_1049,bool)),insert(U_1049),U_1047),bot_bot(fun(U_1049,bool))))) )
      & ( hAPP(fun(U_1049,bool),U_1049,hAPP(U_1049,fun(fun(U_1049,bool),U_1049),partial_flat_lub(U_1049),U_1047),U_1048) = ti(U_1049,U_1047)
        | ~ hBOOL(hAPP(fun(U_1049,bool),bool,hAPP(fun(U_1049,bool),fun(fun(U_1049,bool),bool),ord_less_eq(fun(U_1049,bool)),U_1048),hAPP(fun(U_1049,bool),fun(U_1049,bool),hAPP(U_1049,fun(fun(U_1049,bool),fun(U_1049,bool)),insert(U_1049),U_1047),bot_bot(fun(U_1049,bool))))) ) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ( ! [U_1055,U_1053,U_1051] :
        ( hAPP(fun(U_1055,bool),U_1055,hAPP(U_1055,fun(fun(U_1055,bool),U_1055),partial_flat_lub(U_1055),U_1051),U_1053) = hAPP(fun(U_1055,bool),U_1055,the(U_1055),hAPP(fun(U_1055,bool),fun(U_1055,bool),hAPP(fun(U_1055,fun(fun(U_1055,bool),bool)),fun(fun(U_1055,bool),fun(U_1055,bool)),combc(U_1055,fun(U_1055,bool),bool),member(U_1055)),hAPP(fun(U_1055,bool),fun(U_1055,bool),hAPP(fun(U_1055,bool),fun(fun(U_1055,bool),fun(U_1055,bool)),minus_minus(fun(U_1055,bool)),U_1053),hAPP(fun(U_1055,bool),fun(U_1055,bool),hAPP(U_1055,fun(fun(U_1055,bool),fun(U_1055,bool)),insert(U_1055),U_1051),bot_bot(fun(U_1055,bool))))))
        | hBOOL(hAPP(fun(U_1055,bool),bool,hAPP(fun(U_1055,bool),fun(fun(U_1055,bool),bool),ord_less_eq(fun(U_1055,bool)),U_1053),hAPP(fun(U_1055,bool),fun(U_1055,bool),hAPP(U_1055,fun(fun(U_1055,bool),fun(U_1055,bool)),insert(U_1055),U_1051),bot_bot(fun(U_1055,bool))))) )
    & ! [U_1054,U_1052,U_1050] :
        ( hAPP(fun(U_1054,bool),U_1054,hAPP(U_1054,fun(fun(U_1054,bool),U_1054),partial_flat_lub(U_1054),U_1050),U_1052) = ti(U_1054,U_1050)
        | ~ hBOOL(hAPP(fun(U_1054,bool),bool,hAPP(fun(U_1054,bool),fun(fun(U_1054,bool),bool),ord_less_eq(fun(U_1054,bool)),U_1052),hAPP(fun(U_1054,bool),fun(U_1054,bool),hAPP(U_1054,fun(fun(U_1054,bool),fun(U_1054,bool)),insert(U_1054),U_1050),bot_bot(fun(U_1054,bool))))) ) ),
    inference(miniscope,[status(thm)],[f_270_2]) ).

fof(f_270_4,plain,
    ( ! [U_1053,U_1051,U_1055] :
        ( hAPP(fun(U_1055,bool),U_1055,hAPP(U_1055,fun(fun(U_1055,bool),U_1055),partial_flat_lub(U_1055),U_1051),U_1053) = hAPP(fun(U_1055,bool),U_1055,the(U_1055),hAPP(fun(U_1055,bool),fun(U_1055,bool),hAPP(fun(U_1055,fun(fun(U_1055,bool),bool)),fun(fun(U_1055,bool),fun(U_1055,bool)),combc(U_1055,fun(U_1055,bool),bool),member(U_1055)),hAPP(fun(U_1055,bool),fun(U_1055,bool),hAPP(fun(U_1055,bool),fun(fun(U_1055,bool),fun(U_1055,bool)),minus_minus(fun(U_1055,bool)),U_1053),hAPP(fun(U_1055,bool),fun(U_1055,bool),hAPP(U_1055,fun(fun(U_1055,bool),fun(U_1055,bool)),insert(U_1055),U_1051),bot_bot(fun(U_1055,bool))))))
        | hBOOL(hAPP(fun(U_1055,bool),bool,hAPP(fun(U_1055,bool),fun(fun(U_1055,bool),bool),ord_less_eq(fun(U_1055,bool)),U_1053),hAPP(fun(U_1055,bool),fun(U_1055,bool),hAPP(U_1055,fun(fun(U_1055,bool),fun(U_1055,bool)),insert(U_1055),U_1051),bot_bot(fun(U_1055,bool))))) )
    & ! [U_1054,U_1050,U_1052] :
        ( hAPP(fun(U_1054,bool),U_1054,hAPP(U_1054,fun(fun(U_1054,bool),U_1054),partial_flat_lub(U_1054),U_1050),U_1052) = ti(U_1054,U_1050)
        | ~ hBOOL(hAPP(fun(U_1054,bool),bool,hAPP(fun(U_1054,bool),fun(fun(U_1054,bool),bool),ord_less_eq(fun(U_1054,bool)),U_1052),hAPP(fun(U_1054,bool),fun(U_1054,bool),hAPP(U_1054,fun(fun(U_1054,bool),fun(U_1054,bool)),insert(U_1054),U_1050),bot_bot(fun(U_1054,bool))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_270_3]) ).

cnf(f_270_5,plain,
    ( hAPP(fun(U_1054,bool),U_1054,hAPP(U_1054,fun(fun(U_1054,bool),U_1054),partial_flat_lub(U_1054),U_1050),U_1052) = ti(U_1054,U_1050)
    | ~ hBOOL(hAPP(fun(U_1054,bool),bool,hAPP(fun(U_1054,bool),fun(fun(U_1054,bool),bool),ord_less_eq(fun(U_1054,bool)),U_1052),hAPP(fun(U_1054,bool),fun(U_1054,bool),hAPP(U_1054,fun(fun(U_1054,bool),fun(U_1054,bool)),insert(U_1054),U_1050),bot_bot(fun(U_1054,bool))))) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

cnf(f_270_6,plain,
    ( hAPP(fun(U_1055,bool),U_1055,hAPP(U_1055,fun(fun(U_1055,bool),U_1055),partial_flat_lub(U_1055),U_1051),U_1053) = hAPP(fun(U_1055,bool),U_1055,the(U_1055),hAPP(fun(U_1055,bool),fun(U_1055,bool),hAPP(fun(U_1055,fun(fun(U_1055,bool),bool)),fun(fun(U_1055,bool),fun(U_1055,bool)),combc(U_1055,fun(U_1055,bool),bool),member(U_1055)),hAPP(fun(U_1055,bool),fun(U_1055,bool),hAPP(fun(U_1055,bool),fun(fun(U_1055,bool),fun(U_1055,bool)),minus_minus(fun(U_1055,bool)),U_1053),hAPP(fun(U_1055,bool),fun(U_1055,bool),hAPP(U_1055,fun(fun(U_1055,bool),fun(U_1055,bool)),insert(U_1055),U_1051),bot_bot(fun(U_1055,bool))))))
    | hBOOL(hAPP(fun(U_1055,bool),bool,hAPP(fun(U_1055,bool),fun(fun(U_1055,bool),bool),ord_less_eq(fun(U_1055,bool)),U_1053),hAPP(fun(U_1055,bool),fun(U_1055,bool),hAPP(U_1055,fun(fun(U_1055,bool),fun(U_1055,bool)),insert(U_1055),U_1051),bot_bot(fun(U_1055,bool))))) ),
    inference(clausify,[status(thm)],[f_270_4]) ).

fof(f_271_1,plain,
    ! [X_b,X_1,A_3] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_218_card__Diff__singleton]) ).

fof(f_271_2,plain,
    ! [U_1058,U_1057,U_1056] :
      ( hAPP(fun(U_1058,bool),nat,finite_card(U_1058),hAPP(fun(U_1058,bool),fun(U_1058,bool),hAPP(fun(U_1058,bool),fun(fun(U_1058,bool),fun(U_1058,bool)),minus_minus(fun(U_1058,bool)),U_1056),hAPP(fun(U_1058,bool),fun(U_1058,bool),hAPP(U_1058,fun(fun(U_1058,bool),fun(U_1058,bool)),insert(U_1058),U_1057),bot_bot(fun(U_1058,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1058,bool),nat,finite_card(U_1058),U_1056)),one_one(nat))
      | ~ hBOOL(hAPP(fun(U_1058,bool),bool,hAPP(U_1058,fun(fun(U_1058,bool),bool),member(U_1058),U_1057),U_1056))
      | ~ hBOOL(hAPP(fun(U_1058,bool),bool,finite_finite(U_1058),U_1056)) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

fof(f_271_3,plain,
    ! [U_1058,U_1057,U_1056] :
      ( hAPP(fun(U_1058,bool),nat,finite_card(U_1058),hAPP(fun(U_1058,bool),fun(U_1058,bool),hAPP(fun(U_1058,bool),fun(fun(U_1058,bool),fun(U_1058,bool)),minus_minus(fun(U_1058,bool)),U_1056),hAPP(fun(U_1058,bool),fun(U_1058,bool),hAPP(U_1058,fun(fun(U_1058,bool),fun(U_1058,bool)),insert(U_1058),U_1057),bot_bot(fun(U_1058,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1058,bool),nat,finite_card(U_1058),U_1056)),one_one(nat))
      | ~ hBOOL(hAPP(fun(U_1058,bool),bool,hAPP(U_1058,fun(fun(U_1058,bool),bool),member(U_1058),U_1057),U_1056))
      | ~ hBOOL(hAPP(fun(U_1058,bool),bool,finite_finite(U_1058),U_1056)) ),
    inference(definitional_conversion,[status(esa)],[f_271_2]) ).

cnf(f_271_4,plain,
    ( hAPP(fun(U_1058,bool),nat,finite_card(U_1058),hAPP(fun(U_1058,bool),fun(U_1058,bool),hAPP(fun(U_1058,bool),fun(fun(U_1058,bool),fun(U_1058,bool)),minus_minus(fun(U_1058,bool)),U_1056),hAPP(fun(U_1058,bool),fun(U_1058,bool),hAPP(U_1058,fun(fun(U_1058,bool),fun(U_1058,bool)),insert(U_1058),U_1057),bot_bot(fun(U_1058,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1058,bool),nat,finite_card(U_1058),U_1056)),one_one(nat))
    | ~ hBOOL(hAPP(fun(U_1058,bool),bool,hAPP(U_1058,fun(fun(U_1058,bool),bool),member(U_1058),U_1057),U_1056))
    | ~ hBOOL(hAPP(fun(U_1058,bool),bool,finite_finite(U_1058),U_1056)) ),
    inference(clausify,[status(thm)],[f_271_3]) ).

fof(f_272_1,plain,
    ! [X_b,X_1,A_3] :
      ( ( ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)
          | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) )
        & ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat))
          | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ) )
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_219_card__Diff__singleton__if]) ).

fof(f_272_2,plain,
    ! [U_1061,U_1060,U_1059] :
      ( ( ( hAPP(fun(U_1061,bool),nat,finite_card(U_1061),hAPP(fun(U_1061,bool),fun(U_1061,bool),hAPP(fun(U_1061,bool),fun(fun(U_1061,bool),fun(U_1061,bool)),minus_minus(fun(U_1061,bool)),U_1059),hAPP(fun(U_1061,bool),fun(U_1061,bool),hAPP(U_1061,fun(fun(U_1061,bool),fun(U_1061,bool)),insert(U_1061),U_1060),bot_bot(fun(U_1061,bool))))) = hAPP(fun(U_1061,bool),nat,finite_card(U_1061),U_1059)
          | hBOOL(hAPP(fun(U_1061,bool),bool,hAPP(U_1061,fun(fun(U_1061,bool),bool),member(U_1061),U_1060),U_1059)) )
        & ( hAPP(fun(U_1061,bool),nat,finite_card(U_1061),hAPP(fun(U_1061,bool),fun(U_1061,bool),hAPP(fun(U_1061,bool),fun(fun(U_1061,bool),fun(U_1061,bool)),minus_minus(fun(U_1061,bool)),U_1059),hAPP(fun(U_1061,bool),fun(U_1061,bool),hAPP(U_1061,fun(fun(U_1061,bool),fun(U_1061,bool)),insert(U_1061),U_1060),bot_bot(fun(U_1061,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1061,bool),nat,finite_card(U_1061),U_1059)),one_one(nat))
          | ~ hBOOL(hAPP(fun(U_1061,bool),bool,hAPP(U_1061,fun(fun(U_1061,bool),bool),member(U_1061),U_1060),U_1059)) ) )
      | ~ hBOOL(hAPP(fun(U_1061,bool),bool,finite_finite(U_1061),U_1059)) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

fof(f_272_3,plain,
    ( ! [U_1061,U_1059,U_1060] :
        ( hAPP(fun(U_1061,bool),nat,finite_card(U_1061),hAPP(fun(U_1061,bool),fun(U_1061,bool),hAPP(fun(U_1061,bool),fun(fun(U_1061,bool),fun(U_1061,bool)),minus_minus(fun(U_1061,bool)),U_1059),hAPP(fun(U_1061,bool),fun(U_1061,bool),hAPP(U_1061,fun(fun(U_1061,bool),fun(U_1061,bool)),insert(U_1061),U_1060),bot_bot(fun(U_1061,bool))))) = hAPP(fun(U_1061,bool),nat,finite_card(U_1061),U_1059)
        | hBOOL(hAPP(fun(U_1061,bool),bool,hAPP(U_1061,fun(fun(U_1061,bool),bool),member(U_1061),U_1060),U_1059))
        | ~ sP54(U_1061,U_1059,U_1060) )
    & ! [U_1061,U_1059,U_1060] :
        ( hAPP(fun(U_1061,bool),nat,finite_card(U_1061),hAPP(fun(U_1061,bool),fun(U_1061,bool),hAPP(fun(U_1061,bool),fun(fun(U_1061,bool),fun(U_1061,bool)),minus_minus(fun(U_1061,bool)),U_1059),hAPP(fun(U_1061,bool),fun(U_1061,bool),hAPP(U_1061,fun(fun(U_1061,bool),fun(U_1061,bool)),insert(U_1061),U_1060),bot_bot(fun(U_1061,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1061,bool),nat,finite_card(U_1061),U_1059)),one_one(nat))
        | ~ hBOOL(hAPP(fun(U_1061,bool),bool,hAPP(U_1061,fun(fun(U_1061,bool),bool),member(U_1061),U_1060),U_1059))
        | ~ sP54(U_1061,U_1059,U_1060) )
    & ! [U_1061,U_1059,U_1060] :
        ( sP54(U_1061,U_1059,U_1060)
        | ~ hBOOL(hAPP(fun(U_1061,bool),bool,finite_finite(U_1061),U_1059)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54])],[f_272_2]) ).

cnf(f_272_4,plain,
    ( sP54(U_1061,U_1059,U_1060)
    | ~ hBOOL(hAPP(fun(U_1061,bool),bool,finite_finite(U_1061),U_1059)) ),
    inference(clausify,[status(thm)],[f_272_3]) ).

cnf(f_272_5,plain,
    ( hAPP(fun(U_1061,bool),nat,finite_card(U_1061),hAPP(fun(U_1061,bool),fun(U_1061,bool),hAPP(fun(U_1061,bool),fun(fun(U_1061,bool),fun(U_1061,bool)),minus_minus(fun(U_1061,bool)),U_1059),hAPP(fun(U_1061,bool),fun(U_1061,bool),hAPP(U_1061,fun(fun(U_1061,bool),fun(U_1061,bool)),insert(U_1061),U_1060),bot_bot(fun(U_1061,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1061,bool),nat,finite_card(U_1061),U_1059)),one_one(nat))
    | ~ hBOOL(hAPP(fun(U_1061,bool),bool,hAPP(U_1061,fun(fun(U_1061,bool),bool),member(U_1061),U_1060),U_1059))
    | ~ sP54(U_1061,U_1059,U_1060) ),
    inference(clausify,[status(thm)],[f_272_3]) ).

cnf(f_272_6,plain,
    ( hAPP(fun(U_1061,bool),nat,finite_card(U_1061),hAPP(fun(U_1061,bool),fun(U_1061,bool),hAPP(fun(U_1061,bool),fun(fun(U_1061,bool),fun(U_1061,bool)),minus_minus(fun(U_1061,bool)),U_1059),hAPP(fun(U_1061,bool),fun(U_1061,bool),hAPP(U_1061,fun(fun(U_1061,bool),fun(U_1061,bool)),insert(U_1061),U_1060),bot_bot(fun(U_1061,bool))))) = hAPP(fun(U_1061,bool),nat,finite_card(U_1061),U_1059)
    | hBOOL(hAPP(fun(U_1061,bool),bool,hAPP(U_1061,fun(fun(U_1061,bool),bool),member(U_1061),U_1060),U_1059))
    | ~ sP54(U_1061,U_1059,U_1060) ),
    inference(clausify,[status(thm)],[f_272_3]) ).

fof(f_273_1,plain,
    ! [X_b] :
      ( ! [X_1] :
          ( ( one_one(X_b) = ti(X_b,X_1)
            | ti(X_b,X_1) != one_one(X_b) )
          & ( ti(X_b,X_1) = one_one(X_b)
            | one_one(X_b) != ti(X_b,X_1) ) )
      | ~ one(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_220_one__reorient]) ).

fof(f_273_2,plain,
    ! [U_1063] :
      ( ! [U_1062] :
          ( ( one_one(U_1063) = ti(U_1063,U_1062)
            | ti(U_1063,U_1062) != one_one(U_1063) )
          & ( ti(U_1063,U_1062) = one_one(U_1063)
            | one_one(U_1063) != ti(U_1063,U_1062) ) )
      | ~ one(U_1063) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

fof(f_273_3,plain,
    ! [U_1063] :
      ( ( ! [U_1065] :
            ( one_one(U_1063) = ti(U_1063,U_1065)
            | ti(U_1063,U_1065) != one_one(U_1063) )
        & ! [U_1064] :
            ( ti(U_1063,U_1064) = one_one(U_1063)
            | one_one(U_1063) != ti(U_1063,U_1064) ) )
      | ~ one(U_1063) ),
    inference(miniscope,[status(thm)],[f_273_2]) ).

fof(f_273_4,plain,
    ( ! [U_1063,U_1065,U_1064] :
        ( one_one(U_1063) = ti(U_1063,U_1065)
        | ti(U_1063,U_1065) != one_one(U_1063)
        | ~ sP55(U_1063,U_1065,U_1064) )
    & ! [U_1063,U_1065,U_1064] :
        ( ti(U_1063,U_1064) = one_one(U_1063)
        | one_one(U_1063) != ti(U_1063,U_1064)
        | ~ sP55(U_1063,U_1065,U_1064) )
    & ! [U_1063,U_1065,U_1064] :
        ( sP55(U_1063,U_1065,U_1064)
        | ~ one(U_1063) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_273_3]) ).

cnf(f_273_5,plain,
    ( sP55(U_1063,U_1065,U_1064)
    | ~ one(U_1063) ),
    inference(clausify,[status(thm)],[f_273_4]) ).

cnf(f_273_6,plain,
    ( ti(U_1063,U_1064) = one_one(U_1063)
    | one_one(U_1063) != ti(U_1063,U_1064)
    | ~ sP55(U_1063,U_1065,U_1064) ),
    inference(clausify,[status(thm)],[f_273_4]) ).

cnf(f_273_7,plain,
    ( one_one(U_1063) = ti(U_1063,U_1065)
    | ti(U_1063,U_1065) != one_one(U_1063)
    | ~ sP55(U_1063,U_1065,U_1064) ),
    inference(clausify,[status(thm)],[f_273_4]) ).

fof(f_274_1,plain,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N),
    inference(fof_nnf,[status(thm)],[fact_221_diff__Suc__eq__diff__pred]) ).

fof(f_274_2,plain,
    ! [U_1067,U_1066] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1067),hAPP(nat,nat,suc,U_1066)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1067),one_one(nat))),U_1066),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ! [U_1066,U_1067] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1067),hAPP(nat,nat,suc,U_1066)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1067),one_one(nat))),U_1066),
    inference(definitional_conversion,[status(esa)],[f_274_2]) ).

cnf(f_274_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1067),hAPP(nat,nat,suc,U_1066)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1067),one_one(nat))),U_1066),
    inference(clausify,[status(thm)],[f_274_3]) ).

fof(f_275_1,plain,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat)) = N,
    inference(fof_nnf,[status(thm)],[fact_222_diff__Suc__1]) ).

fof(f_275_2,plain,
    ! [U_1068] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1068)),one_one(nat)) = U_1068,
    inference(variable_rename,[status(thm)],[f_275_1]) ).

fof(f_275_3,plain,
    ! [U_1068] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1068)),one_one(nat)) = U_1068,
    inference(definitional_conversion,[status(esa)],[f_275_2]) ).

cnf(f_275_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1068)),one_one(nat)) = U_1068,
    inference(clausify,[status(thm)],[f_275_3]) ).

fof(f_276_1,plain,
    ! [X_b,B_2,A_2,A_3] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_2))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))),one_one(nat))
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_223_card__Diff__insert]) ).

fof(f_276_2,plain,
    ! [U_1072,U_1071,U_1070,U_1069] :
      ( hAPP(fun(U_1072,bool),nat,finite_card(U_1072),hAPP(fun(U_1072,bool),fun(U_1072,bool),hAPP(fun(U_1072,bool),fun(fun(U_1072,bool),fun(U_1072,bool)),minus_minus(fun(U_1072,bool)),U_1069),hAPP(fun(U_1072,bool),fun(U_1072,bool),hAPP(U_1072,fun(fun(U_1072,bool),fun(U_1072,bool)),insert(U_1072),U_1070),U_1071))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1072,bool),nat,finite_card(U_1072),hAPP(fun(U_1072,bool),fun(U_1072,bool),hAPP(fun(U_1072,bool),fun(fun(U_1072,bool),fun(U_1072,bool)),minus_minus(fun(U_1072,bool)),U_1069),U_1071))),one_one(nat))
      | hBOOL(hAPP(fun(U_1072,bool),bool,hAPP(U_1072,fun(fun(U_1072,bool),bool),member(U_1072),U_1070),U_1071))
      | ~ hBOOL(hAPP(fun(U_1072,bool),bool,hAPP(U_1072,fun(fun(U_1072,bool),bool),member(U_1072),U_1070),U_1069))
      | ~ hBOOL(hAPP(fun(U_1072,bool),bool,finite_finite(U_1072),U_1069)) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

fof(f_276_3,plain,
    ! [U_1072,U_1070,U_1069,U_1071] :
      ( hAPP(fun(U_1072,bool),nat,finite_card(U_1072),hAPP(fun(U_1072,bool),fun(U_1072,bool),hAPP(fun(U_1072,bool),fun(fun(U_1072,bool),fun(U_1072,bool)),minus_minus(fun(U_1072,bool)),U_1069),hAPP(fun(U_1072,bool),fun(U_1072,bool),hAPP(U_1072,fun(fun(U_1072,bool),fun(U_1072,bool)),insert(U_1072),U_1070),U_1071))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1072,bool),nat,finite_card(U_1072),hAPP(fun(U_1072,bool),fun(U_1072,bool),hAPP(fun(U_1072,bool),fun(fun(U_1072,bool),fun(U_1072,bool)),minus_minus(fun(U_1072,bool)),U_1069),U_1071))),one_one(nat))
      | hBOOL(hAPP(fun(U_1072,bool),bool,hAPP(U_1072,fun(fun(U_1072,bool),bool),member(U_1072),U_1070),U_1071))
      | ~ hBOOL(hAPP(fun(U_1072,bool),bool,hAPP(U_1072,fun(fun(U_1072,bool),bool),member(U_1072),U_1070),U_1069))
      | ~ hBOOL(hAPP(fun(U_1072,bool),bool,finite_finite(U_1072),U_1069)) ),
    inference(definitional_conversion,[status(esa)],[f_276_2]) ).

cnf(f_276_4,plain,
    ( hAPP(fun(U_1072,bool),nat,finite_card(U_1072),hAPP(fun(U_1072,bool),fun(U_1072,bool),hAPP(fun(U_1072,bool),fun(fun(U_1072,bool),fun(U_1072,bool)),minus_minus(fun(U_1072,bool)),U_1069),hAPP(fun(U_1072,bool),fun(U_1072,bool),hAPP(U_1072,fun(fun(U_1072,bool),fun(U_1072,bool)),insert(U_1072),U_1070),U_1071))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(U_1072,bool),nat,finite_card(U_1072),hAPP(fun(U_1072,bool),fun(U_1072,bool),hAPP(fun(U_1072,bool),fun(fun(U_1072,bool),fun(U_1072,bool)),minus_minus(fun(U_1072,bool)),U_1069),U_1071))),one_one(nat))
    | hBOOL(hAPP(fun(U_1072,bool),bool,hAPP(U_1072,fun(fun(U_1072,bool),bool),member(U_1072),U_1070),U_1071))
    | ~ hBOOL(hAPP(fun(U_1072,bool),bool,hAPP(U_1072,fun(fun(U_1072,bool),bool),member(U_1072),U_1070),U_1069))
    | ~ hBOOL(hAPP(fun(U_1072,bool),bool,finite_finite(U_1072),U_1069)) ),
    inference(clausify,[status(thm)],[f_276_3]) ).

fof(f_277_1,plain,
    ! [X_b,X_1,A_3] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_224_card_Oinsert__remove]) ).

fof(f_277_2,plain,
    ! [U_1075,U_1074,U_1073] :
      ( hAPP(fun(U_1075,bool),nat,finite_card(U_1075),hAPP(fun(U_1075,bool),fun(U_1075,bool),hAPP(U_1075,fun(fun(U_1075,bool),fun(U_1075,bool)),insert(U_1075),U_1074),U_1073)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1075,bool),nat,finite_card(U_1075),hAPP(fun(U_1075,bool),fun(U_1075,bool),hAPP(fun(U_1075,bool),fun(fun(U_1075,bool),fun(U_1075,bool)),minus_minus(fun(U_1075,bool)),U_1073),hAPP(fun(U_1075,bool),fun(U_1075,bool),hAPP(U_1075,fun(fun(U_1075,bool),fun(U_1075,bool)),insert(U_1075),U_1074),bot_bot(fun(U_1075,bool))))))
      | ~ hBOOL(hAPP(fun(U_1075,bool),bool,finite_finite(U_1075),U_1073)) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

fof(f_277_3,plain,
    ! [U_1074,U_1073,U_1075] :
      ( hAPP(fun(U_1075,bool),nat,finite_card(U_1075),hAPP(fun(U_1075,bool),fun(U_1075,bool),hAPP(U_1075,fun(fun(U_1075,bool),fun(U_1075,bool)),insert(U_1075),U_1074),U_1073)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1075,bool),nat,finite_card(U_1075),hAPP(fun(U_1075,bool),fun(U_1075,bool),hAPP(fun(U_1075,bool),fun(fun(U_1075,bool),fun(U_1075,bool)),minus_minus(fun(U_1075,bool)),U_1073),hAPP(fun(U_1075,bool),fun(U_1075,bool),hAPP(U_1075,fun(fun(U_1075,bool),fun(U_1075,bool)),insert(U_1075),U_1074),bot_bot(fun(U_1075,bool))))))
      | ~ hBOOL(hAPP(fun(U_1075,bool),bool,finite_finite(U_1075),U_1073)) ),
    inference(definitional_conversion,[status(esa)],[f_277_2]) ).

cnf(f_277_4,plain,
    ( hAPP(fun(U_1075,bool),nat,finite_card(U_1075),hAPP(fun(U_1075,bool),fun(U_1075,bool),hAPP(U_1075,fun(fun(U_1075,bool),fun(U_1075,bool)),insert(U_1075),U_1074),U_1073)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1075,bool),nat,finite_card(U_1075),hAPP(fun(U_1075,bool),fun(U_1075,bool),hAPP(fun(U_1075,bool),fun(fun(U_1075,bool),fun(U_1075,bool)),minus_minus(fun(U_1075,bool)),U_1073),hAPP(fun(U_1075,bool),fun(U_1075,bool),hAPP(U_1075,fun(fun(U_1075,bool),fun(U_1075,bool)),insert(U_1075),U_1074),bot_bot(fun(U_1075,bool))))))
    | ~ hBOOL(hAPP(fun(U_1075,bool),bool,finite_finite(U_1075),U_1073)) ),
    inference(clausify,[status(thm)],[f_277_3]) ).

fof(f_278_1,plain,
    ! [X_b,X_1,A_3] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_225_card_Oremove]) ).

fof(f_278_2,plain,
    ! [U_1078,U_1077,U_1076] :
      ( hAPP(fun(U_1078,bool),nat,finite_card(U_1078),U_1076) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1078,bool),nat,finite_card(U_1078),hAPP(fun(U_1078,bool),fun(U_1078,bool),hAPP(fun(U_1078,bool),fun(fun(U_1078,bool),fun(U_1078,bool)),minus_minus(fun(U_1078,bool)),U_1076),hAPP(fun(U_1078,bool),fun(U_1078,bool),hAPP(U_1078,fun(fun(U_1078,bool),fun(U_1078,bool)),insert(U_1078),U_1077),bot_bot(fun(U_1078,bool))))))
      | ~ hBOOL(hAPP(fun(U_1078,bool),bool,hAPP(U_1078,fun(fun(U_1078,bool),bool),member(U_1078),U_1077),U_1076))
      | ~ hBOOL(hAPP(fun(U_1078,bool),bool,finite_finite(U_1078),U_1076)) ),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

fof(f_278_3,plain,
    ! [U_1076,U_1077,U_1078] :
      ( hAPP(fun(U_1078,bool),nat,finite_card(U_1078),U_1076) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1078,bool),nat,finite_card(U_1078),hAPP(fun(U_1078,bool),fun(U_1078,bool),hAPP(fun(U_1078,bool),fun(fun(U_1078,bool),fun(U_1078,bool)),minus_minus(fun(U_1078,bool)),U_1076),hAPP(fun(U_1078,bool),fun(U_1078,bool),hAPP(U_1078,fun(fun(U_1078,bool),fun(U_1078,bool)),insert(U_1078),U_1077),bot_bot(fun(U_1078,bool))))))
      | ~ hBOOL(hAPP(fun(U_1078,bool),bool,hAPP(U_1078,fun(fun(U_1078,bool),bool),member(U_1078),U_1077),U_1076))
      | ~ hBOOL(hAPP(fun(U_1078,bool),bool,finite_finite(U_1078),U_1076)) ),
    inference(definitional_conversion,[status(esa)],[f_278_2]) ).

cnf(f_278_4,plain,
    ( hAPP(fun(U_1078,bool),nat,finite_card(U_1078),U_1076) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1078,bool),nat,finite_card(U_1078),hAPP(fun(U_1078,bool),fun(U_1078,bool),hAPP(fun(U_1078,bool),fun(fun(U_1078,bool),fun(U_1078,bool)),minus_minus(fun(U_1078,bool)),U_1076),hAPP(fun(U_1078,bool),fun(U_1078,bool),hAPP(U_1078,fun(fun(U_1078,bool),fun(U_1078,bool)),insert(U_1078),U_1077),bot_bot(fun(U_1078,bool))))))
    | ~ hBOOL(hAPP(fun(U_1078,bool),bool,hAPP(U_1078,fun(fun(U_1078,bool),bool),member(U_1078),U_1077),U_1076))
    | ~ hBOOL(hAPP(fun(U_1078,bool),bool,finite_finite(U_1078),U_1076)) ),
    inference(clausify,[status(thm)],[f_278_3]) ).

fof(f_279_1,plain,
    ! [X_b] : hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool)))))),
    inference(fof_nnf,[status(thm)],[fact_226_comp__fun__idem__remove]) ).

fof(f_279_2,plain,
    ! [U_1079] : hBOOL(hAPP(fun(U_1079,fun(fun(U_1079,bool),fun(U_1079,bool))),bool,finite_comp_fun_idem(U_1079,fun(U_1079,bool)),hAPP(fun(U_1079,fun(U_1079,bool)),fun(U_1079,fun(fun(U_1079,bool),fun(U_1079,bool))),hAPP(fun(fun(U_1079,bool),fun(fun(U_1079,bool),fun(U_1079,bool))),fun(fun(U_1079,fun(U_1079,bool)),fun(U_1079,fun(fun(U_1079,bool),fun(U_1079,bool)))),combb(fun(U_1079,bool),fun(fun(U_1079,bool),fun(U_1079,bool)),U_1079),hAPP(fun(fun(U_1079,bool),fun(fun(U_1079,bool),fun(U_1079,bool))),fun(fun(U_1079,bool),fun(fun(U_1079,bool),fun(U_1079,bool))),combc(fun(U_1079,bool),fun(U_1079,bool),fun(U_1079,bool)),minus_minus(fun(U_1079,bool)))),hAPP(fun(U_1079,bool),fun(U_1079,fun(U_1079,bool)),hAPP(fun(U_1079,fun(fun(U_1079,bool),fun(U_1079,bool))),fun(fun(U_1079,bool),fun(U_1079,fun(U_1079,bool))),combc(U_1079,fun(U_1079,bool),fun(U_1079,bool)),insert(U_1079)),bot_bot(fun(U_1079,bool)))))),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

fof(f_279_3,plain,
    ! [U_1079] : hBOOL(hAPP(fun(U_1079,fun(fun(U_1079,bool),fun(U_1079,bool))),bool,finite_comp_fun_idem(U_1079,fun(U_1079,bool)),hAPP(fun(U_1079,fun(U_1079,bool)),fun(U_1079,fun(fun(U_1079,bool),fun(U_1079,bool))),hAPP(fun(fun(U_1079,bool),fun(fun(U_1079,bool),fun(U_1079,bool))),fun(fun(U_1079,fun(U_1079,bool)),fun(U_1079,fun(fun(U_1079,bool),fun(U_1079,bool)))),combb(fun(U_1079,bool),fun(fun(U_1079,bool),fun(U_1079,bool)),U_1079),hAPP(fun(fun(U_1079,bool),fun(fun(U_1079,bool),fun(U_1079,bool))),fun(fun(U_1079,bool),fun(fun(U_1079,bool),fun(U_1079,bool))),combc(fun(U_1079,bool),fun(U_1079,bool),fun(U_1079,bool)),minus_minus(fun(U_1079,bool)))),hAPP(fun(U_1079,bool),fun(U_1079,fun(U_1079,bool)),hAPP(fun(U_1079,fun(fun(U_1079,bool),fun(U_1079,bool))),fun(fun(U_1079,bool),fun(U_1079,fun(U_1079,bool))),combc(U_1079,fun(U_1079,bool),fun(U_1079,bool)),insert(U_1079)),bot_bot(fun(U_1079,bool)))))),
    inference(definitional_conversion,[status(esa)],[f_279_2]) ).

cnf(f_279_4,plain,
    hBOOL(hAPP(fun(U_1079,fun(fun(U_1079,bool),fun(U_1079,bool))),bool,finite_comp_fun_idem(U_1079,fun(U_1079,bool)),hAPP(fun(U_1079,fun(U_1079,bool)),fun(U_1079,fun(fun(U_1079,bool),fun(U_1079,bool))),hAPP(fun(fun(U_1079,bool),fun(fun(U_1079,bool),fun(U_1079,bool))),fun(fun(U_1079,fun(U_1079,bool)),fun(U_1079,fun(fun(U_1079,bool),fun(U_1079,bool)))),combb(fun(U_1079,bool),fun(fun(U_1079,bool),fun(U_1079,bool)),U_1079),hAPP(fun(fun(U_1079,bool),fun(fun(U_1079,bool),fun(U_1079,bool))),fun(fun(U_1079,bool),fun(fun(U_1079,bool),fun(U_1079,bool))),combc(fun(U_1079,bool),fun(U_1079,bool),fun(U_1079,bool)),minus_minus(fun(U_1079,bool)))),hAPP(fun(U_1079,bool),fun(U_1079,fun(U_1079,bool)),hAPP(fun(U_1079,fun(fun(U_1079,bool),fun(U_1079,bool))),fun(fun(U_1079,bool),fun(U_1079,fun(U_1079,bool))),combc(U_1079,fun(U_1079,bool),fun(U_1079,bool)),insert(U_1079)),bot_bot(fun(U_1079,bool)))))),
    inference(clausify,[status(thm)],[f_279_3]) ).

fof(f_280_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1)),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1)),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_227_less__eq__nat_Osimps_I2_J]) ).

fof(f_280_2,plain,
    ! [U_1081,U_1080] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1081)),U_1080))
        | ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1081)),U_1080)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1081)),U_1080))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1081)),U_1080)) ) ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

fof(f_280_3,plain,
    ( ! [U_1085,U_1083] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1085)),U_1083))
        | ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1085)),U_1083)) )
    & ! [U_1084,U_1082] :
        ( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1084)),U_1082))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1084)),U_1082)) ) ),
    inference(miniscope,[status(thm)],[f_280_2]) ).

fof(f_280_4,plain,
    ( ! [U_1083,U_1085] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1085)),U_1083))
        | ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1085)),U_1083)) )
    & ! [U_1084,U_1082] :
        ( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1084)),U_1082))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1084)),U_1082)) ) ),
    inference(definitional_conversion,[status(esa)],[f_280_3]) ).

cnf(f_280_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1084)),U_1082))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1084)),U_1082)) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

cnf(f_280_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1085)),U_1083))
    | ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1085)),U_1083)) ),
    inference(clausify,[status(thm)],[f_280_4]) ).

fof(f_281_1,plain,
    ! [X_b] :
      ( ! [A_2,C_1,B] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C_1)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C_1))) ) )
      | ~ ordere236663937imp_le(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_228_add__le__cancel__right]) ).

fof(f_281_2,plain,
    ! [U_1089] :
      ( ! [U_1088,U_1087,U_1086] :
          ( ( hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1088),U_1087)),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1086),U_1087)))
            | ~ hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),U_1088),U_1086)) )
          & ( hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),U_1088),U_1086))
            | ~ hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1088),U_1087)),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1086),U_1087))) ) )
      | ~ ordere236663937imp_le(U_1089) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

fof(f_281_3,plain,
    ! [U_1089] :
      ( ( ! [U_1095,U_1093,U_1091] :
            ( hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1095),U_1093)),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1091),U_1093)))
            | ~ hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),U_1095),U_1091)) )
        & ! [U_1094,U_1092,U_1090] :
            ( hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),U_1094),U_1090))
            | ~ hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1094),U_1092)),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1090),U_1092))) ) )
      | ~ ordere236663937imp_le(U_1089) ),
    inference(miniscope,[status(thm)],[f_281_2]) ).

fof(f_281_4,plain,
    ( ! [U_1092,U_1089,U_1094,U_1090,U_1091,U_1095,U_1093] :
        ( hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1095),U_1093)),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1091),U_1093)))
        | ~ hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),U_1095),U_1091))
        | ~ sP56(U_1092,U_1089,U_1094,U_1090,U_1091,U_1095,U_1093) )
    & ! [U_1092,U_1089,U_1094,U_1090,U_1091,U_1095,U_1093] :
        ( hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),U_1094),U_1090))
        | ~ hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1094),U_1092)),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1090),U_1092)))
        | ~ sP56(U_1092,U_1089,U_1094,U_1090,U_1091,U_1095,U_1093) )
    & ! [U_1092,U_1089,U_1094,U_1090,U_1091,U_1095,U_1093] :
        ( sP56(U_1092,U_1089,U_1094,U_1090,U_1091,U_1095,U_1093)
        | ~ ordere236663937imp_le(U_1089) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56])],[f_281_3]) ).

cnf(f_281_5,plain,
    ( sP56(U_1092,U_1089,U_1094,U_1090,U_1091,U_1095,U_1093)
    | ~ ordere236663937imp_le(U_1089) ),
    inference(clausify,[status(thm)],[f_281_4]) ).

cnf(f_281_6,plain,
    ( hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),U_1094),U_1090))
    | ~ hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1094),U_1092)),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1090),U_1092)))
    | ~ sP56(U_1092,U_1089,U_1094,U_1090,U_1091,U_1095,U_1093) ),
    inference(clausify,[status(thm)],[f_281_4]) ).

cnf(f_281_7,plain,
    ( hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1095),U_1093)),hAPP(U_1089,U_1089,hAPP(U_1089,fun(U_1089,U_1089),plus_plus(U_1089),U_1091),U_1093)))
    | ~ hBOOL(hAPP(U_1089,bool,hAPP(U_1089,fun(U_1089,bool),ord_less_eq(U_1089),U_1095),U_1091))
    | ~ sP56(U_1092,U_1089,U_1094,U_1090,U_1091,U_1095,U_1093) ),
    inference(clausify,[status(thm)],[f_281_4]) ).

fof(f_282_1,plain,
    ! [X_b] :
      ( ! [C_1,A_2,B] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B))) ) )
      | ~ ordere236663937imp_le(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_229_add__le__cancel__left]) ).

fof(f_282_2,plain,
    ! [U_1099] :
      ( ! [U_1098,U_1097,U_1096] :
          ( ( hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1098),U_1097)),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1098),U_1096)))
            | ~ hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),U_1097),U_1096)) )
          & ( hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),U_1097),U_1096))
            | ~ hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1098),U_1097)),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1098),U_1096))) ) )
      | ~ ordere236663937imp_le(U_1099) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

fof(f_282_3,plain,
    ! [U_1099] :
      ( ( ! [U_1105,U_1103,U_1101] :
            ( hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1105),U_1103)),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1105),U_1101)))
            | ~ hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),U_1103),U_1101)) )
        & ! [U_1104,U_1102,U_1100] :
            ( hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),U_1102),U_1100))
            | ~ hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1104),U_1102)),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1104),U_1100))) ) )
      | ~ ordere236663937imp_le(U_1099) ),
    inference(miniscope,[status(thm)],[f_282_2]) ).

fof(f_282_4,plain,
    ( ! [U_1099,U_1100,U_1104,U_1102,U_1101,U_1103,U_1105] :
        ( hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1105),U_1103)),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1105),U_1101)))
        | ~ hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),U_1103),U_1101))
        | ~ sP57(U_1099,U_1100,U_1104,U_1102,U_1101,U_1103,U_1105) )
    & ! [U_1099,U_1100,U_1104,U_1102,U_1101,U_1103,U_1105] :
        ( hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),U_1102),U_1100))
        | ~ hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1104),U_1102)),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1104),U_1100)))
        | ~ sP57(U_1099,U_1100,U_1104,U_1102,U_1101,U_1103,U_1105) )
    & ! [U_1099,U_1100,U_1104,U_1102,U_1101,U_1103,U_1105] :
        ( sP57(U_1099,U_1100,U_1104,U_1102,U_1101,U_1103,U_1105)
        | ~ ordere236663937imp_le(U_1099) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57])],[f_282_3]) ).

cnf(f_282_5,plain,
    ( sP57(U_1099,U_1100,U_1104,U_1102,U_1101,U_1103,U_1105)
    | ~ ordere236663937imp_le(U_1099) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

cnf(f_282_6,plain,
    ( hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),U_1102),U_1100))
    | ~ hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1104),U_1102)),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1104),U_1100)))
    | ~ sP57(U_1099,U_1100,U_1104,U_1102,U_1101,U_1103,U_1105) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

cnf(f_282_7,plain,
    ( hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1105),U_1103)),hAPP(U_1099,U_1099,hAPP(U_1099,fun(U_1099,U_1099),plus_plus(U_1099),U_1105),U_1101)))
    | ~ hBOOL(hAPP(U_1099,bool,hAPP(U_1099,fun(U_1099,bool),ord_less_eq(U_1099),U_1103),U_1101))
    | ~ sP57(U_1099,U_1100,U_1104,U_1102,U_1101,U_1103,U_1105) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

fof(f_283_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) )
      | ~ ordere779506340up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_230_add__right__mono]) ).

fof(f_283_2,plain,
    ! [U_1109] :
      ( ! [U_1108,U_1107,U_1106] :
          ( hBOOL(hAPP(U_1109,bool,hAPP(U_1109,fun(U_1109,bool),ord_less_eq(U_1109),hAPP(U_1109,U_1109,hAPP(U_1109,fun(U_1109,U_1109),plus_plus(U_1109),U_1107),U_1108)),hAPP(U_1109,U_1109,hAPP(U_1109,fun(U_1109,U_1109),plus_plus(U_1109),U_1106),U_1108)))
          | ~ hBOOL(hAPP(U_1109,bool,hAPP(U_1109,fun(U_1109,bool),ord_less_eq(U_1109),U_1107),U_1106)) )
      | ~ ordere779506340up_add(U_1109) ),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

fof(f_283_3,plain,
    ! [U_1109,U_1108,U_1106,U_1107] :
      ( hBOOL(hAPP(U_1109,bool,hAPP(U_1109,fun(U_1109,bool),ord_less_eq(U_1109),hAPP(U_1109,U_1109,hAPP(U_1109,fun(U_1109,U_1109),plus_plus(U_1109),U_1107),U_1108)),hAPP(U_1109,U_1109,hAPP(U_1109,fun(U_1109,U_1109),plus_plus(U_1109),U_1106),U_1108)))
      | ~ hBOOL(hAPP(U_1109,bool,hAPP(U_1109,fun(U_1109,bool),ord_less_eq(U_1109),U_1107),U_1106))
      | ~ ordere779506340up_add(U_1109) ),
    inference(definitional_conversion,[status(esa)],[f_283_2]) ).

cnf(f_283_4,plain,
    ( hBOOL(hAPP(U_1109,bool,hAPP(U_1109,fun(U_1109,bool),ord_less_eq(U_1109),hAPP(U_1109,U_1109,hAPP(U_1109,fun(U_1109,U_1109),plus_plus(U_1109),U_1107),U_1108)),hAPP(U_1109,U_1109,hAPP(U_1109,fun(U_1109,U_1109),plus_plus(U_1109),U_1106),U_1108)))
    | ~ hBOOL(hAPP(U_1109,bool,hAPP(U_1109,fun(U_1109,bool),ord_less_eq(U_1109),U_1107),U_1106))
    | ~ ordere779506340up_add(U_1109) ),
    inference(clausify,[status(thm)],[f_283_3]) ).

fof(f_284_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) )
      | ~ ordere779506340up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_231_add__left__mono]) ).

fof(f_284_2,plain,
    ! [U_1113] :
      ( ! [U_1112,U_1111,U_1110] :
          ( hBOOL(hAPP(U_1113,bool,hAPP(U_1113,fun(U_1113,bool),ord_less_eq(U_1113),hAPP(U_1113,U_1113,hAPP(U_1113,fun(U_1113,U_1113),plus_plus(U_1113),U_1112),U_1111)),hAPP(U_1113,U_1113,hAPP(U_1113,fun(U_1113,U_1113),plus_plus(U_1113),U_1112),U_1110)))
          | ~ hBOOL(hAPP(U_1113,bool,hAPP(U_1113,fun(U_1113,bool),ord_less_eq(U_1113),U_1111),U_1110)) )
      | ~ ordere779506340up_add(U_1113) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

fof(f_284_3,plain,
    ! [U_1113,U_1110,U_1111,U_1112] :
      ( hBOOL(hAPP(U_1113,bool,hAPP(U_1113,fun(U_1113,bool),ord_less_eq(U_1113),hAPP(U_1113,U_1113,hAPP(U_1113,fun(U_1113,U_1113),plus_plus(U_1113),U_1112),U_1111)),hAPP(U_1113,U_1113,hAPP(U_1113,fun(U_1113,U_1113),plus_plus(U_1113),U_1112),U_1110)))
      | ~ hBOOL(hAPP(U_1113,bool,hAPP(U_1113,fun(U_1113,bool),ord_less_eq(U_1113),U_1111),U_1110))
      | ~ ordere779506340up_add(U_1113) ),
    inference(definitional_conversion,[status(esa)],[f_284_2]) ).

cnf(f_284_4,plain,
    ( hBOOL(hAPP(U_1113,bool,hAPP(U_1113,fun(U_1113,bool),ord_less_eq(U_1113),hAPP(U_1113,U_1113,hAPP(U_1113,fun(U_1113,U_1113),plus_plus(U_1113),U_1112),U_1111)),hAPP(U_1113,U_1113,hAPP(U_1113,fun(U_1113,U_1113),plus_plus(U_1113),U_1112),U_1110)))
    | ~ hBOOL(hAPP(U_1113,bool,hAPP(U_1113,fun(U_1113,bool),ord_less_eq(U_1113),U_1111),U_1110))
    | ~ ordere779506340up_add(U_1113) ),
    inference(clausify,[status(thm)],[f_284_3]) ).

fof(f_285_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) )
      | ~ ordere779506340up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_232_add__mono]) ).

fof(f_285_2,plain,
    ! [U_1118] :
      ( ! [U_1117,U_1116,U_1115,U_1114] :
          ( hBOOL(hAPP(U_1118,bool,hAPP(U_1118,fun(U_1118,bool),ord_less_eq(U_1118),hAPP(U_1118,U_1118,hAPP(U_1118,fun(U_1118,U_1118),plus_plus(U_1118),U_1115),U_1117)),hAPP(U_1118,U_1118,hAPP(U_1118,fun(U_1118,U_1118),plus_plus(U_1118),U_1114),U_1116)))
          | ~ hBOOL(hAPP(U_1118,bool,hAPP(U_1118,fun(U_1118,bool),ord_less_eq(U_1118),U_1117),U_1116))
          | ~ hBOOL(hAPP(U_1118,bool,hAPP(U_1118,fun(U_1118,bool),ord_less_eq(U_1118),U_1115),U_1114)) )
      | ~ ordere779506340up_add(U_1118) ),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

fof(f_285_3,plain,
    ! [U_1115,U_1118,U_1114,U_1116,U_1117] :
      ( hBOOL(hAPP(U_1118,bool,hAPP(U_1118,fun(U_1118,bool),ord_less_eq(U_1118),hAPP(U_1118,U_1118,hAPP(U_1118,fun(U_1118,U_1118),plus_plus(U_1118),U_1115),U_1117)),hAPP(U_1118,U_1118,hAPP(U_1118,fun(U_1118,U_1118),plus_plus(U_1118),U_1114),U_1116)))
      | ~ hBOOL(hAPP(U_1118,bool,hAPP(U_1118,fun(U_1118,bool),ord_less_eq(U_1118),U_1117),U_1116))
      | ~ hBOOL(hAPP(U_1118,bool,hAPP(U_1118,fun(U_1118,bool),ord_less_eq(U_1118),U_1115),U_1114))
      | ~ ordere779506340up_add(U_1118) ),
    inference(definitional_conversion,[status(esa)],[f_285_2]) ).

cnf(f_285_4,plain,
    ( hBOOL(hAPP(U_1118,bool,hAPP(U_1118,fun(U_1118,bool),ord_less_eq(U_1118),hAPP(U_1118,U_1118,hAPP(U_1118,fun(U_1118,U_1118),plus_plus(U_1118),U_1115),U_1117)),hAPP(U_1118,U_1118,hAPP(U_1118,fun(U_1118,U_1118),plus_plus(U_1118),U_1114),U_1116)))
    | ~ hBOOL(hAPP(U_1118,bool,hAPP(U_1118,fun(U_1118,bool),ord_less_eq(U_1118),U_1117),U_1116))
    | ~ hBOOL(hAPP(U_1118,bool,hAPP(U_1118,fun(U_1118,bool),ord_less_eq(U_1118),U_1115),U_1114))
    | ~ ordere779506340up_add(U_1118) ),
    inference(clausify,[status(thm)],[f_285_3]) ).

fof(f_286_1,plain,
    ! [X_a] :
      ( ! [A_1,C,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C))) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_233_add__le__imp__le__right]) ).

fof(f_286_2,plain,
    ! [U_1122] :
      ( ! [U_1121,U_1120,U_1119] :
          ( hBOOL(hAPP(U_1122,bool,hAPP(U_1122,fun(U_1122,bool),ord_less_eq(U_1122),U_1121),U_1119))
          | ~ hBOOL(hAPP(U_1122,bool,hAPP(U_1122,fun(U_1122,bool),ord_less_eq(U_1122),hAPP(U_1122,U_1122,hAPP(U_1122,fun(U_1122,U_1122),plus_plus(U_1122),U_1121),U_1120)),hAPP(U_1122,U_1122,hAPP(U_1122,fun(U_1122,U_1122),plus_plus(U_1122),U_1119),U_1120))) )
      | ~ ordere236663937imp_le(U_1122) ),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

fof(f_286_3,plain,
    ! [U_1120,U_1122,U_1119,U_1121] :
      ( hBOOL(hAPP(U_1122,bool,hAPP(U_1122,fun(U_1122,bool),ord_less_eq(U_1122),U_1121),U_1119))
      | ~ hBOOL(hAPP(U_1122,bool,hAPP(U_1122,fun(U_1122,bool),ord_less_eq(U_1122),hAPP(U_1122,U_1122,hAPP(U_1122,fun(U_1122,U_1122),plus_plus(U_1122),U_1121),U_1120)),hAPP(U_1122,U_1122,hAPP(U_1122,fun(U_1122,U_1122),plus_plus(U_1122),U_1119),U_1120)))
      | ~ ordere236663937imp_le(U_1122) ),
    inference(definitional_conversion,[status(esa)],[f_286_2]) ).

cnf(f_286_4,plain,
    ( hBOOL(hAPP(U_1122,bool,hAPP(U_1122,fun(U_1122,bool),ord_less_eq(U_1122),U_1121),U_1119))
    | ~ hBOOL(hAPP(U_1122,bool,hAPP(U_1122,fun(U_1122,bool),ord_less_eq(U_1122),hAPP(U_1122,U_1122,hAPP(U_1122,fun(U_1122,U_1122),plus_plus(U_1122),U_1121),U_1120)),hAPP(U_1122,U_1122,hAPP(U_1122,fun(U_1122,U_1122),plus_plus(U_1122),U_1119),U_1120)))
    | ~ ordere236663937imp_le(U_1122) ),
    inference(clausify,[status(thm)],[f_286_3]) ).

fof(f_287_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_234_add__le__imp__le__left]) ).

fof(f_287_2,plain,
    ! [U_1126] :
      ( ! [U_1125,U_1124,U_1123] :
          ( hBOOL(hAPP(U_1126,bool,hAPP(U_1126,fun(U_1126,bool),ord_less_eq(U_1126),U_1124),U_1123))
          | ~ hBOOL(hAPP(U_1126,bool,hAPP(U_1126,fun(U_1126,bool),ord_less_eq(U_1126),hAPP(U_1126,U_1126,hAPP(U_1126,fun(U_1126,U_1126),plus_plus(U_1126),U_1125),U_1124)),hAPP(U_1126,U_1126,hAPP(U_1126,fun(U_1126,U_1126),plus_plus(U_1126),U_1125),U_1123))) )
      | ~ ordere236663937imp_le(U_1126) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

fof(f_287_3,plain,
    ! [U_1123,U_1126,U_1124,U_1125] :
      ( hBOOL(hAPP(U_1126,bool,hAPP(U_1126,fun(U_1126,bool),ord_less_eq(U_1126),U_1124),U_1123))
      | ~ hBOOL(hAPP(U_1126,bool,hAPP(U_1126,fun(U_1126,bool),ord_less_eq(U_1126),hAPP(U_1126,U_1126,hAPP(U_1126,fun(U_1126,U_1126),plus_plus(U_1126),U_1125),U_1124)),hAPP(U_1126,U_1126,hAPP(U_1126,fun(U_1126,U_1126),plus_plus(U_1126),U_1125),U_1123)))
      | ~ ordere236663937imp_le(U_1126) ),
    inference(definitional_conversion,[status(esa)],[f_287_2]) ).

cnf(f_287_4,plain,
    ( hBOOL(hAPP(U_1126,bool,hAPP(U_1126,fun(U_1126,bool),ord_less_eq(U_1126),U_1124),U_1123))
    | ~ hBOOL(hAPP(U_1126,bool,hAPP(U_1126,fun(U_1126,bool),ord_less_eq(U_1126),hAPP(U_1126,U_1126,hAPP(U_1126,fun(U_1126,U_1126),plus_plus(U_1126),U_1125),U_1124)),hAPP(U_1126,U_1126,hAPP(U_1126,fun(U_1126,U_1126),plus_plus(U_1126),U_1125),U_1123)))
    | ~ ordere236663937imp_le(U_1126) ),
    inference(clausify,[status(thm)],[f_287_3]) ).

fof(f_288_1,plain,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),
    inference(fof_nnf,[status(thm)],[fact_235_add__Suc__right]) ).

fof(f_288_2,plain,
    ! [U_1128,U_1127] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1128),hAPP(nat,nat,suc,U_1127)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1128),U_1127)),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

fof(f_288_3,plain,
    ! [U_1128,U_1127] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1128),hAPP(nat,nat,suc,U_1127)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1128),U_1127)),
    inference(definitional_conversion,[status(esa)],[f_288_2]) ).

cnf(f_288_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1128),hAPP(nat,nat,suc,U_1127)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1128),U_1127)),
    inference(clausify,[status(thm)],[f_288_3]) ).

fof(f_289_1,plain,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),
    inference(fof_nnf,[status(thm)],[fact_236_add__Suc]) ).

fof(f_289_2,plain,
    ! [U_1130,U_1129] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1130)),U_1129) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1130),U_1129)),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

fof(f_289_3,plain,
    ! [U_1129,U_1130] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1130)),U_1129) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1130),U_1129)),
    inference(definitional_conversion,[status(esa)],[f_289_2]) ).

cnf(f_289_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1130)),U_1129) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1130),U_1129)),
    inference(clausify,[status(thm)],[f_289_3]) ).

fof(f_290_1,plain,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N)),
    inference(fof_nnf,[status(thm)],[fact_237_add__Suc__shift]) ).

fof(f_290_2,plain,
    ! [U_1132,U_1131] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1132)),U_1131) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1132),hAPP(nat,nat,suc,U_1131)),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

fof(f_290_3,plain,
    ! [U_1131,U_1132] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1132)),U_1131) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1132),hAPP(nat,nat,suc,U_1131)),
    inference(definitional_conversion,[status(esa)],[f_290_2]) ).

cnf(f_290_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,U_1132)),U_1131) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1132),hAPP(nat,nat,suc,U_1131)),
    inference(clausify,[status(thm)],[f_290_3]) ).

fof(f_291_1,plain,
    ! [X_b,X_c,X_1,Z_1,F] :
      ( hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_1)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_1)
      | ~ hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) ),
    inference(fof_nnf,[status(thm)],[fact_238_comp__fun__idem_Ofun__left__idem]) ).

fof(f_291_2,plain,
    ! [U_1137,U_1136,U_1135,U_1134,U_1133] :
      ( hAPP(U_1136,U_1136,hAPP(U_1137,fun(U_1136,U_1136),U_1133,U_1135),hAPP(U_1136,U_1136,hAPP(U_1137,fun(U_1136,U_1136),U_1133,U_1135),U_1134)) = hAPP(U_1136,U_1136,hAPP(U_1137,fun(U_1136,U_1136),U_1133,U_1135),U_1134)
      | ~ hBOOL(hAPP(fun(U_1137,fun(U_1136,U_1136)),bool,finite_comp_fun_idem(U_1137,U_1136),U_1133)) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

fof(f_291_3,plain,
    ! [U_1133,U_1136,U_1135,U_1134,U_1137] :
      ( hAPP(U_1136,U_1136,hAPP(U_1137,fun(U_1136,U_1136),U_1133,U_1135),hAPP(U_1136,U_1136,hAPP(U_1137,fun(U_1136,U_1136),U_1133,U_1135),U_1134)) = hAPP(U_1136,U_1136,hAPP(U_1137,fun(U_1136,U_1136),U_1133,U_1135),U_1134)
      | ~ hBOOL(hAPP(fun(U_1137,fun(U_1136,U_1136)),bool,finite_comp_fun_idem(U_1137,U_1136),U_1133)) ),
    inference(definitional_conversion,[status(esa)],[f_291_2]) ).

cnf(f_291_4,plain,
    ( hAPP(U_1136,U_1136,hAPP(U_1137,fun(U_1136,U_1136),U_1133,U_1135),hAPP(U_1136,U_1136,hAPP(U_1137,fun(U_1136,U_1136),U_1133,U_1135),U_1134)) = hAPP(U_1136,U_1136,hAPP(U_1137,fun(U_1136,U_1136),U_1133,U_1135),U_1134)
    | ~ hBOOL(hAPP(fun(U_1137,fun(U_1136,U_1136)),bool,finite_comp_fun_idem(U_1137,U_1136),U_1133)) ),
    inference(clausify,[status(thm)],[f_291_3]) ).

fof(f_292_1,plain,
    ! [M_1,K_2,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K_2)
        | M_1 != Na )
      & ( M_1 = Na
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Na),K_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_239_nat__add__right__cancel]) ).

fof(f_292_2,plain,
    ! [U_1140,U_1139,U_1138] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1140),U_1139) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1138),U_1139)
        | U_1140 != U_1138 )
      & ( U_1140 = U_1138
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1140),U_1139) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1138),U_1139) ) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

fof(f_292_3,plain,
    ( ! [U_1146,U_1144,U_1142] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1146),U_1144) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1142),U_1144)
        | U_1146 != U_1142 )
    & ! [U_1145,U_1143,U_1141] :
        ( U_1145 = U_1141
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1145),U_1143) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1141),U_1143) ) ),
    inference(miniscope,[status(thm)],[f_292_2]) ).

fof(f_292_4,plain,
    ( ! [U_1144,U_1146,U_1142] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1146),U_1144) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1142),U_1144)
        | U_1146 != U_1142 )
    & ! [U_1141,U_1143,U_1145] :
        ( U_1145 = U_1141
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1145),U_1143) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1141),U_1143) ) ),
    inference(definitional_conversion,[status(esa)],[f_292_3]) ).

cnf(f_292_5,plain,
    ( U_1145 = U_1141
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1145),U_1143) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1141),U_1143) ),
    inference(clausify,[status(thm)],[f_292_4]) ).

cnf(f_292_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1146),U_1144) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1142),U_1144)
    | U_1146 != U_1142 ),
    inference(clausify,[status(thm)],[f_292_4]) ).

fof(f_293_1,plain,
    ! [K_2,M_1,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),Na)
        | M_1 != Na )
      & ( M_1 = Na
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M_1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_240_nat__add__left__cancel]) ).

fof(f_293_2,plain,
    ! [U_1149,U_1148,U_1147] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1149),U_1148) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1149),U_1147)
        | U_1148 != U_1147 )
      & ( U_1148 = U_1147
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1149),U_1148) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1149),U_1147) ) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ( ! [U_1155,U_1153,U_1151] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1155),U_1153) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1155),U_1151)
        | U_1153 != U_1151 )
    & ! [U_1154,U_1152,U_1150] :
        ( U_1152 = U_1150
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1154),U_1152) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1154),U_1150) ) ),
    inference(miniscope,[status(thm)],[f_293_2]) ).

fof(f_293_4,plain,
    ( ! [U_1151,U_1153,U_1155] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1155),U_1153) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1155),U_1151)
        | U_1153 != U_1151 )
    & ! [U_1154,U_1150,U_1152] :
        ( U_1152 = U_1150
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1154),U_1152) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1154),U_1150) ) ),
    inference(definitional_conversion,[status(esa)],[f_293_3]) ).

cnf(f_293_5,plain,
    ( U_1152 = U_1150
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1154),U_1152) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1154),U_1150) ),
    inference(clausify,[status(thm)],[f_293_4]) ).

cnf(f_293_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1155),U_1153) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1155),U_1151)
    | U_1153 != U_1151 ),
    inference(clausify,[status(thm)],[f_293_4]) ).

fof(f_294_1,plain,
    ! [M,N,K] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K)),
    inference(fof_nnf,[status(thm)],[fact_241_nat__add__assoc]) ).

fof(f_294_2,plain,
    ! [U_1158,U_1157,U_1156] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1158),U_1157)),U_1156) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1158),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1157),U_1156)),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

fof(f_294_3,plain,
    ! [U_1156,U_1157,U_1158] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1158),U_1157)),U_1156) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1158),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1157),U_1156)),
    inference(definitional_conversion,[status(esa)],[f_294_2]) ).

cnf(f_294_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1158),U_1157)),U_1156) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1158),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1157),U_1156)),
    inference(clausify,[status(thm)],[f_294_3]) ).

fof(f_295_1,plain,
    ! [X,Y,Z] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z)),
    inference(fof_nnf,[status(thm)],[fact_242_nat__add__left__commute]) ).

fof(f_295_2,plain,
    ! [U_1161,U_1160,U_1159] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1161),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1160),U_1159)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1160),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1161),U_1159)),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

fof(f_295_3,plain,
    ! [U_1159,U_1161,U_1160] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1161),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1160),U_1159)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1160),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1161),U_1159)),
    inference(definitional_conversion,[status(esa)],[f_295_2]) ).

cnf(f_295_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1161),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1160),U_1159)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1160),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1161),U_1159)),
    inference(clausify,[status(thm)],[f_295_3]) ).

fof(f_296_1,plain,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M),
    inference(fof_nnf,[status(thm)],[fact_243_nat__add__commute]) ).

fof(f_296_2,plain,
    ! [U_1163,U_1162] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1163),U_1162) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1162),U_1163),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ! [U_1163,U_1162] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1163),U_1162) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1162),U_1163),
    inference(definitional_conversion,[status(esa)],[f_296_2]) ).

cnf(f_296_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1163),U_1162) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1162),U_1163),
    inference(clausify,[status(thm)],[f_296_3]) ).

fof(f_297_1,plain,
    ! [X_a] :
      ( ! [B_1,A_1,C] :
          ( ti(X_a,B_1) = ti(X_a,C)
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_1) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) )
      | ~ cancel_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_244_add__right__imp__eq]) ).

fof(f_297_2,plain,
    ! [U_1167] :
      ( ! [U_1166,U_1165,U_1164] :
          ( ti(U_1167,U_1166) = ti(U_1167,U_1164)
          | hAPP(U_1167,U_1167,hAPP(U_1167,fun(U_1167,U_1167),plus_plus(U_1167),U_1166),U_1165) != hAPP(U_1167,U_1167,hAPP(U_1167,fun(U_1167,U_1167),plus_plus(U_1167),U_1164),U_1165) )
      | ~ cancel_semigroup_add(U_1167) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

fof(f_297_3,plain,
    ! [U_1164,U_1165,U_1166,U_1167] :
      ( ti(U_1167,U_1166) = ti(U_1167,U_1164)
      | hAPP(U_1167,U_1167,hAPP(U_1167,fun(U_1167,U_1167),plus_plus(U_1167),U_1166),U_1165) != hAPP(U_1167,U_1167,hAPP(U_1167,fun(U_1167,U_1167),plus_plus(U_1167),U_1164),U_1165)
      | ~ cancel_semigroup_add(U_1167) ),
    inference(definitional_conversion,[status(esa)],[f_297_2]) ).

cnf(f_297_4,plain,
    ( ti(U_1167,U_1166) = ti(U_1167,U_1164)
    | hAPP(U_1167,U_1167,hAPP(U_1167,fun(U_1167,U_1167),plus_plus(U_1167),U_1166),U_1165) != hAPP(U_1167,U_1167,hAPP(U_1167,fun(U_1167,U_1167),plus_plus(U_1167),U_1164),U_1165)
    | ~ cancel_semigroup_add(U_1167) ),
    inference(clausify,[status(thm)],[f_297_3]) ).

fof(f_298_1,plain,
    ! [X_a] :
      ( ! [A_1,B_1,C] :
          ( ti(X_a,B_1) = ti(X_a,C)
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) )
      | ~ cancel146912293up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_245_add__imp__eq]) ).

fof(f_298_2,plain,
    ! [U_1171] :
      ( ! [U_1170,U_1169,U_1168] :
          ( ti(U_1171,U_1169) = ti(U_1171,U_1168)
          | hAPP(U_1171,U_1171,hAPP(U_1171,fun(U_1171,U_1171),plus_plus(U_1171),U_1170),U_1169) != hAPP(U_1171,U_1171,hAPP(U_1171,fun(U_1171,U_1171),plus_plus(U_1171),U_1170),U_1168) )
      | ~ cancel146912293up_add(U_1171) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

fof(f_298_3,plain,
    ! [U_1168,U_1169,U_1171,U_1170] :
      ( ti(U_1171,U_1169) = ti(U_1171,U_1168)
      | hAPP(U_1171,U_1171,hAPP(U_1171,fun(U_1171,U_1171),plus_plus(U_1171),U_1170),U_1169) != hAPP(U_1171,U_1171,hAPP(U_1171,fun(U_1171,U_1171),plus_plus(U_1171),U_1170),U_1168)
      | ~ cancel146912293up_add(U_1171) ),
    inference(definitional_conversion,[status(esa)],[f_298_2]) ).

cnf(f_298_4,plain,
    ( ti(U_1171,U_1169) = ti(U_1171,U_1168)
    | hAPP(U_1171,U_1171,hAPP(U_1171,fun(U_1171,U_1171),plus_plus(U_1171),U_1170),U_1169) != hAPP(U_1171,U_1171,hAPP(U_1171,fun(U_1171,U_1171),plus_plus(U_1171),U_1170),U_1168)
    | ~ cancel146912293up_add(U_1171) ),
    inference(clausify,[status(thm)],[f_298_3]) ).

fof(f_299_1,plain,
    ! [X_a] :
      ( ! [A_1,B_1,C] :
          ( ti(X_a,B_1) = ti(X_a,C)
          | hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) )
      | ~ cancel_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_246_add__left__imp__eq]) ).

fof(f_299_2,plain,
    ! [U_1175] :
      ( ! [U_1174,U_1173,U_1172] :
          ( ti(U_1175,U_1173) = ti(U_1175,U_1172)
          | hAPP(U_1175,U_1175,hAPP(U_1175,fun(U_1175,U_1175),plus_plus(U_1175),U_1174),U_1173) != hAPP(U_1175,U_1175,hAPP(U_1175,fun(U_1175,U_1175),plus_plus(U_1175),U_1174),U_1172) )
      | ~ cancel_semigroup_add(U_1175) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

fof(f_299_3,plain,
    ! [U_1172,U_1173,U_1175,U_1174] :
      ( ti(U_1175,U_1173) = ti(U_1175,U_1172)
      | hAPP(U_1175,U_1175,hAPP(U_1175,fun(U_1175,U_1175),plus_plus(U_1175),U_1174),U_1173) != hAPP(U_1175,U_1175,hAPP(U_1175,fun(U_1175,U_1175),plus_plus(U_1175),U_1174),U_1172)
      | ~ cancel_semigroup_add(U_1175) ),
    inference(definitional_conversion,[status(esa)],[f_299_2]) ).

cnf(f_299_4,plain,
    ( ti(U_1175,U_1173) = ti(U_1175,U_1172)
    | hAPP(U_1175,U_1175,hAPP(U_1175,fun(U_1175,U_1175),plus_plus(U_1175),U_1174),U_1173) != hAPP(U_1175,U_1175,hAPP(U_1175,fun(U_1175,U_1175),plus_plus(U_1175),U_1174),U_1172)
    | ~ cancel_semigroup_add(U_1175) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

fof(f_300_1,plain,
    ! [X_b] :
      ( ! [B,A_2,C_1] :
          ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)
            | ti(X_b,B) != ti(X_b,C_1) )
          & ( ti(X_b,B) = ti(X_b,C_1)
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),A_2) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2) ) )
      | ~ cancel_semigroup_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_247_add__right__cancel]) ).

fof(f_300_2,plain,
    ! [U_1179] :
      ( ! [U_1178,U_1177,U_1176] :
          ( ( hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1178),U_1177) = hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1176),U_1177)
            | ti(U_1179,U_1178) != ti(U_1179,U_1176) )
          & ( ti(U_1179,U_1178) = ti(U_1179,U_1176)
            | hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1178),U_1177) != hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1176),U_1177) ) )
      | ~ cancel_semigroup_add(U_1179) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

fof(f_300_3,plain,
    ! [U_1179] :
      ( ( ! [U_1185,U_1183,U_1181] :
            ( hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1185),U_1183) = hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1181),U_1183)
            | ti(U_1179,U_1185) != ti(U_1179,U_1181) )
        & ! [U_1184,U_1182,U_1180] :
            ( ti(U_1179,U_1184) = ti(U_1179,U_1180)
            | hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1184),U_1182) != hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1180),U_1182) ) )
      | ~ cancel_semigroup_add(U_1179) ),
    inference(miniscope,[status(thm)],[f_300_2]) ).

fof(f_300_4,plain,
    ( ! [U_1185,U_1183,U_1179,U_1181,U_1180,U_1182,U_1184] :
        ( hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1185),U_1183) = hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1181),U_1183)
        | ti(U_1179,U_1185) != ti(U_1179,U_1181)
        | ~ sP58(U_1185,U_1183,U_1179,U_1181,U_1180,U_1182,U_1184) )
    & ! [U_1185,U_1183,U_1179,U_1181,U_1180,U_1182,U_1184] :
        ( ti(U_1179,U_1184) = ti(U_1179,U_1180)
        | hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1184),U_1182) != hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1180),U_1182)
        | ~ sP58(U_1185,U_1183,U_1179,U_1181,U_1180,U_1182,U_1184) )
    & ! [U_1185,U_1183,U_1179,U_1181,U_1180,U_1182,U_1184] :
        ( sP58(U_1185,U_1183,U_1179,U_1181,U_1180,U_1182,U_1184)
        | ~ cancel_semigroup_add(U_1179) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58])],[f_300_3]) ).

cnf(f_300_5,plain,
    ( sP58(U_1185,U_1183,U_1179,U_1181,U_1180,U_1182,U_1184)
    | ~ cancel_semigroup_add(U_1179) ),
    inference(clausify,[status(thm)],[f_300_4]) ).

cnf(f_300_6,plain,
    ( ti(U_1179,U_1184) = ti(U_1179,U_1180)
    | hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1184),U_1182) != hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1180),U_1182)
    | ~ sP58(U_1185,U_1183,U_1179,U_1181,U_1180,U_1182,U_1184) ),
    inference(clausify,[status(thm)],[f_300_4]) ).

cnf(f_300_7,plain,
    ( hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1185),U_1183) = hAPP(U_1179,U_1179,hAPP(U_1179,fun(U_1179,U_1179),plus_plus(U_1179),U_1181),U_1183)
    | ti(U_1179,U_1185) != ti(U_1179,U_1181)
    | ~ sP58(U_1185,U_1183,U_1179,U_1181,U_1180,U_1182,U_1184) ),
    inference(clausify,[status(thm)],[f_300_4]) ).

fof(f_301_1,plain,
    ! [X_b] :
      ( ! [A_2,B,C_1] :
          ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)
            | ti(X_b,B) != ti(X_b,C_1) )
          & ( ti(X_b,B) = ti(X_b,C_1)
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1) ) )
      | ~ cancel_semigroup_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_248_add__left__cancel]) ).

fof(f_301_2,plain,
    ! [U_1189] :
      ( ! [U_1188,U_1187,U_1186] :
          ( ( hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1188),U_1187) = hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1188),U_1186)
            | ti(U_1189,U_1187) != ti(U_1189,U_1186) )
          & ( ti(U_1189,U_1187) = ti(U_1189,U_1186)
            | hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1188),U_1187) != hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1188),U_1186) ) )
      | ~ cancel_semigroup_add(U_1189) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

fof(f_301_3,plain,
    ! [U_1189] :
      ( ( ! [U_1195,U_1193,U_1191] :
            ( hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1195),U_1193) = hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1195),U_1191)
            | ti(U_1189,U_1193) != ti(U_1189,U_1191) )
        & ! [U_1194,U_1192,U_1190] :
            ( ti(U_1189,U_1192) = ti(U_1189,U_1190)
            | hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1194),U_1192) != hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1194),U_1190) ) )
      | ~ cancel_semigroup_add(U_1189) ),
    inference(miniscope,[status(thm)],[f_301_2]) ).

fof(f_301_4,plain,
    ( ! [U_1191,U_1190,U_1195,U_1192,U_1194,U_1193,U_1189] :
        ( hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1195),U_1193) = hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1195),U_1191)
        | ti(U_1189,U_1193) != ti(U_1189,U_1191)
        | ~ sP59(U_1191,U_1190,U_1195,U_1192,U_1194,U_1193,U_1189) )
    & ! [U_1191,U_1190,U_1195,U_1192,U_1194,U_1193,U_1189] :
        ( ti(U_1189,U_1192) = ti(U_1189,U_1190)
        | hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1194),U_1192) != hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1194),U_1190)
        | ~ sP59(U_1191,U_1190,U_1195,U_1192,U_1194,U_1193,U_1189) )
    & ! [U_1191,U_1190,U_1195,U_1192,U_1194,U_1193,U_1189] :
        ( sP59(U_1191,U_1190,U_1195,U_1192,U_1194,U_1193,U_1189)
        | ~ cancel_semigroup_add(U_1189) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_301_3]) ).

cnf(f_301_5,plain,
    ( sP59(U_1191,U_1190,U_1195,U_1192,U_1194,U_1193,U_1189)
    | ~ cancel_semigroup_add(U_1189) ),
    inference(clausify,[status(thm)],[f_301_4]) ).

cnf(f_301_6,plain,
    ( ti(U_1189,U_1192) = ti(U_1189,U_1190)
    | hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1194),U_1192) != hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1194),U_1190)
    | ~ sP59(U_1191,U_1190,U_1195,U_1192,U_1194,U_1193,U_1189) ),
    inference(clausify,[status(thm)],[f_301_4]) ).

cnf(f_301_7,plain,
    ( hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1195),U_1193) = hAPP(U_1189,U_1189,hAPP(U_1189,fun(U_1189,U_1189),plus_plus(U_1189),U_1195),U_1191)
    | ti(U_1189,U_1193) != ti(U_1189,U_1191)
    | ~ sP59(U_1191,U_1190,U_1195,U_1192,U_1194,U_1193,U_1189) ),
    inference(clausify,[status(thm)],[f_301_4]) ).

fof(f_302_1,plain,
    ! [X_a] :
      ( ! [A_1,B_1,C] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C))
      | ~ ab_semigroup_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_249_ab__semigroup__add__class_Oadd__ac_I1_J]) ).

fof(f_302_2,plain,
    ! [U_1199] :
      ( ! [U_1198,U_1197,U_1196] : hAPP(U_1199,U_1199,hAPP(U_1199,fun(U_1199,U_1199),plus_plus(U_1199),hAPP(U_1199,U_1199,hAPP(U_1199,fun(U_1199,U_1199),plus_plus(U_1199),U_1198),U_1197)),U_1196) = hAPP(U_1199,U_1199,hAPP(U_1199,fun(U_1199,U_1199),plus_plus(U_1199),U_1198),hAPP(U_1199,U_1199,hAPP(U_1199,fun(U_1199,U_1199),plus_plus(U_1199),U_1197),U_1196))
      | ~ ab_semigroup_add(U_1199) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ! [U_1198,U_1197,U_1196,U_1199] :
      ( hAPP(U_1199,U_1199,hAPP(U_1199,fun(U_1199,U_1199),plus_plus(U_1199),hAPP(U_1199,U_1199,hAPP(U_1199,fun(U_1199,U_1199),plus_plus(U_1199),U_1198),U_1197)),U_1196) = hAPP(U_1199,U_1199,hAPP(U_1199,fun(U_1199,U_1199),plus_plus(U_1199),U_1198),hAPP(U_1199,U_1199,hAPP(U_1199,fun(U_1199,U_1199),plus_plus(U_1199),U_1197),U_1196))
      | ~ ab_semigroup_add(U_1199) ),
    inference(definitional_conversion,[status(esa)],[f_302_2]) ).

cnf(f_302_4,plain,
    ( hAPP(U_1199,U_1199,hAPP(U_1199,fun(U_1199,U_1199),plus_plus(U_1199),hAPP(U_1199,U_1199,hAPP(U_1199,fun(U_1199,U_1199),plus_plus(U_1199),U_1198),U_1197)),U_1196) = hAPP(U_1199,U_1199,hAPP(U_1199,fun(U_1199,U_1199),plus_plus(U_1199),U_1198),hAPP(U_1199,U_1199,hAPP(U_1199,fun(U_1199,U_1199),plus_plus(U_1199),U_1197),U_1196))
    | ~ ab_semigroup_add(U_1199) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

fof(f_303_1,plain,
    ! [M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N) = M,
    inference(fof_nnf,[status(thm)],[fact_250_diff__add__inverse2]) ).

fof(f_303_2,plain,
    ! [U_1201,U_1200] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1201),U_1200)),U_1200) = U_1201,
    inference(variable_rename,[status(thm)],[f_303_1]) ).

fof(f_303_3,plain,
    ! [U_1200,U_1201] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1201),U_1200)),U_1200) = U_1201,
    inference(definitional_conversion,[status(esa)],[f_303_2]) ).

cnf(f_303_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1201),U_1200)),U_1200) = U_1201,
    inference(clausify,[status(thm)],[f_303_3]) ).

fof(f_304_1,plain,
    ! [N,M] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),N) = M,
    inference(fof_nnf,[status(thm)],[fact_251_diff__add__inverse]) ).

fof(f_304_2,plain,
    ! [U_1203,U_1202] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1203),U_1202)),U_1203) = U_1202,
    inference(variable_rename,[status(thm)],[f_304_1]) ).

fof(f_304_3,plain,
    ! [U_1202,U_1203] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1203),U_1202)),U_1203) = U_1202,
    inference(definitional_conversion,[status(esa)],[f_304_2]) ).

cnf(f_304_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1203),U_1202)),U_1203) = U_1202,
    inference(clausify,[status(thm)],[f_304_3]) ).

fof(f_305_1,plain,
    ! [I,J_2,K] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J_2)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K)),
    inference(fof_nnf,[status(thm)],[fact_252_diff__diff__left]) ).

fof(f_305_2,plain,
    ! [U_1206,U_1205,U_1204] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1206),U_1205)),U_1204) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1206),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1205),U_1204)),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

fof(f_305_3,plain,
    ! [U_1204,U_1205,U_1206] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1206),U_1205)),U_1204) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1206),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1205),U_1204)),
    inference(definitional_conversion,[status(esa)],[f_305_2]) ).

cnf(f_305_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1206),U_1205)),U_1204) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1206),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1205),U_1204)),
    inference(clausify,[status(thm)],[f_305_3]) ).

fof(f_306_1,plain,
    ! [K,M,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N),
    inference(fof_nnf,[status(thm)],[fact_253_diff__cancel]) ).

fof(f_306_2,plain,
    ! [U_1209,U_1208,U_1207] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1209),U_1208)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1209),U_1207)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1208),U_1207),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ! [U_1207,U_1208,U_1209] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1209),U_1208)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1209),U_1207)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1208),U_1207),
    inference(definitional_conversion,[status(esa)],[f_306_2]) ).

cnf(f_306_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1209),U_1208)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1209),U_1207)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1208),U_1207),
    inference(clausify,[status(thm)],[f_306_3]) ).

fof(f_307_1,plain,
    ! [M,K,N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N),
    inference(fof_nnf,[status(thm)],[fact_254_diff__cancel2]) ).

fof(f_307_2,plain,
    ! [U_1212,U_1211,U_1210] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1212),U_1211)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1210),U_1211)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1212),U_1210),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

fof(f_307_3,plain,
    ! [U_1210,U_1211,U_1212] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1212),U_1211)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1210),U_1211)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1212),U_1210),
    inference(definitional_conversion,[status(esa)],[f_307_2]) ).

cnf(f_307_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1212),U_1211)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1210),U_1211)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1212),U_1210),
    inference(clausify,[status(thm)],[f_307_3]) ).

fof(f_308_1,plain,
    ! [N,M] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))),
    inference(fof_nnf,[status(thm)],[fact_255_le__add2]) ).

fof(f_308_2,plain,
    ! [U_1214,U_1213] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1214),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1213),U_1214))),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

fof(f_308_3,plain,
    ! [U_1214,U_1213] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1214),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1213),U_1214))),
    inference(definitional_conversion,[status(esa)],[f_308_2]) ).

cnf(f_308_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1214),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1213),U_1214))),
    inference(clausify,[status(thm)],[f_308_3]) ).

fof(f_309_1,plain,
    ! [N,M] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M))),
    inference(fof_nnf,[status(thm)],[fact_256_le__add1]) ).

fof(f_309_2,plain,
    ! [U_1216,U_1215] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1216),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1216),U_1215))),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

fof(f_309_3,plain,
    ! [U_1216,U_1215] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1216),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1216),U_1215))),
    inference(definitional_conversion,[status(esa)],[f_309_2]) ).

cnf(f_309_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1216),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1216),U_1215))),
    inference(clausify,[status(thm)],[f_309_3]) ).

fof(f_310_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
        | ! [K_1] : Na != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1) )
      & ( ? [K_1] : Na = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_257_le__iff__add]) ).

fof(f_310_2,plain,
    ! [U_1220,U_1219] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1220),U_1219))
        | ! [U_1218] : U_1219 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1220),U_1218) )
      & ( ? [U_1217] : U_1219 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1220),U_1217)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1220),U_1219)) ) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

fof(f_310_3,plain,
    ( ! [U_1224,U_1222] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1224),U_1222))
        | ! [U_1218] : U_1222 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1224),U_1218) )
    & ! [U_1223,U_1221] :
        ( ? [U_1217] : U_1221 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1223),U_1217)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1223),U_1221)) ) ),
    inference(miniscope,[status(thm)],[f_310_2]) ).

fof(f_310_4,plain,
    ( ! [U_1224,U_1222] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1224),U_1222))
        | ! [U_1218] : U_1222 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1224),U_1218) )
    & ! [U_1223,U_1221] :
        ( U_1221 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1223),sK44(U_1223,U_1221))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1223),U_1221)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_1217,sK44(U_1223,U_1221))],[f_310_3]) ).

fof(f_310_5,plain,
    ( ! [U_1224,U_1222,U_1218] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1224),U_1222))
        | U_1222 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1224),U_1218) )
    & ! [U_1221,U_1223] :
        ( U_1221 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1223),sK44(U_1223,U_1221))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1223),U_1221)) ) ),
    inference(definitional_conversion,[status(esa)],[f_310_4]) ).

cnf(f_310_6,plain,
    ( U_1221 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1223),sK44(U_1223,U_1221))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1223),U_1221)) ),
    inference(clausify,[status(thm)],[f_310_5]) ).

cnf(f_310_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1224),U_1222))
    | U_1222 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1224),U_1218) ),
    inference(clausify,[status(thm)],[f_310_5]) ).

fof(f_311_1,plain,
    ! [K_2,M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_258_nat__add__left__cancel__le]) ).

fof(f_311_2,plain,
    ! [U_1227,U_1226,U_1225] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1227),U_1226)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1227),U_1225)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1226),U_1225)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1226),U_1225))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1227),U_1226)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1227),U_1225))) ) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

fof(f_311_3,plain,
    ( ! [U_1233,U_1231,U_1229] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1233),U_1231)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1233),U_1229)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1231),U_1229)) )
    & ! [U_1232,U_1230,U_1228] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1230),U_1228))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1232),U_1230)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1232),U_1228))) ) ),
    inference(miniscope,[status(thm)],[f_311_2]) ).

fof(f_311_4,plain,
    ( ! [U_1229,U_1231,U_1233] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1233),U_1231)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1233),U_1229)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1231),U_1229)) )
    & ! [U_1230,U_1228,U_1232] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1230),U_1228))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1232),U_1230)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1232),U_1228))) ) ),
    inference(definitional_conversion,[status(esa)],[f_311_3]) ).

cnf(f_311_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1230),U_1228))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1232),U_1230)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1232),U_1228))) ),
    inference(clausify,[status(thm)],[f_311_4]) ).

cnf(f_311_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1233),U_1231)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1233),U_1229)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1231),U_1229)) ),
    inference(clausify,[status(thm)],[f_311_4]) ).

fof(f_312_1,plain,
    ! [M,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_259_trans__le__add1]) ).

fof(f_312_2,plain,
    ! [U_1236,U_1235,U_1234] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1235),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1234),U_1236)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1235),U_1234)) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

fof(f_312_3,plain,
    ! [U_1234,U_1236,U_1235] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1235),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1234),U_1236)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1235),U_1234)) ),
    inference(definitional_conversion,[status(esa)],[f_312_2]) ).

cnf(f_312_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1235),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1234),U_1236)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1235),U_1234)) ),
    inference(clausify,[status(thm)],[f_312_3]) ).

fof(f_313_1,plain,
    ! [M,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_2)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_260_trans__le__add2]) ).

fof(f_313_2,plain,
    ! [U_1239,U_1238,U_1237] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1238),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1239),U_1237)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1238),U_1237)) ),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

fof(f_313_3,plain,
    ! [U_1238,U_1237,U_1239] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1238),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1239),U_1237)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1238),U_1237)) ),
    inference(definitional_conversion,[status(esa)],[f_313_2]) ).

cnf(f_313_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1238),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1239),U_1237)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1238),U_1237)) ),
    inference(clausify,[status(thm)],[f_313_3]) ).

fof(f_314_1,plain,
    ! [K,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_261_add__le__mono1]) ).

fof(f_314_2,plain,
    ! [U_1242,U_1241,U_1240] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1241),U_1242)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1240),U_1242)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1241),U_1240)) ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

fof(f_314_3,plain,
    ! [U_1240,U_1241,U_1242] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1241),U_1242)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1240),U_1242)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1241),U_1240)) ),
    inference(definitional_conversion,[status(esa)],[f_314_2]) ).

cnf(f_314_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1241),U_1242)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1240),U_1242)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1241),U_1240)) ),
    inference(clausify,[status(thm)],[f_314_3]) ).

fof(f_315_1,plain,
    ! [K,L,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_262_add__le__mono]) ).

fof(f_315_2,plain,
    ! [U_1246,U_1245,U_1244,U_1243] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1244),U_1246)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1243),U_1245)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1246),U_1245))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1244),U_1243)) ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

fof(f_315_3,plain,
    ! [U_1243,U_1244,U_1245,U_1246] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1244),U_1246)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1243),U_1245)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1246),U_1245))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1244),U_1243)) ),
    inference(definitional_conversion,[status(esa)],[f_315_2]) ).

cnf(f_315_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1244),U_1246)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1243),U_1245)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1246),U_1245))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1244),U_1243)) ),
    inference(clausify,[status(thm)],[f_315_3]) ).

fof(f_316_1,plain,
    ! [M,K,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_263_add__leD2]) ).

fof(f_316_2,plain,
    ! [U_1249,U_1248,U_1247] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1248),U_1247))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1249),U_1248)),U_1247)) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

fof(f_316_3,plain,
    ! [U_1247,U_1248,U_1249] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1248),U_1247))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1249),U_1248)),U_1247)) ),
    inference(definitional_conversion,[status(esa)],[f_316_2]) ).

cnf(f_316_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1248),U_1247))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1249),U_1248)),U_1247)) ),
    inference(clausify,[status(thm)],[f_316_3]) ).

fof(f_317_1,plain,
    ! [M,K,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_264_add__leD1]) ).

fof(f_317_2,plain,
    ! [U_1252,U_1251,U_1250] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1252),U_1250))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1252),U_1251)),U_1250)) ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

fof(f_317_3,plain,
    ! [U_1250,U_1251,U_1252] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1252),U_1250))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1252),U_1251)),U_1250)) ),
    inference(definitional_conversion,[status(esa)],[f_317_2]) ).

cnf(f_317_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1252),U_1250))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1252),U_1251)),U_1250)) ),
    inference(clausify,[status(thm)],[f_317_3]) ).

fof(f_318_1,plain,
    ! [M,K,N] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_265_add__leE]) ).

fof(f_318_2,plain,
    ! [U_1255,U_1254,U_1253] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1254),U_1253))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1255),U_1253)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1255),U_1254)),U_1253)) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ( ! [U_1253,U_1254,U_1255] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1254),U_1253))
        | ~ sP60(U_1253,U_1254,U_1255) )
    & ! [U_1253,U_1254,U_1255] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1255),U_1253))
        | ~ sP60(U_1253,U_1254,U_1255) )
    & ! [U_1253,U_1254,U_1255] :
        ( sP60(U_1253,U_1254,U_1255)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1255),U_1254)),U_1253)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60])],[f_318_2]) ).

cnf(f_318_4,plain,
    ( sP60(U_1253,U_1254,U_1255)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1255),U_1254)),U_1253)) ),
    inference(clausify,[status(thm)],[f_318_3]) ).

cnf(f_318_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1255),U_1253))
    | ~ sP60(U_1253,U_1254,U_1255) ),
    inference(clausify,[status(thm)],[f_318_3]) ).

cnf(f_318_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1254),U_1253))
    | ~ sP60(U_1253,U_1254,U_1255) ),
    inference(clausify,[status(thm)],[f_318_3]) ).

fof(f_319_1,plain,
    ! [X_a] :
      ( ! [A_1,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B_1)),B_1) = ti(X_a,A_1)
      | ~ group_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_266_diff__add__cancel]) ).

fof(f_319_2,plain,
    ! [U_1258] :
      ( ! [U_1257,U_1256] : hAPP(U_1258,U_1258,hAPP(U_1258,fun(U_1258,U_1258),plus_plus(U_1258),hAPP(U_1258,U_1258,hAPP(U_1258,fun(U_1258,U_1258),minus_minus(U_1258),U_1257),U_1256)),U_1256) = ti(U_1258,U_1257)
      | ~ group_add(U_1258) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

fof(f_319_3,plain,
    ! [U_1256,U_1258,U_1257] :
      ( hAPP(U_1258,U_1258,hAPP(U_1258,fun(U_1258,U_1258),plus_plus(U_1258),hAPP(U_1258,U_1258,hAPP(U_1258,fun(U_1258,U_1258),minus_minus(U_1258),U_1257),U_1256)),U_1256) = ti(U_1258,U_1257)
      | ~ group_add(U_1258) ),
    inference(definitional_conversion,[status(esa)],[f_319_2]) ).

cnf(f_319_4,plain,
    ( hAPP(U_1258,U_1258,hAPP(U_1258,fun(U_1258,U_1258),plus_plus(U_1258),hAPP(U_1258,U_1258,hAPP(U_1258,fun(U_1258,U_1258),minus_minus(U_1258),U_1257),U_1256)),U_1256) = ti(U_1258,U_1257)
    | ~ group_add(U_1258) ),
    inference(clausify,[status(thm)],[f_319_3]) ).

fof(f_320_1,plain,
    ! [X_a] :
      ( ! [A_1,B_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1)),B_1) = ti(X_a,A_1)
      | ~ group_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_267_add__diff__cancel]) ).

fof(f_320_2,plain,
    ! [U_1261] :
      ( ! [U_1260,U_1259] : hAPP(U_1261,U_1261,hAPP(U_1261,fun(U_1261,U_1261),minus_minus(U_1261),hAPP(U_1261,U_1261,hAPP(U_1261,fun(U_1261,U_1261),plus_plus(U_1261),U_1260),U_1259)),U_1259) = ti(U_1261,U_1260)
      | ~ group_add(U_1261) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

fof(f_320_3,plain,
    ! [U_1261,U_1259,U_1260] :
      ( hAPP(U_1261,U_1261,hAPP(U_1261,fun(U_1261,U_1261),minus_minus(U_1261),hAPP(U_1261,U_1261,hAPP(U_1261,fun(U_1261,U_1261),plus_plus(U_1261),U_1260),U_1259)),U_1259) = ti(U_1261,U_1260)
      | ~ group_add(U_1261) ),
    inference(definitional_conversion,[status(esa)],[f_320_2]) ).

cnf(f_320_4,plain,
    ( hAPP(U_1261,U_1261,hAPP(U_1261,fun(U_1261,U_1261),minus_minus(U_1261),hAPP(U_1261,U_1261,hAPP(U_1261,fun(U_1261,U_1261),plus_plus(U_1261),U_1260),U_1259)),U_1259) = ti(U_1261,U_1260)
    | ~ group_add(U_1261) ),
    inference(clausify,[status(thm)],[f_320_3]) ).

fof(f_321_1,plain,
    ! [X_b] : hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),insert(X_b))),
    inference(fof_nnf,[status(thm)],[fact_268_comp__fun__idem__insert]) ).

fof(f_321_2,plain,
    ! [U_1262] : hBOOL(hAPP(fun(U_1262,fun(fun(U_1262,bool),fun(U_1262,bool))),bool,finite_comp_fun_idem(U_1262,fun(U_1262,bool)),insert(U_1262))),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

fof(f_321_3,plain,
    ! [U_1262] : hBOOL(hAPP(fun(U_1262,fun(fun(U_1262,bool),fun(U_1262,bool))),bool,finite_comp_fun_idem(U_1262,fun(U_1262,bool)),insert(U_1262))),
    inference(definitional_conversion,[status(esa)],[f_321_2]) ).

cnf(f_321_4,plain,
    hBOOL(hAPP(fun(U_1262,fun(fun(U_1262,bool),fun(U_1262,bool))),bool,finite_comp_fun_idem(U_1262,fun(U_1262,bool)),insert(U_1262))),
    inference(clausify,[status(thm)],[f_321_3]) ).

fof(f_322_1,plain,
    ! [I,K,J_2] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)),I)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_269_diff__add__assoc2]) ).

fof(f_322_2,plain,
    ! [U_1265,U_1264,U_1263] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1263),U_1265)),U_1264) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1263),U_1264)),U_1265)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1264),U_1263)) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

fof(f_322_3,plain,
    ! [U_1263,U_1264,U_1265] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1263),U_1265)),U_1264) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1263),U_1264)),U_1265)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1264),U_1263)) ),
    inference(definitional_conversion,[status(esa)],[f_322_2]) ).

cnf(f_322_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1263),U_1265)),U_1264) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1263),U_1264)),U_1265)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1264),U_1263)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

fof(f_323_1,plain,
    ! [I,K,J_2] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)),I) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I)),K)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_270_add__diff__assoc2]) ).

fof(f_323_2,plain,
    ! [U_1268,U_1267,U_1266] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1266),U_1267)),U_1268) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1266),U_1268)),U_1267)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1267),U_1266)) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

fof(f_323_3,plain,
    ! [U_1267,U_1266,U_1268] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1266),U_1267)),U_1268) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1266),U_1268)),U_1267)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1267),U_1266)) ),
    inference(definitional_conversion,[status(esa)],[f_323_2]) ).

cnf(f_323_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1266),U_1267)),U_1268) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1266),U_1268)),U_1267)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1267),U_1266)) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

fof(f_324_1,plain,
    ! [I,K,J_2] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_2)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_271_diff__add__assoc]) ).

fof(f_324_2,plain,
    ! [U_1271,U_1270,U_1269] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1271),U_1269)),U_1270) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1271),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1269),U_1270))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1270),U_1269)) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

fof(f_324_3,plain,
    ! [U_1270,U_1269,U_1271] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1271),U_1269)),U_1270) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1271),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1269),U_1270))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1270),U_1269)) ),
    inference(definitional_conversion,[status(esa)],[f_324_2]) ).

cnf(f_324_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1271),U_1269)),U_1270) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1271),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1269),U_1270))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1270),U_1269)) ),
    inference(clausify,[status(thm)],[f_324_3]) ).

fof(f_325_1,plain,
    ! [K_2,I_1,J_1] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1) = K_2
          | J_1 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),I_1) )
        & ( J_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),I_1)
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1) != K_2 ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_272_le__imp__diff__is__add]) ).

fof(f_325_2,plain,
    ! [U_1274,U_1273,U_1272] :
      ( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1272),U_1273) = U_1274
          | U_1272 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1274),U_1273) )
        & ( U_1272 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1274),U_1273)
          | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1272),U_1273) != U_1274 ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1273),U_1272)) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

fof(f_325_3,plain,
    ( ! [U_1274,U_1273,U_1272] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1272),U_1273) = U_1274
        | U_1272 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1274),U_1273)
        | ~ sP61(U_1274,U_1273,U_1272) )
    & ! [U_1274,U_1273,U_1272] :
        ( U_1272 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1274),U_1273)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1272),U_1273) != U_1274
        | ~ sP61(U_1274,U_1273,U_1272) )
    & ! [U_1274,U_1273,U_1272] :
        ( sP61(U_1274,U_1273,U_1272)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1273),U_1272)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_325_2]) ).

cnf(f_325_4,plain,
    ( sP61(U_1274,U_1273,U_1272)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1273),U_1272)) ),
    inference(clausify,[status(thm)],[f_325_3]) ).

cnf(f_325_5,plain,
    ( U_1272 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1274),U_1273)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1272),U_1273) != U_1274
    | ~ sP61(U_1274,U_1273,U_1272) ),
    inference(clausify,[status(thm)],[f_325_3]) ).

cnf(f_325_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1272),U_1273) = U_1274
    | U_1272 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1274),U_1273)
    | ~ sP61(U_1274,U_1273,U_1272) ),
    inference(clausify,[status(thm)],[f_325_3]) ).

fof(f_326_1,plain,
    ! [N,M] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N) = M
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) ),
    inference(fof_nnf,[status(thm)],[fact_273_le__add__diff__inverse2]) ).

fof(f_326_2,plain,
    ! [U_1276,U_1275] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1275),U_1276)),U_1276) = U_1275
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1276),U_1275)) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

fof(f_326_3,plain,
    ! [U_1275,U_1276] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1275),U_1276)),U_1276) = U_1275
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1276),U_1275)) ),
    inference(definitional_conversion,[status(esa)],[f_326_2]) ).

cnf(f_326_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1275),U_1276)),U_1276) = U_1275
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1276),U_1275)) ),
    inference(clausify,[status(thm)],[f_326_3]) ).

fof(f_327_1,plain,
    ! [I_1,K_2,J_1] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_2)),J_1)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_2)),J_1))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_274_le__diff__conv2]) ).

fof(f_327_2,plain,
    ! [U_1279,U_1278,U_1277] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1279),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1277),U_1278)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1279),U_1278)),U_1277)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1279),U_1278)),U_1277))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1279),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1277),U_1278))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1278),U_1277)) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

fof(f_327_3,plain,
    ( ! [U_1278,U_1279,U_1277] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1279),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1277),U_1278)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1279),U_1278)),U_1277))
        | ~ sP62(U_1278,U_1279,U_1277) )
    & ! [U_1278,U_1279,U_1277] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1279),U_1278)),U_1277))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1279),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1277),U_1278)))
        | ~ sP62(U_1278,U_1279,U_1277) )
    & ! [U_1278,U_1279,U_1277] :
        ( sP62(U_1278,U_1279,U_1277)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1278),U_1277)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_327_2]) ).

cnf(f_327_4,plain,
    ( sP62(U_1278,U_1279,U_1277)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1278),U_1277)) ),
    inference(clausify,[status(thm)],[f_327_3]) ).

cnf(f_327_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1279),U_1278)),U_1277))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1279),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1277),U_1278)))
    | ~ sP62(U_1278,U_1279,U_1277) ),
    inference(clausify,[status(thm)],[f_327_3]) ).

cnf(f_327_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1279),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1277),U_1278)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1279),U_1278)),U_1277))
    | ~ sP62(U_1278,U_1279,U_1277) ),
    inference(clausify,[status(thm)],[f_327_3]) ).

fof(f_328_1,plain,
    ! [I,K,J_2] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_2)),K)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_275_add__diff__assoc]) ).

fof(f_328_2,plain,
    ! [U_1282,U_1281,U_1280] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1282),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1280),U_1281)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1282),U_1280)),U_1281)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1281),U_1280)) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

fof(f_328_3,plain,
    ! [U_1280,U_1281,U_1282] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1282),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1280),U_1281)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1282),U_1280)),U_1281)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1281),U_1280)) ),
    inference(definitional_conversion,[status(esa)],[f_328_2]) ).

cnf(f_328_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1282),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1280),U_1281)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1282),U_1280)),U_1281)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1281),U_1280)) ),
    inference(clausify,[status(thm)],[f_328_3]) ).

fof(f_329_1,plain,
    ! [N,M] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) ),
    inference(fof_nnf,[status(thm)],[fact_276_le__add__diff__inverse]) ).

fof(f_329_2,plain,
    ! [U_1284,U_1283] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1284),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1283),U_1284)) = U_1283
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1284),U_1283)) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

fof(f_329_3,plain,
    ! [U_1283,U_1284] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1284),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1283),U_1284)) = U_1283
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1284),U_1283)) ),
    inference(definitional_conversion,[status(esa)],[f_329_2]) ).

cnf(f_329_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1284),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1283),U_1284)) = U_1283
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1284),U_1283)) ),
    inference(clausify,[status(thm)],[f_329_3]) ).

fof(f_330_1,plain,
    ! [M,K,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),K)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N)) ),
    inference(fof_nnf,[status(thm)],[fact_277_le__add__diff]) ).

fof(f_330_2,plain,
    ! [U_1287,U_1286,U_1285] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1287),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1285),U_1287)),U_1286)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1286),U_1285)) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

fof(f_330_3,plain,
    ! [U_1285,U_1286,U_1287] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1287),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1285),U_1287)),U_1286)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1286),U_1285)) ),
    inference(definitional_conversion,[status(esa)],[f_330_2]) ).

cnf(f_330_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1287),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1285),U_1287)),U_1286)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1286),U_1285)) ),
    inference(clausify,[status(thm)],[f_330_3]) ).

fof(f_331_1,plain,
    ! [J_1,K_2,I_1] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)),I_1))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_2))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_2)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)),I_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_278_le__diff__conv]) ).

fof(f_331_2,plain,
    ! [U_1290,U_1289,U_1288] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1290),U_1289)),U_1288))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1290),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1288),U_1289))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1290),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1288),U_1289)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1290),U_1289)),U_1288)) ) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

fof(f_331_3,plain,
    ( ! [U_1296,U_1294,U_1292] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1296),U_1294)),U_1292))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1296),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1292),U_1294))) )
    & ! [U_1295,U_1293,U_1291] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1295),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1291),U_1293)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1295),U_1293)),U_1291)) ) ),
    inference(miniscope,[status(thm)],[f_331_2]) ).

fof(f_331_4,plain,
    ( ! [U_1296,U_1292,U_1294] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1296),U_1294)),U_1292))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1296),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1292),U_1294))) )
    & ! [U_1293,U_1295,U_1291] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1295),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1291),U_1293)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1295),U_1293)),U_1291)) ) ),
    inference(definitional_conversion,[status(esa)],[f_331_3]) ).

cnf(f_331_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1295),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1291),U_1293)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1295),U_1293)),U_1291)) ),
    inference(clausify,[status(thm)],[f_331_4]) ).

cnf(f_331_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1296),U_1294)),U_1292))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1296),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1292),U_1294))) ),
    inference(clausify,[status(thm)],[f_331_4]) ).

fof(f_332_1,plain,
    ! [I,K,J_2] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J_2)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_279_diff__diff__right]) ).

fof(f_332_2,plain,
    ! [U_1299,U_1298,U_1297] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1299),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1297),U_1298)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1299),U_1298)),U_1297)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1298),U_1297)) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

fof(f_332_3,plain,
    ! [U_1299,U_1297,U_1298] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1299),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1297),U_1298)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1299),U_1298)),U_1297)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1298),U_1297)) ),
    inference(definitional_conversion,[status(esa)],[f_332_2]) ).

cnf(f_332_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1299),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1297),U_1298)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1299),U_1298)),U_1297)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1298),U_1297)) ),
    inference(clausify,[status(thm)],[f_332_3]) ).

fof(f_333_1,plain,
    ! [N] : hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat)),
    inference(fof_nnf,[status(thm)],[fact_280_Suc__eq__plus1]) ).

fof(f_333_2,plain,
    ! [U_1300] : hAPP(nat,nat,suc,U_1300) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1300),one_one(nat)),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

fof(f_333_3,plain,
    ! [U_1300] : hAPP(nat,nat,suc,U_1300) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1300),one_one(nat)),
    inference(definitional_conversion,[status(esa)],[f_333_2]) ).

cnf(f_333_4,plain,
    hAPP(nat,nat,suc,U_1300) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1300),one_one(nat)),
    inference(clausify,[status(thm)],[f_333_3]) ).

fof(f_334_1,plain,
    ! [N] : hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N),
    inference(fof_nnf,[status(thm)],[fact_281_Suc__eq__plus1__left]) ).

fof(f_334_2,plain,
    ! [U_1301] : hAPP(nat,nat,suc,U_1301) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_1301),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

fof(f_334_3,plain,
    ! [U_1301] : hAPP(nat,nat,suc,U_1301) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_1301),
    inference(definitional_conversion,[status(esa)],[f_334_2]) ).

cnf(f_334_4,plain,
    hAPP(nat,nat,suc,U_1301) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),U_1301),
    inference(clausify,[status(thm)],[f_334_3]) ).

fof(f_335_1,plain,
    ! [X_b,F1,F2,Nat_2] : hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),hAPP(nat,nat,suc,Nat_2)) = hAPP(nat,X_b,F2,Nat_2),
    inference(fof_nnf,[status(thm)],[fact_282_nat__case__Suc]) ).

fof(f_335_2,plain,
    ! [U_1305,U_1304,U_1303,U_1302] : hAPP(nat,U_1305,hAPP(fun(nat,U_1305),fun(nat,U_1305),hAPP(U_1305,fun(fun(nat,U_1305),fun(nat,U_1305)),nat_case(U_1305),U_1304),U_1303),hAPP(nat,nat,suc,U_1302)) = hAPP(nat,U_1305,U_1303,U_1302),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

fof(f_335_3,plain,
    ! [U_1303,U_1305,U_1302,U_1304] : hAPP(nat,U_1305,hAPP(fun(nat,U_1305),fun(nat,U_1305),hAPP(U_1305,fun(fun(nat,U_1305),fun(nat,U_1305)),nat_case(U_1305),U_1304),U_1303),hAPP(nat,nat,suc,U_1302)) = hAPP(nat,U_1305,U_1303,U_1302),
    inference(definitional_conversion,[status(esa)],[f_335_2]) ).

cnf(f_335_4,plain,
    hAPP(nat,U_1305,hAPP(fun(nat,U_1305),fun(nat,U_1305),hAPP(U_1305,fun(fun(nat,U_1305),fun(nat,U_1305)),nat_case(U_1305),U_1304),U_1303),hAPP(nat,nat,suc,U_1302)) = hAPP(nat,U_1305,U_1303,U_1302),
    inference(clausify,[status(thm)],[f_335_3]) ).

fof(f_336_1,plain,
    ! [M,K,J_2] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K))),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,J_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_283_diff__Suc__diff__eq2]) ).

fof(f_336_2,plain,
    ! [U_1308,U_1307,U_1306] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1306),U_1307))),U_1308) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1306)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1307),U_1308))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1307),U_1306)) ),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

fof(f_336_3,plain,
    ! [U_1306,U_1307,U_1308] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1306),U_1307))),U_1308) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1306)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1307),U_1308))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1307),U_1306)) ),
    inference(definitional_conversion,[status(esa)],[f_336_2]) ).

cnf(f_336_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1306),U_1307))),U_1308) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1306)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1307),U_1308))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1307),U_1306)) ),
    inference(clausify,[status(thm)],[f_336_3]) ).

fof(f_337_1,plain,
    ! [M,K,J_2] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,suc,J_2))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_284_diff__Suc__diff__eq1]) ).

fof(f_337_2,plain,
    ! [U_1311,U_1310,U_1309] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1311),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1309),U_1310))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1311),U_1310)),hAPP(nat,nat,suc,U_1309))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1310),U_1309)) ),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

fof(f_337_3,plain,
    ! [U_1310,U_1309,U_1311] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1311),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1309),U_1310))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1311),U_1310)),hAPP(nat,nat,suc,U_1309))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1310),U_1309)) ),
    inference(definitional_conversion,[status(esa)],[f_337_2]) ).

cnf(f_337_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1311),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1309),U_1310))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1311),U_1310)),hAPP(nat,nat,suc,U_1309))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1310),U_1309)) ),
    inference(clausify,[status(thm)],[f_337_3]) ).

fof(f_338_1,plain,
    ! [X_b,X_1,A_3] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))
      | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_285_card_Oinsert]) ).

fof(f_338_2,plain,
    ! [U_1314,U_1313,U_1312] :
      ( hAPP(fun(U_1314,bool),nat,finite_card(U_1314),hAPP(fun(U_1314,bool),fun(U_1314,bool),hAPP(U_1314,fun(fun(U_1314,bool),fun(U_1314,bool)),insert(U_1314),U_1313),U_1312)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1314,bool),nat,finite_card(U_1314),U_1312))
      | hBOOL(hAPP(fun(U_1314,bool),bool,hAPP(U_1314,fun(fun(U_1314,bool),bool),member(U_1314),U_1313),U_1312))
      | ~ hBOOL(hAPP(fun(U_1314,bool),bool,finite_finite(U_1314),U_1312)) ),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

fof(f_338_3,plain,
    ! [U_1312,U_1314,U_1313] :
      ( hAPP(fun(U_1314,bool),nat,finite_card(U_1314),hAPP(fun(U_1314,bool),fun(U_1314,bool),hAPP(U_1314,fun(fun(U_1314,bool),fun(U_1314,bool)),insert(U_1314),U_1313),U_1312)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1314,bool),nat,finite_card(U_1314),U_1312))
      | hBOOL(hAPP(fun(U_1314,bool),bool,hAPP(U_1314,fun(fun(U_1314,bool),bool),member(U_1314),U_1313),U_1312))
      | ~ hBOOL(hAPP(fun(U_1314,bool),bool,finite_finite(U_1314),U_1312)) ),
    inference(definitional_conversion,[status(esa)],[f_338_2]) ).

cnf(f_338_4,plain,
    ( hAPP(fun(U_1314,bool),nat,finite_card(U_1314),hAPP(fun(U_1314,bool),fun(U_1314,bool),hAPP(U_1314,fun(fun(U_1314,bool),fun(U_1314,bool)),insert(U_1314),U_1313),U_1312)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(U_1314,bool),nat,finite_card(U_1314),U_1312))
    | hBOOL(hAPP(fun(U_1314,bool),bool,hAPP(U_1314,fun(fun(U_1314,bool),bool),member(U_1314),U_1313),U_1312))
    | ~ hBOOL(hAPP(fun(U_1314,bool),bool,finite_finite(U_1314),U_1312)) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

fof(f_339_1,plain,
    ! [Z,X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_286_termination__basic__simps_I3_J]) ).

fof(f_339_2,plain,
    ! [U_1317,U_1316,U_1315] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1316),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1315),U_1317)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1316),U_1315)) ),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

fof(f_339_3,plain,
    ! [U_1316,U_1315,U_1317] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1316),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1315),U_1317)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1316),U_1315)) ),
    inference(definitional_conversion,[status(esa)],[f_339_2]) ).

cnf(f_339_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1316),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1315),U_1317)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1316),U_1315)) ),
    inference(clausify,[status(thm)],[f_339_3]) ).

fof(f_340_1,plain,
    ! [Y,X,Z] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_287_termination__basic__simps_I4_J]) ).

fof(f_340_2,plain,
    ! [U_1320,U_1319,U_1318] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1319),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1320),U_1318)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1319),U_1318)) ),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

fof(f_340_3,plain,
    ! [U_1319,U_1318,U_1320] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1319),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1320),U_1318)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1319),U_1318)) ),
    inference(definitional_conversion,[status(esa)],[f_340_2]) ).

cnf(f_340_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1319),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1320),U_1318)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1319),U_1318)) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

fof(f_341_1,plain,
    ! [X_b,Y_1,X_1,A_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_288_card__Diff2__less]) ).

fof(f_341_2,plain,
    ! [U_1324,U_1323,U_1322,U_1321] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1324,bool),nat,finite_card(U_1324),hAPP(fun(U_1324,bool),fun(U_1324,bool),hAPP(fun(U_1324,bool),fun(fun(U_1324,bool),fun(U_1324,bool)),minus_minus(fun(U_1324,bool)),hAPP(fun(U_1324,bool),fun(U_1324,bool),hAPP(fun(U_1324,bool),fun(fun(U_1324,bool),fun(U_1324,bool)),minus_minus(fun(U_1324,bool)),U_1321),hAPP(fun(U_1324,bool),fun(U_1324,bool),hAPP(U_1324,fun(fun(U_1324,bool),fun(U_1324,bool)),insert(U_1324),U_1322),bot_bot(fun(U_1324,bool))))),hAPP(fun(U_1324,bool),fun(U_1324,bool),hAPP(U_1324,fun(fun(U_1324,bool),fun(U_1324,bool)),insert(U_1324),U_1323),bot_bot(fun(U_1324,bool)))))),hAPP(fun(U_1324,bool),nat,finite_card(U_1324),U_1321)))
      | ~ hBOOL(hAPP(fun(U_1324,bool),bool,hAPP(U_1324,fun(fun(U_1324,bool),bool),member(U_1324),U_1323),U_1321))
      | ~ hBOOL(hAPP(fun(U_1324,bool),bool,hAPP(U_1324,fun(fun(U_1324,bool),bool),member(U_1324),U_1322),U_1321))
      | ~ hBOOL(hAPP(fun(U_1324,bool),bool,finite_finite(U_1324),U_1321)) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

fof(f_341_3,plain,
    ! [U_1322,U_1321,U_1324,U_1323] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1324,bool),nat,finite_card(U_1324),hAPP(fun(U_1324,bool),fun(U_1324,bool),hAPP(fun(U_1324,bool),fun(fun(U_1324,bool),fun(U_1324,bool)),minus_minus(fun(U_1324,bool)),hAPP(fun(U_1324,bool),fun(U_1324,bool),hAPP(fun(U_1324,bool),fun(fun(U_1324,bool),fun(U_1324,bool)),minus_minus(fun(U_1324,bool)),U_1321),hAPP(fun(U_1324,bool),fun(U_1324,bool),hAPP(U_1324,fun(fun(U_1324,bool),fun(U_1324,bool)),insert(U_1324),U_1322),bot_bot(fun(U_1324,bool))))),hAPP(fun(U_1324,bool),fun(U_1324,bool),hAPP(U_1324,fun(fun(U_1324,bool),fun(U_1324,bool)),insert(U_1324),U_1323),bot_bot(fun(U_1324,bool)))))),hAPP(fun(U_1324,bool),nat,finite_card(U_1324),U_1321)))
      | ~ hBOOL(hAPP(fun(U_1324,bool),bool,hAPP(U_1324,fun(fun(U_1324,bool),bool),member(U_1324),U_1323),U_1321))
      | ~ hBOOL(hAPP(fun(U_1324,bool),bool,hAPP(U_1324,fun(fun(U_1324,bool),bool),member(U_1324),U_1322),U_1321))
      | ~ hBOOL(hAPP(fun(U_1324,bool),bool,finite_finite(U_1324),U_1321)) ),
    inference(definitional_conversion,[status(esa)],[f_341_2]) ).

cnf(f_341_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1324,bool),nat,finite_card(U_1324),hAPP(fun(U_1324,bool),fun(U_1324,bool),hAPP(fun(U_1324,bool),fun(fun(U_1324,bool),fun(U_1324,bool)),minus_minus(fun(U_1324,bool)),hAPP(fun(U_1324,bool),fun(U_1324,bool),hAPP(fun(U_1324,bool),fun(fun(U_1324,bool),fun(U_1324,bool)),minus_minus(fun(U_1324,bool)),U_1321),hAPP(fun(U_1324,bool),fun(U_1324,bool),hAPP(U_1324,fun(fun(U_1324,bool),fun(U_1324,bool)),insert(U_1324),U_1322),bot_bot(fun(U_1324,bool))))),hAPP(fun(U_1324,bool),fun(U_1324,bool),hAPP(U_1324,fun(fun(U_1324,bool),fun(U_1324,bool)),insert(U_1324),U_1323),bot_bot(fun(U_1324,bool)))))),hAPP(fun(U_1324,bool),nat,finite_card(U_1324),U_1321)))
    | ~ hBOOL(hAPP(fun(U_1324,bool),bool,hAPP(U_1324,fun(fun(U_1324,bool),bool),member(U_1324),U_1323),U_1321))
    | ~ hBOOL(hAPP(fun(U_1324,bool),bool,hAPP(U_1324,fun(fun(U_1324,bool),bool),member(U_1324),U_1322),U_1321))
    | ~ hBOOL(hAPP(fun(U_1324,bool),bool,finite_finite(U_1324),U_1321)) ),
    inference(clausify,[status(thm)],[f_341_3]) ).

fof(f_342_1,plain,
    ! [X_b,X_1,A_3] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_289_card__Diff1__less]) ).

fof(f_342_2,plain,
    ! [U_1327,U_1326,U_1325] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1327,bool),nat,finite_card(U_1327),hAPP(fun(U_1327,bool),fun(U_1327,bool),hAPP(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool)),minus_minus(fun(U_1327,bool)),U_1325),hAPP(fun(U_1327,bool),fun(U_1327,bool),hAPP(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool)),insert(U_1327),U_1326),bot_bot(fun(U_1327,bool)))))),hAPP(fun(U_1327,bool),nat,finite_card(U_1327),U_1325)))
      | ~ hBOOL(hAPP(fun(U_1327,bool),bool,hAPP(U_1327,fun(fun(U_1327,bool),bool),member(U_1327),U_1326),U_1325))
      | ~ hBOOL(hAPP(fun(U_1327,bool),bool,finite_finite(U_1327),U_1325)) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

fof(f_342_3,plain,
    ! [U_1325,U_1327,U_1326] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1327,bool),nat,finite_card(U_1327),hAPP(fun(U_1327,bool),fun(U_1327,bool),hAPP(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool)),minus_minus(fun(U_1327,bool)),U_1325),hAPP(fun(U_1327,bool),fun(U_1327,bool),hAPP(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool)),insert(U_1327),U_1326),bot_bot(fun(U_1327,bool)))))),hAPP(fun(U_1327,bool),nat,finite_card(U_1327),U_1325)))
      | ~ hBOOL(hAPP(fun(U_1327,bool),bool,hAPP(U_1327,fun(fun(U_1327,bool),bool),member(U_1327),U_1326),U_1325))
      | ~ hBOOL(hAPP(fun(U_1327,bool),bool,finite_finite(U_1327),U_1325)) ),
    inference(definitional_conversion,[status(esa)],[f_342_2]) ).

cnf(f_342_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1327,bool),nat,finite_card(U_1327),hAPP(fun(U_1327,bool),fun(U_1327,bool),hAPP(fun(U_1327,bool),fun(fun(U_1327,bool),fun(U_1327,bool)),minus_minus(fun(U_1327,bool)),U_1325),hAPP(fun(U_1327,bool),fun(U_1327,bool),hAPP(U_1327,fun(fun(U_1327,bool),fun(U_1327,bool)),insert(U_1327),U_1326),bot_bot(fun(U_1327,bool)))))),hAPP(fun(U_1327,bool),nat,finite_card(U_1327),U_1325)))
    | ~ hBOOL(hAPP(fun(U_1327,bool),bool,hAPP(U_1327,fun(fun(U_1327,bool),bool),member(U_1327),U_1326),U_1325))
    | ~ hBOOL(hAPP(fun(U_1327,bool),bool,finite_finite(U_1327),U_1325)) ),
    inference(clausify,[status(thm)],[f_342_3]) ).

fof(f_343_1,plain,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N))),
    inference(fof_nnf,[status(thm)],[fact_290_lessI]) ).

fof(f_343_2,plain,
    ! [U_1328] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1328),hAPP(nat,nat,suc,U_1328))),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

fof(f_343_3,plain,
    ! [U_1328] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1328),hAPP(nat,nat,suc,U_1328))),
    inference(definitional_conversion,[status(esa)],[f_343_2]) ).

cnf(f_343_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1328),hAPP(nat,nat,suc,U_1328))),
    inference(clausify,[status(thm)],[f_343_3]) ).

fof(f_344_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_291_Suc__mono]) ).

fof(f_344_2,plain,
    ! [U_1330,U_1329] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1330)),hAPP(nat,nat,suc,U_1329)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1330),U_1329)) ),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

fof(f_344_3,plain,
    ! [U_1329,U_1330] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1330)),hAPP(nat,nat,suc,U_1329)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1330),U_1329)) ),
    inference(definitional_conversion,[status(esa)],[f_344_2]) ).

cnf(f_344_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1330)),hAPP(nat,nat,suc,U_1329)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1330),U_1329)) ),
    inference(clausify,[status(thm)],[f_344_3]) ).

fof(f_345_1,plain,
    ! [K_2] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),K_2)))),
    inference(fof_nnf,[status(thm)],[fact_292_finite__Collect__less__nat]) ).

fof(f_345_2,plain,
    ! [U_1331] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1331)))),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

fof(f_345_3,plain,
    ! [U_1331] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1331)))),
    inference(definitional_conversion,[status(esa)],[f_345_2]) ).

cnf(f_345_4,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1331)))),
    inference(clausify,[status(thm)],[f_345_3]) ).

fof(f_346_1,plain,
    ! [Z,X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_293_termination__basic__simps_I1_J]) ).

fof(f_346_2,plain,
    ! [U_1334,U_1333,U_1332] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1333),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1332),U_1334)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1333),U_1332)) ),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

fof(f_346_3,plain,
    ! [U_1333,U_1332,U_1334] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1333),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1332),U_1334)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1333),U_1332)) ),
    inference(definitional_conversion,[status(esa)],[f_346_2]) ).

cnf(f_346_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1333),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1332),U_1334)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1333),U_1332)) ),
    inference(clausify,[status(thm)],[f_346_3]) ).

fof(f_347_1,plain,
    ! [Y,X,Z] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_294_termination__basic__simps_I2_J]) ).

fof(f_347_2,plain,
    ! [U_1337,U_1336,U_1335] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1336),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1337),U_1335)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1336),U_1335)) ),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

fof(f_347_3,plain,
    ! [U_1336,U_1335,U_1337] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1336),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1337),U_1335)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1336),U_1335)) ),
    inference(definitional_conversion,[status(esa)],[f_347_2]) ).

cnf(f_347_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1336),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1337),U_1335)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1336),U_1335)) ),
    inference(clausify,[status(thm)],[f_347_3]) ).

fof(f_348_1,plain,
    ! [I,J_2,K] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_2)),K)) ),
    inference(fof_nnf,[status(thm)],[fact_295_add__lessD1]) ).

fof(f_348_2,plain,
    ! [U_1340,U_1339,U_1338] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1340),U_1338))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1340),U_1339)),U_1338)) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ! [U_1338,U_1339,U_1340] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1340),U_1338))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1340),U_1339)),U_1338)) ),
    inference(definitional_conversion,[status(esa)],[f_348_2]) ).

cnf(f_348_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1340),U_1338))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1340),U_1339)),U_1338)) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

fof(f_349_1,plain,
    ! [M,N,K,L] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L)) ),
    inference(fof_nnf,[status(thm)],[fact_296_less__add__eq__less]) ).

fof(f_349_2,plain,
    ! [U_1344,U_1343,U_1342,U_1341] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1344),U_1343))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1344),U_1341) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1342),U_1343)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1342),U_1341)) ),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

fof(f_349_3,plain,
    ! [U_1342,U_1341,U_1343,U_1344] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1344),U_1343))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1344),U_1341) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1342),U_1343)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1342),U_1341)) ),
    inference(definitional_conversion,[status(esa)],[f_349_2]) ).

cnf(f_349_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1344),U_1343))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1344),U_1341) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1342),U_1343)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1342),U_1341)) ),
    inference(clausify,[status(thm)],[f_349_3]) ).

fof(f_350_1,plain,
    ! [K,L,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_297_add__less__mono]) ).

fof(f_350_2,plain,
    ! [U_1348,U_1347,U_1346,U_1345] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1346),U_1348)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1345),U_1347)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1348),U_1347))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1346),U_1345)) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

fof(f_350_3,plain,
    ! [U_1346,U_1345,U_1347,U_1348] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1346),U_1348)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1345),U_1347)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1348),U_1347))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1346),U_1345)) ),
    inference(definitional_conversion,[status(esa)],[f_350_2]) ).

cnf(f_350_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1346),U_1348)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1345),U_1347)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1348),U_1347))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1346),U_1345)) ),
    inference(clausify,[status(thm)],[f_350_3]) ).

fof(f_351_1,plain,
    ! [K,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_298_add__less__mono1]) ).

fof(f_351_2,plain,
    ! [U_1351,U_1350,U_1349] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1350),U_1351)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1349),U_1351)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1350),U_1349)) ),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

fof(f_351_3,plain,
    ! [U_1350,U_1349,U_1351] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1350),U_1351)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1349),U_1351)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1350),U_1349)) ),
    inference(definitional_conversion,[status(esa)],[f_351_2]) ).

cnf(f_351_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1350),U_1351)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1349),U_1351)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1350),U_1349)) ),
    inference(clausify,[status(thm)],[f_351_3]) ).

fof(f_352_1,plain,
    ! [M,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_2)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_299_trans__less__add2]) ).

fof(f_352_2,plain,
    ! [U_1354,U_1353,U_1352] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1353),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1354),U_1352)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1353),U_1352)) ),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

fof(f_352_3,plain,
    ! [U_1353,U_1352,U_1354] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1353),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1354),U_1352)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1353),U_1352)) ),
    inference(definitional_conversion,[status(esa)],[f_352_2]) ).

cnf(f_352_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1353),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1354),U_1352)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1353),U_1352)) ),
    inference(clausify,[status(thm)],[f_352_3]) ).

fof(f_353_1,plain,
    ! [M,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_300_trans__less__add1]) ).

fof(f_353_2,plain,
    ! [U_1357,U_1356,U_1355] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1356),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1355),U_1357)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1356),U_1355)) ),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

fof(f_353_3,plain,
    ! [U_1355,U_1356,U_1357] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1356),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1355),U_1357)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1356),U_1355)) ),
    inference(definitional_conversion,[status(esa)],[f_353_2]) ).

cnf(f_353_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1356),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1355),U_1357)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1356),U_1355)) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

fof(f_354_1,plain,
    ! [K_2,M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_2),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_301_nat__add__left__cancel__less]) ).

fof(f_354_2,plain,
    ! [U_1360,U_1359,U_1358] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1360),U_1359)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1360),U_1358)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1359),U_1358)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1359),U_1358))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1360),U_1359)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1360),U_1358))) ) ),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

fof(f_354_3,plain,
    ( ! [U_1366,U_1364,U_1362] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1366),U_1364)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1366),U_1362)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1364),U_1362)) )
    & ! [U_1365,U_1363,U_1361] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1363),U_1361))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1365),U_1363)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1365),U_1361))) ) ),
    inference(miniscope,[status(thm)],[f_354_2]) ).

fof(f_354_4,plain,
    ( ! [U_1362,U_1364,U_1366] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1366),U_1364)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1366),U_1362)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1364),U_1362)) )
    & ! [U_1365,U_1363,U_1361] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1363),U_1361))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1365),U_1363)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1365),U_1361))) ) ),
    inference(definitional_conversion,[status(esa)],[f_354_3]) ).

cnf(f_354_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1363),U_1361))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1365),U_1363)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1365),U_1361))) ),
    inference(clausify,[status(thm)],[f_354_4]) ).

cnf(f_354_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1366),U_1364)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1366),U_1362)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1364),U_1362)) ),
    inference(clausify,[status(thm)],[f_354_4]) ).

fof(f_355_1,plain,
    ! [J_2,I] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I)),I)),
    inference(fof_nnf,[status(thm)],[fact_302_not__add__less2]) ).

fof(f_355_2,plain,
    ! [U_1368,U_1367] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1368),U_1367)),U_1367)),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

fof(f_355_3,plain,
    ! [U_1368,U_1367] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1368),U_1367)),U_1367)),
    inference(definitional_conversion,[status(esa)],[f_355_2]) ).

cnf(f_355_4,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1368),U_1367)),U_1367)),
    inference(clausify,[status(thm)],[f_355_3]) ).

fof(f_356_1,plain,
    ! [I,J_2] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J_2)),I)),
    inference(fof_nnf,[status(thm)],[fact_303_not__add__less1]) ).

fof(f_356_2,plain,
    ! [U_1370,U_1369] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1370),U_1369)),U_1370)),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ! [U_1369,U_1370] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1370),U_1369)),U_1370)),
    inference(definitional_conversion,[status(esa)],[f_356_2]) ).

cnf(f_356_4,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1370),U_1369)),U_1370)),
    inference(clausify,[status(thm)],[f_356_3]) ).

fof(f_357_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1))) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_304_add__less__imp__less__left]) ).

fof(f_357_2,plain,
    ! [U_1374] :
      ( ! [U_1373,U_1372,U_1371] :
          ( hBOOL(hAPP(U_1374,bool,hAPP(U_1374,fun(U_1374,bool),ord_less(U_1374),U_1372),U_1371))
          | ~ hBOOL(hAPP(U_1374,bool,hAPP(U_1374,fun(U_1374,bool),ord_less(U_1374),hAPP(U_1374,U_1374,hAPP(U_1374,fun(U_1374,U_1374),plus_plus(U_1374),U_1373),U_1372)),hAPP(U_1374,U_1374,hAPP(U_1374,fun(U_1374,U_1374),plus_plus(U_1374),U_1373),U_1371))) )
      | ~ ordere236663937imp_le(U_1374) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

fof(f_357_3,plain,
    ! [U_1374,U_1371,U_1372,U_1373] :
      ( hBOOL(hAPP(U_1374,bool,hAPP(U_1374,fun(U_1374,bool),ord_less(U_1374),U_1372),U_1371))
      | ~ hBOOL(hAPP(U_1374,bool,hAPP(U_1374,fun(U_1374,bool),ord_less(U_1374),hAPP(U_1374,U_1374,hAPP(U_1374,fun(U_1374,U_1374),plus_plus(U_1374),U_1373),U_1372)),hAPP(U_1374,U_1374,hAPP(U_1374,fun(U_1374,U_1374),plus_plus(U_1374),U_1373),U_1371)))
      | ~ ordere236663937imp_le(U_1374) ),
    inference(definitional_conversion,[status(esa)],[f_357_2]) ).

cnf(f_357_4,plain,
    ( hBOOL(hAPP(U_1374,bool,hAPP(U_1374,fun(U_1374,bool),ord_less(U_1374),U_1372),U_1371))
    | ~ hBOOL(hAPP(U_1374,bool,hAPP(U_1374,fun(U_1374,bool),ord_less(U_1374),hAPP(U_1374,U_1374,hAPP(U_1374,fun(U_1374,U_1374),plus_plus(U_1374),U_1373),U_1372)),hAPP(U_1374,U_1374,hAPP(U_1374,fun(U_1374,U_1374),plus_plus(U_1374),U_1373),U_1371)))
    | ~ ordere236663937imp_le(U_1374) ),
    inference(clausify,[status(thm)],[f_357_3]) ).

fof(f_358_1,plain,
    ! [X_a] :
      ( ! [A_1,C,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C))) )
      | ~ ordere236663937imp_le(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_305_add__less__imp__less__right]) ).

fof(f_358_2,plain,
    ! [U_1378] :
      ( ! [U_1377,U_1376,U_1375] :
          ( hBOOL(hAPP(U_1378,bool,hAPP(U_1378,fun(U_1378,bool),ord_less(U_1378),U_1377),U_1375))
          | ~ hBOOL(hAPP(U_1378,bool,hAPP(U_1378,fun(U_1378,bool),ord_less(U_1378),hAPP(U_1378,U_1378,hAPP(U_1378,fun(U_1378,U_1378),plus_plus(U_1378),U_1377),U_1376)),hAPP(U_1378,U_1378,hAPP(U_1378,fun(U_1378,U_1378),plus_plus(U_1378),U_1375),U_1376))) )
      | ~ ordere236663937imp_le(U_1378) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

fof(f_358_3,plain,
    ! [U_1378,U_1375,U_1376,U_1377] :
      ( hBOOL(hAPP(U_1378,bool,hAPP(U_1378,fun(U_1378,bool),ord_less(U_1378),U_1377),U_1375))
      | ~ hBOOL(hAPP(U_1378,bool,hAPP(U_1378,fun(U_1378,bool),ord_less(U_1378),hAPP(U_1378,U_1378,hAPP(U_1378,fun(U_1378,U_1378),plus_plus(U_1378),U_1377),U_1376)),hAPP(U_1378,U_1378,hAPP(U_1378,fun(U_1378,U_1378),plus_plus(U_1378),U_1375),U_1376)))
      | ~ ordere236663937imp_le(U_1378) ),
    inference(definitional_conversion,[status(esa)],[f_358_2]) ).

cnf(f_358_4,plain,
    ( hBOOL(hAPP(U_1378,bool,hAPP(U_1378,fun(U_1378,bool),ord_less(U_1378),U_1377),U_1375))
    | ~ hBOOL(hAPP(U_1378,bool,hAPP(U_1378,fun(U_1378,bool),ord_less(U_1378),hAPP(U_1378,U_1378,hAPP(U_1378,fun(U_1378,U_1378),plus_plus(U_1378),U_1377),U_1376)),hAPP(U_1378,U_1378,hAPP(U_1378,fun(U_1378,U_1378),plus_plus(U_1378),U_1375),U_1376)))
    | ~ ordere236663937imp_le(U_1378) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

fof(f_359_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_306_add__strict__mono]) ).

fof(f_359_2,plain,
    ! [U_1383] :
      ( ! [U_1382,U_1381,U_1380,U_1379] :
          ( hBOOL(hAPP(U_1383,bool,hAPP(U_1383,fun(U_1383,bool),ord_less(U_1383),hAPP(U_1383,U_1383,hAPP(U_1383,fun(U_1383,U_1383),plus_plus(U_1383),U_1380),U_1382)),hAPP(U_1383,U_1383,hAPP(U_1383,fun(U_1383,U_1383),plus_plus(U_1383),U_1379),U_1381)))
          | ~ hBOOL(hAPP(U_1383,bool,hAPP(U_1383,fun(U_1383,bool),ord_less(U_1383),U_1382),U_1381))
          | ~ hBOOL(hAPP(U_1383,bool,hAPP(U_1383,fun(U_1383,bool),ord_less(U_1383),U_1380),U_1379)) )
      | ~ ordere223160158up_add(U_1383) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ! [U_1383,U_1379,U_1380,U_1381,U_1382] :
      ( hBOOL(hAPP(U_1383,bool,hAPP(U_1383,fun(U_1383,bool),ord_less(U_1383),hAPP(U_1383,U_1383,hAPP(U_1383,fun(U_1383,U_1383),plus_plus(U_1383),U_1380),U_1382)),hAPP(U_1383,U_1383,hAPP(U_1383,fun(U_1383,U_1383),plus_plus(U_1383),U_1379),U_1381)))
      | ~ hBOOL(hAPP(U_1383,bool,hAPP(U_1383,fun(U_1383,bool),ord_less(U_1383),U_1382),U_1381))
      | ~ hBOOL(hAPP(U_1383,bool,hAPP(U_1383,fun(U_1383,bool),ord_less(U_1383),U_1380),U_1379))
      | ~ ordere223160158up_add(U_1383) ),
    inference(definitional_conversion,[status(esa)],[f_359_2]) ).

cnf(f_359_4,plain,
    ( hBOOL(hAPP(U_1383,bool,hAPP(U_1383,fun(U_1383,bool),ord_less(U_1383),hAPP(U_1383,U_1383,hAPP(U_1383,fun(U_1383,U_1383),plus_plus(U_1383),U_1380),U_1382)),hAPP(U_1383,U_1383,hAPP(U_1383,fun(U_1383,U_1383),plus_plus(U_1383),U_1379),U_1381)))
    | ~ hBOOL(hAPP(U_1383,bool,hAPP(U_1383,fun(U_1383,bool),ord_less(U_1383),U_1382),U_1381))
    | ~ hBOOL(hAPP(U_1383,bool,hAPP(U_1383,fun(U_1383,bool),ord_less(U_1383),U_1380),U_1379))
    | ~ ordere223160158up_add(U_1383) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

fof(f_360_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_307_add__strict__left__mono]) ).

fof(f_360_2,plain,
    ! [U_1387] :
      ( ! [U_1386,U_1385,U_1384] :
          ( hBOOL(hAPP(U_1387,bool,hAPP(U_1387,fun(U_1387,bool),ord_less(U_1387),hAPP(U_1387,U_1387,hAPP(U_1387,fun(U_1387,U_1387),plus_plus(U_1387),U_1386),U_1385)),hAPP(U_1387,U_1387,hAPP(U_1387,fun(U_1387,U_1387),plus_plus(U_1387),U_1386),U_1384)))
          | ~ hBOOL(hAPP(U_1387,bool,hAPP(U_1387,fun(U_1387,bool),ord_less(U_1387),U_1385),U_1384)) )
      | ~ ordere223160158up_add(U_1387) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

fof(f_360_3,plain,
    ! [U_1386,U_1385,U_1384,U_1387] :
      ( hBOOL(hAPP(U_1387,bool,hAPP(U_1387,fun(U_1387,bool),ord_less(U_1387),hAPP(U_1387,U_1387,hAPP(U_1387,fun(U_1387,U_1387),plus_plus(U_1387),U_1386),U_1385)),hAPP(U_1387,U_1387,hAPP(U_1387,fun(U_1387,U_1387),plus_plus(U_1387),U_1386),U_1384)))
      | ~ hBOOL(hAPP(U_1387,bool,hAPP(U_1387,fun(U_1387,bool),ord_less(U_1387),U_1385),U_1384))
      | ~ ordere223160158up_add(U_1387) ),
    inference(definitional_conversion,[status(esa)],[f_360_2]) ).

cnf(f_360_4,plain,
    ( hBOOL(hAPP(U_1387,bool,hAPP(U_1387,fun(U_1387,bool),ord_less(U_1387),hAPP(U_1387,U_1387,hAPP(U_1387,fun(U_1387,U_1387),plus_plus(U_1387),U_1386),U_1385)),hAPP(U_1387,U_1387,hAPP(U_1387,fun(U_1387,U_1387),plus_plus(U_1387),U_1386),U_1384)))
    | ~ hBOOL(hAPP(U_1387,bool,hAPP(U_1387,fun(U_1387,bool),ord_less(U_1387),U_1385),U_1384))
    | ~ ordere223160158up_add(U_1387) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

fof(f_361_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_308_add__strict__right__mono]) ).

fof(f_361_2,plain,
    ! [U_1391] :
      ( ! [U_1390,U_1389,U_1388] :
          ( hBOOL(hAPP(U_1391,bool,hAPP(U_1391,fun(U_1391,bool),ord_less(U_1391),hAPP(U_1391,U_1391,hAPP(U_1391,fun(U_1391,U_1391),plus_plus(U_1391),U_1389),U_1390)),hAPP(U_1391,U_1391,hAPP(U_1391,fun(U_1391,U_1391),plus_plus(U_1391),U_1388),U_1390)))
          | ~ hBOOL(hAPP(U_1391,bool,hAPP(U_1391,fun(U_1391,bool),ord_less(U_1391),U_1389),U_1388)) )
      | ~ ordere223160158up_add(U_1391) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

fof(f_361_3,plain,
    ! [U_1391,U_1389,U_1388,U_1390] :
      ( hBOOL(hAPP(U_1391,bool,hAPP(U_1391,fun(U_1391,bool),ord_less(U_1391),hAPP(U_1391,U_1391,hAPP(U_1391,fun(U_1391,U_1391),plus_plus(U_1391),U_1389),U_1390)),hAPP(U_1391,U_1391,hAPP(U_1391,fun(U_1391,U_1391),plus_plus(U_1391),U_1388),U_1390)))
      | ~ hBOOL(hAPP(U_1391,bool,hAPP(U_1391,fun(U_1391,bool),ord_less(U_1391),U_1389),U_1388))
      | ~ ordere223160158up_add(U_1391) ),
    inference(definitional_conversion,[status(esa)],[f_361_2]) ).

cnf(f_361_4,plain,
    ( hBOOL(hAPP(U_1391,bool,hAPP(U_1391,fun(U_1391,bool),ord_less(U_1391),hAPP(U_1391,U_1391,hAPP(U_1391,fun(U_1391,U_1391),plus_plus(U_1391),U_1389),U_1390)),hAPP(U_1391,U_1391,hAPP(U_1391,fun(U_1391,U_1391),plus_plus(U_1391),U_1388),U_1390)))
    | ~ hBOOL(hAPP(U_1391,bool,hAPP(U_1391,fun(U_1391,bool),ord_less(U_1391),U_1389),U_1388))
    | ~ ordere223160158up_add(U_1391) ),
    inference(clausify,[status(thm)],[f_361_3]) ).

fof(f_362_1,plain,
    ! [X_b] :
      ( ! [C_1,A_2,B] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),C_1),B))) ) )
      | ~ ordere236663937imp_le(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_309_add__less__cancel__left]) ).

fof(f_362_2,plain,
    ! [U_1395] :
      ( ! [U_1394,U_1393,U_1392] :
          ( ( hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1394),U_1393)),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1394),U_1392)))
            | ~ hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),U_1393),U_1392)) )
          & ( hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),U_1393),U_1392))
            | ~ hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1394),U_1393)),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1394),U_1392))) ) )
      | ~ ordere236663937imp_le(U_1395) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

fof(f_362_3,plain,
    ! [U_1395] :
      ( ( ! [U_1401,U_1399,U_1397] :
            ( hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1401),U_1399)),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1401),U_1397)))
            | ~ hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),U_1399),U_1397)) )
        & ! [U_1400,U_1398,U_1396] :
            ( hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),U_1398),U_1396))
            | ~ hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1400),U_1398)),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1400),U_1396))) ) )
      | ~ ordere236663937imp_le(U_1395) ),
    inference(miniscope,[status(thm)],[f_362_2]) ).

fof(f_362_4,plain,
    ( ! [U_1400,U_1398,U_1395,U_1396,U_1397,U_1399,U_1401] :
        ( hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1401),U_1399)),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1401),U_1397)))
        | ~ hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),U_1399),U_1397))
        | ~ sP63(U_1400,U_1398,U_1395,U_1396,U_1397,U_1399,U_1401) )
    & ! [U_1400,U_1398,U_1395,U_1396,U_1397,U_1399,U_1401] :
        ( hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),U_1398),U_1396))
        | ~ hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1400),U_1398)),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1400),U_1396)))
        | ~ sP63(U_1400,U_1398,U_1395,U_1396,U_1397,U_1399,U_1401) )
    & ! [U_1400,U_1398,U_1395,U_1396,U_1397,U_1399,U_1401] :
        ( sP63(U_1400,U_1398,U_1395,U_1396,U_1397,U_1399,U_1401)
        | ~ ordere236663937imp_le(U_1395) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_362_3]) ).

cnf(f_362_5,plain,
    ( sP63(U_1400,U_1398,U_1395,U_1396,U_1397,U_1399,U_1401)
    | ~ ordere236663937imp_le(U_1395) ),
    inference(clausify,[status(thm)],[f_362_4]) ).

cnf(f_362_6,plain,
    ( hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),U_1398),U_1396))
    | ~ hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1400),U_1398)),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1400),U_1396)))
    | ~ sP63(U_1400,U_1398,U_1395,U_1396,U_1397,U_1399,U_1401) ),
    inference(clausify,[status(thm)],[f_362_4]) ).

cnf(f_362_7,plain,
    ( hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1401),U_1399)),hAPP(U_1395,U_1395,hAPP(U_1395,fun(U_1395,U_1395),plus_plus(U_1395),U_1401),U_1397)))
    | ~ hBOOL(hAPP(U_1395,bool,hAPP(U_1395,fun(U_1395,bool),ord_less(U_1395),U_1399),U_1397))
    | ~ sP63(U_1400,U_1398,U_1395,U_1396,U_1397,U_1399,U_1401) ),
    inference(clausify,[status(thm)],[f_362_4]) ).

fof(f_363_1,plain,
    ! [X_b] :
      ( ! [A_2,C_1,B] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C_1)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),C_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),B),C_1))) ) )
      | ~ ordere236663937imp_le(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_310_add__less__cancel__right]) ).

fof(f_363_2,plain,
    ! [U_1405] :
      ( ! [U_1404,U_1403,U_1402] :
          ( ( hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1404),U_1403)),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1402),U_1403)))
            | ~ hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),U_1404),U_1402)) )
          & ( hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),U_1404),U_1402))
            | ~ hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1404),U_1403)),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1402),U_1403))) ) )
      | ~ ordere236663937imp_le(U_1405) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

fof(f_363_3,plain,
    ! [U_1405] :
      ( ( ! [U_1411,U_1409,U_1407] :
            ( hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1411),U_1409)),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1407),U_1409)))
            | ~ hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),U_1411),U_1407)) )
        & ! [U_1410,U_1408,U_1406] :
            ( hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),U_1410),U_1406))
            | ~ hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1410),U_1408)),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1406),U_1408))) ) )
      | ~ ordere236663937imp_le(U_1405) ),
    inference(miniscope,[status(thm)],[f_363_2]) ).

fof(f_363_4,plain,
    ( ! [U_1406,U_1405,U_1408,U_1407,U_1410,U_1411,U_1409] :
        ( hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1411),U_1409)),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1407),U_1409)))
        | ~ hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),U_1411),U_1407))
        | ~ sP64(U_1406,U_1405,U_1408,U_1407,U_1410,U_1411,U_1409) )
    & ! [U_1406,U_1405,U_1408,U_1407,U_1410,U_1411,U_1409] :
        ( hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),U_1410),U_1406))
        | ~ hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1410),U_1408)),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1406),U_1408)))
        | ~ sP64(U_1406,U_1405,U_1408,U_1407,U_1410,U_1411,U_1409) )
    & ! [U_1406,U_1405,U_1408,U_1407,U_1410,U_1411,U_1409] :
        ( sP64(U_1406,U_1405,U_1408,U_1407,U_1410,U_1411,U_1409)
        | ~ ordere236663937imp_le(U_1405) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64])],[f_363_3]) ).

cnf(f_363_5,plain,
    ( sP64(U_1406,U_1405,U_1408,U_1407,U_1410,U_1411,U_1409)
    | ~ ordere236663937imp_le(U_1405) ),
    inference(clausify,[status(thm)],[f_363_4]) ).

cnf(f_363_6,plain,
    ( hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),U_1410),U_1406))
    | ~ hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1410),U_1408)),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1406),U_1408)))
    | ~ sP64(U_1406,U_1405,U_1408,U_1407,U_1410,U_1411,U_1409) ),
    inference(clausify,[status(thm)],[f_363_4]) ).

cnf(f_363_7,plain,
    ( hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1411),U_1409)),hAPP(U_1405,U_1405,hAPP(U_1405,fun(U_1405,U_1405),plus_plus(U_1405),U_1407),U_1409)))
    | ~ hBOOL(hAPP(U_1405,bool,hAPP(U_1405,fun(U_1405,bool),ord_less(U_1405),U_1411),U_1407))
    | ~ sP64(U_1406,U_1405,U_1408,U_1407,U_1410,U_1411,U_1409) ),
    inference(clausify,[status(thm)],[f_363_4]) ).

fof(f_364_1,plain,
    ! [X_b] :
      ( ! [A_2,B,C_1,D_1] :
          ( ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B))
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D_1)) )
            & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),D_1))
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B)) ) )
          | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),C_1),D_1) )
      | ~ ordered_ab_group_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_311_diff__eq__diff__less]) ).

fof(f_364_2,plain,
    ! [U_1416] :
      ( ! [U_1415,U_1414,U_1413,U_1412] :
          ( ( ( hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1415),U_1414))
              | ~ hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1413),U_1412)) )
            & ( hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1413),U_1412))
              | ~ hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1415),U_1414)) ) )
          | hAPP(U_1416,U_1416,hAPP(U_1416,fun(U_1416,U_1416),minus_minus(U_1416),U_1415),U_1414) != hAPP(U_1416,U_1416,hAPP(U_1416,fun(U_1416,U_1416),minus_minus(U_1416),U_1413),U_1412) )
      | ~ ordered_ab_group_add(U_1416) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

fof(f_364_3,plain,
    ( ! [U_1413,U_1415,U_1412,U_1416,U_1414] :
        ( hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1415),U_1414))
        | ~ hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1413),U_1412))
        | ~ sP65(U_1413,U_1415,U_1412,U_1416,U_1414) )
    & ! [U_1413,U_1415,U_1412,U_1416,U_1414] :
        ( hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1413),U_1412))
        | ~ hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1415),U_1414))
        | ~ sP65(U_1413,U_1415,U_1412,U_1416,U_1414) )
    & ! [U_1413,U_1415,U_1412,U_1416,U_1414] :
        ( sP65(U_1413,U_1415,U_1412,U_1416,U_1414)
        | hAPP(U_1416,U_1416,hAPP(U_1416,fun(U_1416,U_1416),minus_minus(U_1416),U_1415),U_1414) != hAPP(U_1416,U_1416,hAPP(U_1416,fun(U_1416,U_1416),minus_minus(U_1416),U_1413),U_1412)
        | ~ ordered_ab_group_add(U_1416) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_364_2]) ).

cnf(f_364_4,plain,
    ( sP65(U_1413,U_1415,U_1412,U_1416,U_1414)
    | hAPP(U_1416,U_1416,hAPP(U_1416,fun(U_1416,U_1416),minus_minus(U_1416),U_1415),U_1414) != hAPP(U_1416,U_1416,hAPP(U_1416,fun(U_1416,U_1416),minus_minus(U_1416),U_1413),U_1412)
    | ~ ordered_ab_group_add(U_1416) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

cnf(f_364_5,plain,
    ( hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1413),U_1412))
    | ~ hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1415),U_1414))
    | ~ sP65(U_1413,U_1415,U_1412,U_1416,U_1414) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

cnf(f_364_6,plain,
    ( hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1415),U_1414))
    | ~ hBOOL(hAPP(U_1416,bool,hAPP(U_1416,fun(U_1416,bool),ord_less(U_1416),U_1413),U_1412))
    | ~ sP65(U_1413,U_1415,U_1412,U_1416,U_1414) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

fof(f_365_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_312_Suc__less__SucD]) ).

fof(f_365_2,plain,
    ! [U_1418,U_1417] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1418),U_1417))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1418)),hAPP(nat,nat,suc,U_1417))) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

fof(f_365_3,plain,
    ! [U_1418,U_1417] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1418),U_1417))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1418)),hAPP(nat,nat,suc,U_1417))) ),
    inference(definitional_conversion,[status(esa)],[f_365_2]) ).

cnf(f_365_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1418),U_1417))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1418)),hAPP(nat,nat,suc,U_1417))) ),
    inference(clausify,[status(thm)],[f_365_3]) ).

fof(f_366_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_313_Suc__lessD]) ).

fof(f_366_2,plain,
    ! [U_1420,U_1419] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1420),U_1419))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1420)),U_1419)) ),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

fof(f_366_3,plain,
    ! [U_1419,U_1420] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1420),U_1419))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1420)),U_1419)) ),
    inference(definitional_conversion,[status(esa)],[f_366_2]) ).

cnf(f_366_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1420),U_1419))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1420)),U_1419)) ),
    inference(clausify,[status(thm)],[f_366_3]) ).

fof(f_367_1,plain,
    ! [M,N] :
      ( M = N
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_314_less__SucE]) ).

fof(f_367_2,plain,
    ! [U_1422,U_1421] :
      ( U_1422 = U_1421
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1422),U_1421))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1422),hAPP(nat,nat,suc,U_1421))) ),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

fof(f_367_3,plain,
    ! [U_1422,U_1421] :
      ( U_1422 = U_1421
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1422),U_1421))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1422),hAPP(nat,nat,suc,U_1421))) ),
    inference(definitional_conversion,[status(esa)],[f_367_2]) ).

cnf(f_367_4,plain,
    ( U_1422 = U_1421
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1422),U_1421))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1422),hAPP(nat,nat,suc,U_1421))) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

fof(f_368_1,plain,
    ! [K,I,J_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J_2)) ),
    inference(fof_nnf,[status(thm)],[fact_315_less__trans__Suc]) ).

fof(f_368_2,plain,
    ! [U_1425,U_1424,U_1423] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1424)),U_1425))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1423),U_1425))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1424),U_1423)) ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

fof(f_368_3,plain,
    ! [U_1424,U_1423,U_1425] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1424)),U_1425))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1423),U_1425))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1424),U_1423)) ),
    inference(definitional_conversion,[status(esa)],[f_368_2]) ).

cnf(f_368_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1424)),U_1425))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1423),U_1425))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1424),U_1423)) ),
    inference(clausify,[status(thm)],[f_368_3]) ).

fof(f_369_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N))
      | hAPP(nat,nat,suc,M) = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_316_Suc__lessI]) ).

fof(f_369_2,plain,
    ! [U_1427,U_1426] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1427)),U_1426))
      | hAPP(nat,nat,suc,U_1427) = U_1426
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1427),U_1426)) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

fof(f_369_3,plain,
    ! [U_1427,U_1426] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1427)),U_1426))
      | hAPP(nat,nat,suc,U_1427) = U_1426
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1427),U_1426)) ),
    inference(definitional_conversion,[status(esa)],[f_369_2]) ).

cnf(f_369_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1427)),U_1426))
    | hAPP(nat,nat,suc,U_1427) = U_1426
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1427),U_1426)) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

fof(f_370_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_317_less__SucI]) ).

fof(f_370_2,plain,
    ! [U_1429,U_1428] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1429),hAPP(nat,nat,suc,U_1428)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1429),U_1428)) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

fof(f_370_3,plain,
    ! [U_1429,U_1428] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1429),hAPP(nat,nat,suc,U_1428)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1429),U_1428)) ),
    inference(definitional_conversion,[status(esa)],[f_370_2]) ).

cnf(f_370_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1429),hAPP(nat,nat,suc,U_1428)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1429),U_1428)) ),
    inference(clausify,[status(thm)],[f_370_3]) ).

fof(f_371_1,plain,
    ! [N,M] :
      ( M = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) ),
    inference(fof_nnf,[status(thm)],[fact_318_less__antisym]) ).

fof(f_371_2,plain,
    ! [U_1431,U_1430] :
      ( U_1430 = U_1431
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1431),hAPP(nat,nat,suc,U_1430)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1431),U_1430)) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

fof(f_371_3,plain,
    ! [U_1430,U_1431] :
      ( U_1430 = U_1431
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1431),hAPP(nat,nat,suc,U_1430)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1431),U_1430)) ),
    inference(definitional_conversion,[status(esa)],[f_371_2]) ).

cnf(f_371_4,plain,
    ( U_1430 = U_1431
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1431),hAPP(nat,nat,suc,U_1430)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1431),U_1430)) ),
    inference(clausify,[status(thm)],[f_371_3]) ).

fof(f_372_1,plain,
    ! [Na,M_1] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_1)))
          | Na != M_1 )
        & ( Na = M_1
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_1))) ) )
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_319_not__less__less__Suc__eq]) ).

fof(f_372_2,plain,
    ! [U_1433,U_1432] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1433),hAPP(nat,nat,suc,U_1432)))
          | U_1433 != U_1432 )
        & ( U_1433 = U_1432
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1433),hAPP(nat,nat,suc,U_1432))) ) )
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1433),U_1432)) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

fof(f_372_3,plain,
    ( ! [U_1432,U_1433] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1433),hAPP(nat,nat,suc,U_1432)))
        | U_1433 != U_1432
        | ~ sP66(U_1432,U_1433) )
    & ! [U_1432,U_1433] :
        ( U_1433 = U_1432
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1433),hAPP(nat,nat,suc,U_1432)))
        | ~ sP66(U_1432,U_1433) )
    & ! [U_1432,U_1433] :
        ( sP66(U_1432,U_1433)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1433),U_1432)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66])],[f_372_2]) ).

cnf(f_372_4,plain,
    ( sP66(U_1432,U_1433)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1433),U_1432)) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

cnf(f_372_5,plain,
    ( U_1433 = U_1432
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1433),hAPP(nat,nat,suc,U_1432)))
    | ~ sP66(U_1432,U_1433) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

cnf(f_372_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1433),hAPP(nat,nat,suc,U_1432)))
    | U_1433 != U_1432
    | ~ sP66(U_1432,U_1433) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

fof(f_373_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_320_Suc__less__eq]) ).

fof(f_373_2,plain,
    ! [U_1435,U_1434] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1435)),hAPP(nat,nat,suc,U_1434)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1435),U_1434)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1435),U_1434))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1435)),hAPP(nat,nat,suc,U_1434))) ) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

fof(f_373_3,plain,
    ( ! [U_1439,U_1437] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1439)),hAPP(nat,nat,suc,U_1437)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1439),U_1437)) )
    & ! [U_1438,U_1436] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1438),U_1436))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1438)),hAPP(nat,nat,suc,U_1436))) ) ),
    inference(miniscope,[status(thm)],[f_373_2]) ).

fof(f_373_4,plain,
    ( ! [U_1437,U_1439] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1439)),hAPP(nat,nat,suc,U_1437)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1439),U_1437)) )
    & ! [U_1436,U_1438] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1438),U_1436))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1438)),hAPP(nat,nat,suc,U_1436))) ) ),
    inference(definitional_conversion,[status(esa)],[f_373_3]) ).

cnf(f_373_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1438),U_1436))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1438)),hAPP(nat,nat,suc,U_1436))) ),
    inference(clausify,[status(thm)],[f_373_4]) ).

cnf(f_373_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1439)),hAPP(nat,nat,suc,U_1437)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1439),U_1437)) ),
    inference(clausify,[status(thm)],[f_373_4]) ).

fof(f_374_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,Na)))
        | ( M_1 != Na
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) )
      & ( M_1 = Na
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_321_less__Suc__eq]) ).

fof(f_374_2,plain,
    ! [U_1441,U_1440] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1441),hAPP(nat,nat,suc,U_1440)))
        | ( U_1441 != U_1440
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1441),U_1440)) ) )
      & ( U_1441 = U_1440
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1441),U_1440))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1441),hAPP(nat,nat,suc,U_1440))) ) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

fof(f_374_3,plain,
    ( ! [U_1445,U_1443] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1445),hAPP(nat,nat,suc,U_1443)))
        | ( U_1445 != U_1443
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1445),U_1443)) ) )
    & ! [U_1444,U_1442] :
        ( U_1444 = U_1442
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1444),U_1442))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1444),hAPP(nat,nat,suc,U_1442))) ) ),
    inference(miniscope,[status(thm)],[f_374_2]) ).

fof(f_374_4,plain,
    ( ! [U_1445,U_1443] :
        ( U_1445 != U_1443
        | ~ sP67(U_1445,U_1443) )
    & ! [U_1445,U_1443] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1445),U_1443))
        | ~ sP67(U_1445,U_1443) )
    & ! [U_1445,U_1443] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1445),hAPP(nat,nat,suc,U_1443)))
        | sP67(U_1445,U_1443) )
    & ! [U_1442,U_1444] :
        ( U_1444 = U_1442
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1444),U_1442))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1444),hAPP(nat,nat,suc,U_1442))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67])],[f_374_3]) ).

cnf(f_374_5,plain,
    ( U_1444 = U_1442
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1444),U_1442))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1444),hAPP(nat,nat,suc,U_1442))) ),
    inference(clausify,[status(thm)],[f_374_4]) ).

cnf(f_374_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1445),hAPP(nat,nat,suc,U_1443)))
    | sP67(U_1445,U_1443) ),
    inference(clausify,[status(thm)],[f_374_4]) ).

cnf(f_374_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1445),U_1443))
    | ~ sP67(U_1445,U_1443) ),
    inference(clausify,[status(thm)],[f_374_4]) ).

cnf(f_374_8,plain,
    ( U_1445 != U_1443
    | ~ sP67(U_1445,U_1443) ),
    inference(clausify,[status(thm)],[f_374_4]) ).

fof(f_375_1,plain,
    ! [M_1,Na] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_1))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_1)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_322_not__less__eq]) ).

fof(f_375_2,plain,
    ! [U_1447,U_1446] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1447),U_1446))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1446),hAPP(nat,nat,suc,U_1447))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1446),hAPP(nat,nat,suc,U_1447)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1447),U_1446)) ) ),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

fof(f_375_3,plain,
    ( ! [U_1451,U_1449] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1451),U_1449))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1449),hAPP(nat,nat,suc,U_1451))) )
    & ! [U_1450,U_1448] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1448),hAPP(nat,nat,suc,U_1450)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1450),U_1448)) ) ),
    inference(miniscope,[status(thm)],[f_375_2]) ).

fof(f_375_4,plain,
    ( ! [U_1449,U_1451] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1451),U_1449))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1449),hAPP(nat,nat,suc,U_1451))) )
    & ! [U_1448,U_1450] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1448),hAPP(nat,nat,suc,U_1450)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1450),U_1448)) ) ),
    inference(definitional_conversion,[status(esa)],[f_375_3]) ).

cnf(f_375_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1448),hAPP(nat,nat,suc,U_1450)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1450),U_1448)) ),
    inference(clausify,[status(thm)],[f_375_4]) ).

cnf(f_375_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1451),U_1449))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1449),hAPP(nat,nat,suc,U_1451))) ),
    inference(clausify,[status(thm)],[f_375_4]) ).

fof(f_376_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
      | ( M != N
        & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ) ),
    inference(fof_nnf,[status(thm)],[fact_323_less__or__eq__imp__le]) ).

fof(f_376_2,plain,
    ! [U_1453,U_1452] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1453),U_1452))
      | ( U_1453 != U_1452
        & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1453),U_1452)) ) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

fof(f_376_3,plain,
    ( ! [U_1453,U_1452] :
        ( U_1453 != U_1452
        | ~ sP68(U_1453,U_1452) )
    & ! [U_1453,U_1452] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1453),U_1452))
        | ~ sP68(U_1453,U_1452) )
    & ! [U_1453,U_1452] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1453),U_1452))
        | sP68(U_1453,U_1452) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68])],[f_376_2]) ).

cnf(f_376_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1453),U_1452))
    | sP68(U_1453,U_1452) ),
    inference(clausify,[status(thm)],[f_376_3]) ).

cnf(f_376_5,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1453),U_1452))
    | ~ sP68(U_1453,U_1452) ),
    inference(clausify,[status(thm)],[f_376_3]) ).

cnf(f_376_6,plain,
    ( U_1453 != U_1452
    | ~ sP68(U_1453,U_1452) ),
    inference(clausify,[status(thm)],[f_376_3]) ).

fof(f_377_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
      | M = N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_324_le__neq__implies__less]) ).

fof(f_377_2,plain,
    ! [U_1455,U_1454] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1455),U_1454))
      | U_1455 = U_1454
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1455),U_1454)) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

fof(f_377_3,plain,
    ! [U_1454,U_1455] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1455),U_1454))
      | U_1455 = U_1454
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1455),U_1454)) ),
    inference(definitional_conversion,[status(esa)],[f_377_2]) ).

cnf(f_377_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1455),U_1454))
    | U_1455 = U_1454
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1455),U_1454)) ),
    inference(clausify,[status(thm)],[f_377_3]) ).

fof(f_378_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_325_less__imp__le__nat]) ).

fof(f_378_2,plain,
    ! [U_1457,U_1456] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1457),U_1456))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1457),U_1456)) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

fof(f_378_3,plain,
    ! [U_1457,U_1456] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1457),U_1456))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1457),U_1456)) ),
    inference(definitional_conversion,[status(esa)],[f_378_2]) ).

cnf(f_378_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1457),U_1456))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1457),U_1456)) ),
    inference(clausify,[status(thm)],[f_378_3]) ).

fof(f_379_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
        | ( M_1 != Na
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) )
      & ( M_1 = Na
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_326_le__eq__less__or__eq]) ).

fof(f_379_2,plain,
    ! [U_1459,U_1458] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1459),U_1458))
        | ( U_1459 != U_1458
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1459),U_1458)) ) )
      & ( U_1459 = U_1458
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1459),U_1458))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1459),U_1458)) ) ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

fof(f_379_3,plain,
    ( ! [U_1463,U_1461] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1463),U_1461))
        | ( U_1463 != U_1461
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1463),U_1461)) ) )
    & ! [U_1462,U_1460] :
        ( U_1462 = U_1460
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1462),U_1460))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1462),U_1460)) ) ),
    inference(miniscope,[status(thm)],[f_379_2]) ).

fof(f_379_4,plain,
    ( ! [U_1463,U_1461] :
        ( U_1463 != U_1461
        | ~ sP69(U_1463,U_1461) )
    & ! [U_1463,U_1461] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1463),U_1461))
        | ~ sP69(U_1463,U_1461) )
    & ! [U_1463,U_1461] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1463),U_1461))
        | sP69(U_1463,U_1461) )
    & ! [U_1460,U_1462] :
        ( U_1462 = U_1460
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1462),U_1460))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1462),U_1460)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69])],[f_379_3]) ).

cnf(f_379_5,plain,
    ( U_1462 = U_1460
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1462),U_1460))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1462),U_1460)) ),
    inference(clausify,[status(thm)],[f_379_4]) ).

cnf(f_379_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1463),U_1461))
    | sP69(U_1463,U_1461) ),
    inference(clausify,[status(thm)],[f_379_4]) ).

cnf(f_379_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1463),U_1461))
    | ~ sP69(U_1463,U_1461) ),
    inference(clausify,[status(thm)],[f_379_4]) ).

cnf(f_379_8,plain,
    ( U_1463 != U_1461
    | ~ sP69(U_1463,U_1461) ),
    inference(clausify,[status(thm)],[f_379_4]) ).

fof(f_380_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
        | M_1 = Na
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) )
      & ( ( M_1 != Na
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_327_nat__less__le]) ).

fof(f_380_2,plain,
    ! [U_1465,U_1464] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1465),U_1464))
        | U_1465 = U_1464
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1465),U_1464)) )
      & ( ( U_1465 != U_1464
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1465),U_1464)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1465),U_1464)) ) ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

fof(f_380_3,plain,
    ( ! [U_1469,U_1467] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1469),U_1467))
        | U_1469 = U_1467
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1469),U_1467)) )
    & ! [U_1468,U_1466] :
        ( ( U_1468 != U_1466
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1468),U_1466)) )
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1468),U_1466)) ) ),
    inference(miniscope,[status(thm)],[f_380_2]) ).

fof(f_380_4,plain,
    ( ! [U_1466,U_1468] :
        ( U_1468 != U_1466
        | ~ sP70(U_1466,U_1468) )
    & ! [U_1466,U_1468] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1468),U_1466))
        | ~ sP70(U_1466,U_1468) )
    & ! [U_1467,U_1469] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1469),U_1467))
        | U_1469 = U_1467
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1469),U_1467)) )
    & ! [U_1466,U_1468] :
        ( sP70(U_1466,U_1468)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1468),U_1466)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP70])],[f_380_3]) ).

cnf(f_380_5,plain,
    ( sP70(U_1466,U_1468)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1468),U_1466)) ),
    inference(clausify,[status(thm)],[f_380_4]) ).

cnf(f_380_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1469),U_1467))
    | U_1469 = U_1467
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1469),U_1467)) ),
    inference(clausify,[status(thm)],[f_380_4]) ).

cnf(f_380_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1468),U_1466))
    | ~ sP70(U_1466,U_1468) ),
    inference(clausify,[status(thm)],[f_380_4]) ).

cnf(f_380_8,plain,
    ( U_1468 != U_1466
    | ~ sP70(U_1466,U_1468) ),
    inference(clausify,[status(thm)],[f_380_4]) ).

fof(f_381_1,plain,
    ! [L,M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_328_diff__less__mono2]) ).

fof(f_381_2,plain,
    ! [U_1472,U_1471,U_1470] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1472),U_1470)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1472),U_1471)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1471),U_1472))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1471),U_1470)) ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

fof(f_381_3,plain,
    ! [U_1472,U_1471,U_1470] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1472),U_1470)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1472),U_1471)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1471),U_1472))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1471),U_1470)) ),
    inference(definitional_conversion,[status(esa)],[f_381_2]) ).

cnf(f_381_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1472),U_1470)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1472),U_1471)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1471),U_1472))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1471),U_1470)) ),
    inference(clausify,[status(thm)],[f_381_3]) ).

fof(f_382_1,plain,
    ! [N,J_2,K] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),N)),K))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K)) ),
    inference(fof_nnf,[status(thm)],[fact_329_less__imp__diff__less]) ).

fof(f_382_2,plain,
    ! [U_1475,U_1474,U_1473] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1474),U_1475)),U_1473))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1474),U_1473)) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

fof(f_382_3,plain,
    ! [U_1474,U_1473,U_1475] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1474),U_1475)),U_1473))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1474),U_1473)) ),
    inference(definitional_conversion,[status(esa)],[f_382_2]) ).

cnf(f_382_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1474),U_1475)),U_1473))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1474),U_1473)) ),
    inference(clausify,[status(thm)],[f_382_3]) ).

fof(f_383_1,plain,
    ! [X_a] :
      ( ! [X] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X))
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_330_order__less__irrefl]) ).

fof(f_383_2,plain,
    ! [U_1477] :
      ( ! [U_1476] : ~ hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less(U_1477),U_1476),U_1476))
      | ~ preorder(U_1477) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

fof(f_383_3,plain,
    ! [U_1477,U_1476] :
      ( ~ hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less(U_1477),U_1476),U_1476))
      | ~ preorder(U_1477) ),
    inference(definitional_conversion,[status(esa)],[f_383_2]) ).

cnf(f_383_4,plain,
    ( ~ hBOOL(hAPP(U_1477,bool,hAPP(U_1477,fun(U_1477,bool),ord_less(U_1477),U_1476),U_1476))
    | ~ preorder(U_1477) ),
    inference(clausify,[status(thm)],[f_383_3]) ).

fof(f_384_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_1] :
          ( ( ti(X_b,X_1) != ti(X_b,Y_1)
            | ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1))
              & ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) ) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
            | ti(X_b,X_1) = ti(X_b,Y_1) ) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_331_linorder__neq__iff]) ).

fof(f_384_2,plain,
    ! [U_1480] :
      ( ! [U_1479,U_1478] :
          ( ( ti(U_1480,U_1479) != ti(U_1480,U_1478)
            | ( ~ hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1478),U_1479))
              & ~ hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1479),U_1478)) ) )
          & ( hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1478),U_1479))
            | hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1479),U_1478))
            | ti(U_1480,U_1479) = ti(U_1480,U_1478) ) )
      | ~ linorder(U_1480) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ! [U_1480] :
      ( ( ! [U_1484,U_1482] :
            ( ti(U_1480,U_1484) != ti(U_1480,U_1482)
            | ( ~ hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1482),U_1484))
              & ~ hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1484),U_1482)) ) )
        & ! [U_1483,U_1481] :
            ( hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1481),U_1483))
            | hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1483),U_1481))
            | ti(U_1480,U_1483) = ti(U_1480,U_1481) ) )
      | ~ linorder(U_1480) ),
    inference(miniscope,[status(thm)],[f_384_2]) ).

fof(f_384_4,plain,
    ( ! [U_1480,U_1482,U_1484] :
        ( ~ hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1482),U_1484))
        | ~ sP71(U_1480,U_1482,U_1484) )
    & ! [U_1480,U_1482,U_1484] :
        ( ~ hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1484),U_1482))
        | ~ sP71(U_1480,U_1482,U_1484) )
    & ! [U_1483,U_1480,U_1481,U_1482,U_1484] :
        ( ti(U_1480,U_1484) != ti(U_1480,U_1482)
        | sP71(U_1480,U_1482,U_1484)
        | ~ sP72(U_1483,U_1480,U_1481,U_1482,U_1484) )
    & ! [U_1483,U_1480,U_1481,U_1482,U_1484] :
        ( hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1481),U_1483))
        | hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1483),U_1481))
        | ti(U_1480,U_1483) = ti(U_1480,U_1481)
        | ~ sP72(U_1483,U_1480,U_1481,U_1482,U_1484) )
    & ! [U_1483,U_1480,U_1481,U_1482,U_1484] :
        ( sP72(U_1483,U_1480,U_1481,U_1482,U_1484)
        | ~ linorder(U_1480) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71,sP72])],[f_384_3]) ).

cnf(f_384_5,plain,
    ( sP72(U_1483,U_1480,U_1481,U_1482,U_1484)
    | ~ linorder(U_1480) ),
    inference(clausify,[status(thm)],[f_384_4]) ).

cnf(f_384_6,plain,
    ( hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1481),U_1483))
    | hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1483),U_1481))
    | ti(U_1480,U_1483) = ti(U_1480,U_1481)
    | ~ sP72(U_1483,U_1480,U_1481,U_1482,U_1484) ),
    inference(clausify,[status(thm)],[f_384_4]) ).

cnf(f_384_7,plain,
    ( ti(U_1480,U_1484) != ti(U_1480,U_1482)
    | sP71(U_1480,U_1482,U_1484)
    | ~ sP72(U_1483,U_1480,U_1481,U_1482,U_1484) ),
    inference(clausify,[status(thm)],[f_384_4]) ).

cnf(f_384_8,plain,
    ( ~ hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1484),U_1482))
    | ~ sP71(U_1480,U_1482,U_1484) ),
    inference(clausify,[status(thm)],[f_384_4]) ).

cnf(f_384_9,plain,
    ( ~ hBOOL(hAPP(U_1480,bool,hAPP(U_1480,fun(U_1480,bool),ord_less(U_1480),U_1482),U_1484))
    | ~ sP71(U_1480,U_1482,U_1484) ),
    inference(clausify,[status(thm)],[f_384_4]) ).

fof(f_385_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_1] :
          ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
            | ( ti(X_b,X_1) != ti(X_b,Y_1)
              & ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) ) )
          & ( ti(X_b,X_1) = ti(X_b,Y_1)
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) ) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_332_not__less__iff__gr__or__eq]) ).

fof(f_385_2,plain,
    ! [U_1487] :
      ( ! [U_1486,U_1485] :
          ( ( ~ hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1486),U_1485))
            | ( ti(U_1487,U_1486) != ti(U_1487,U_1485)
              & ~ hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1485),U_1486)) ) )
          & ( ti(U_1487,U_1486) = ti(U_1487,U_1485)
            | hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1485),U_1486))
            | hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1486),U_1485)) ) )
      | ~ linorder(U_1487) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

fof(f_385_3,plain,
    ! [U_1487] :
      ( ( ! [U_1491,U_1489] :
            ( ~ hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1491),U_1489))
            | ( ti(U_1487,U_1491) != ti(U_1487,U_1489)
              & ~ hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1489),U_1491)) ) )
        & ! [U_1490,U_1488] :
            ( ti(U_1487,U_1490) = ti(U_1487,U_1488)
            | hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1488),U_1490))
            | hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1490),U_1488)) ) )
      | ~ linorder(U_1487) ),
    inference(miniscope,[status(thm)],[f_385_2]) ).

fof(f_385_4,plain,
    ( ! [U_1487,U_1491,U_1489] :
        ( ti(U_1487,U_1491) != ti(U_1487,U_1489)
        | ~ sP73(U_1487,U_1491,U_1489) )
    & ! [U_1487,U_1491,U_1489] :
        ( ~ hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1489),U_1491))
        | ~ sP73(U_1487,U_1491,U_1489) )
    & ! [U_1490,U_1488,U_1487,U_1491,U_1489] :
        ( ~ hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1491),U_1489))
        | sP73(U_1487,U_1491,U_1489)
        | ~ sP74(U_1490,U_1488,U_1487,U_1491,U_1489) )
    & ! [U_1490,U_1488,U_1487,U_1491,U_1489] :
        ( ti(U_1487,U_1490) = ti(U_1487,U_1488)
        | hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1488),U_1490))
        | hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1490),U_1488))
        | ~ sP74(U_1490,U_1488,U_1487,U_1491,U_1489) )
    & ! [U_1490,U_1488,U_1487,U_1491,U_1489] :
        ( sP74(U_1490,U_1488,U_1487,U_1491,U_1489)
        | ~ linorder(U_1487) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73,sP74])],[f_385_3]) ).

cnf(f_385_5,plain,
    ( sP74(U_1490,U_1488,U_1487,U_1491,U_1489)
    | ~ linorder(U_1487) ),
    inference(clausify,[status(thm)],[f_385_4]) ).

cnf(f_385_6,plain,
    ( ti(U_1487,U_1490) = ti(U_1487,U_1488)
    | hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1488),U_1490))
    | hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1490),U_1488))
    | ~ sP74(U_1490,U_1488,U_1487,U_1491,U_1489) ),
    inference(clausify,[status(thm)],[f_385_4]) ).

cnf(f_385_7,plain,
    ( ~ hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1491),U_1489))
    | sP73(U_1487,U_1491,U_1489)
    | ~ sP74(U_1490,U_1488,U_1487,U_1491,U_1489) ),
    inference(clausify,[status(thm)],[f_385_4]) ).

cnf(f_385_8,plain,
    ( ~ hBOOL(hAPP(U_1487,bool,hAPP(U_1487,fun(U_1487,bool),ord_less(U_1487),U_1489),U_1491))
    | ~ sP73(U_1487,U_1491,U_1489) ),
    inference(clausify,[status(thm)],[f_385_4]) ).

cnf(f_385_9,plain,
    ( ti(U_1487,U_1491) != ti(U_1487,U_1489)
    | ~ sP73(U_1487,U_1491,U_1489) ),
    inference(clausify,[status(thm)],[f_385_4]) ).

fof(f_386_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | ti(X_a,X) = ti(X_a,Y)
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_333_linorder__less__linear]) ).

fof(f_386_2,plain,
    ! [U_1494] :
      ( ! [U_1493,U_1492] :
          ( hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1492),U_1493))
          | ti(U_1494,U_1493) = ti(U_1494,U_1492)
          | hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1493),U_1492)) )
      | ~ linorder(U_1494) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

fof(f_386_3,plain,
    ! [U_1494,U_1493,U_1492] :
      ( hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1492),U_1493))
      | ti(U_1494,U_1493) = ti(U_1494,U_1492)
      | hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1493),U_1492))
      | ~ linorder(U_1494) ),
    inference(definitional_conversion,[status(esa)],[f_386_2]) ).

cnf(f_386_4,plain,
    ( hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1492),U_1493))
    | ti(U_1494,U_1493) = ti(U_1494,U_1492)
    | hBOOL(hAPP(U_1494,bool,hAPP(U_1494,fun(U_1494,bool),ord_less(U_1494),U_1493),U_1492))
    | ~ linorder(U_1494) ),
    inference(clausify,[status(thm)],[f_386_3]) ).

fof(f_387_1,plain,
    ! [X_b] :
      ( ! [Y_1,X_1] :
          ( ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
              | ti(X_b,X_1) != ti(X_b,Y_1) )
            & ( ti(X_b,X_1) = ti(X_b,Y_1)
              | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) ) )
          | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_334_linorder__antisym__conv3]) ).

fof(f_387_2,plain,
    ! [U_1497] :
      ( ! [U_1496,U_1495] :
          ( ( ( ~ hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1495),U_1496))
              | ti(U_1497,U_1495) != ti(U_1497,U_1496) )
            & ( ti(U_1497,U_1495) = ti(U_1497,U_1496)
              | hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1495),U_1496)) ) )
          | hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1496),U_1495)) )
      | ~ linorder(U_1497) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

fof(f_387_3,plain,
    ( ! [U_1497,U_1495,U_1496] :
        ( ~ hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1495),U_1496))
        | ti(U_1497,U_1495) != ti(U_1497,U_1496)
        | ~ sP75(U_1497,U_1495,U_1496) )
    & ! [U_1497,U_1495,U_1496] :
        ( ti(U_1497,U_1495) = ti(U_1497,U_1496)
        | hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1495),U_1496))
        | ~ sP75(U_1497,U_1495,U_1496) )
    & ! [U_1497,U_1495,U_1496] :
        ( sP75(U_1497,U_1495,U_1496)
        | hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1496),U_1495))
        | ~ linorder(U_1497) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75])],[f_387_2]) ).

cnf(f_387_4,plain,
    ( sP75(U_1497,U_1495,U_1496)
    | hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1496),U_1495))
    | ~ linorder(U_1497) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

cnf(f_387_5,plain,
    ( ti(U_1497,U_1495) = ti(U_1497,U_1496)
    | hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1495),U_1496))
    | ~ sP75(U_1497,U_1495,U_1496) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

cnf(f_387_6,plain,
    ( ~ hBOOL(hAPP(U_1497,bool,hAPP(U_1497,fun(U_1497,bool),ord_less(U_1497),U_1495),U_1496))
    | ti(U_1497,U_1495) != ti(U_1497,U_1496)
    | ~ sP75(U_1497,U_1495,U_1496) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

fof(f_388_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
          | ti(X_a,X) = ti(X_a,Y) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_335_linorder__neqE]) ).

fof(f_388_2,plain,
    ! [U_1500] :
      ( ! [U_1499,U_1498] :
          ( hBOOL(hAPP(U_1500,bool,hAPP(U_1500,fun(U_1500,bool),ord_less(U_1500),U_1498),U_1499))
          | hBOOL(hAPP(U_1500,bool,hAPP(U_1500,fun(U_1500,bool),ord_less(U_1500),U_1499),U_1498))
          | ti(U_1500,U_1499) = ti(U_1500,U_1498) )
      | ~ linorder(U_1500) ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

fof(f_388_3,plain,
    ! [U_1499,U_1500,U_1498] :
      ( hBOOL(hAPP(U_1500,bool,hAPP(U_1500,fun(U_1500,bool),ord_less(U_1500),U_1498),U_1499))
      | hBOOL(hAPP(U_1500,bool,hAPP(U_1500,fun(U_1500,bool),ord_less(U_1500),U_1499),U_1498))
      | ti(U_1500,U_1499) = ti(U_1500,U_1498)
      | ~ linorder(U_1500) ),
    inference(definitional_conversion,[status(esa)],[f_388_2]) ).

cnf(f_388_4,plain,
    ( hBOOL(hAPP(U_1500,bool,hAPP(U_1500,fun(U_1500,bool),ord_less(U_1500),U_1498),U_1499))
    | hBOOL(hAPP(U_1500,bool,hAPP(U_1500,fun(U_1500,bool),ord_less(U_1500),U_1499),U_1498))
    | ti(U_1500,U_1499) = ti(U_1500,U_1498)
    | ~ linorder(U_1500) ),
    inference(clausify,[status(thm)],[f_388_3]) ).

fof(f_389_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ti(X_a,X) != ti(X_a,Y)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_336_less__imp__neq]) ).

fof(f_389_2,plain,
    ! [U_1503] :
      ( ! [U_1502,U_1501] :
          ( ti(U_1503,U_1502) != ti(U_1503,U_1501)
          | ~ hBOOL(hAPP(U_1503,bool,hAPP(U_1503,fun(U_1503,bool),ord_less(U_1503),U_1502),U_1501)) )
      | ~ order(U_1503) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

fof(f_389_3,plain,
    ! [U_1502,U_1501,U_1503] :
      ( ti(U_1503,U_1502) != ti(U_1503,U_1501)
      | ~ hBOOL(hAPP(U_1503,bool,hAPP(U_1503,fun(U_1503,bool),ord_less(U_1503),U_1502),U_1501))
      | ~ order(U_1503) ),
    inference(definitional_conversion,[status(esa)],[f_389_2]) ).

cnf(f_389_4,plain,
    ( ti(U_1503,U_1502) != ti(U_1503,U_1501)
    | ~ hBOOL(hAPP(U_1503,bool,hAPP(U_1503,fun(U_1503,bool),ord_less(U_1503),U_1502),U_1501))
    | ~ order(U_1503) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

fof(f_390_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_337_order__less__not__sym]) ).

fof(f_390_2,plain,
    ! [U_1506] :
      ( ! [U_1505,U_1504] :
          ( ~ hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),U_1504),U_1505))
          | ~ hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),U_1505),U_1504)) )
      | ~ preorder(U_1506) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

fof(f_390_3,plain,
    ! [U_1505,U_1506,U_1504] :
      ( ~ hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),U_1504),U_1505))
      | ~ hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),U_1505),U_1504))
      | ~ preorder(U_1506) ),
    inference(definitional_conversion,[status(esa)],[f_390_2]) ).

cnf(f_390_4,plain,
    ( ~ hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),U_1504),U_1505))
    | ~ hBOOL(hAPP(U_1506,bool,hAPP(U_1506,fun(U_1506,bool),ord_less(U_1506),U_1505),U_1504))
    | ~ preorder(U_1506) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

fof(f_391_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_338_order__less__imp__not__less]) ).

fof(f_391_2,plain,
    ! [U_1509] :
      ( ! [U_1508,U_1507] :
          ( ~ hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less(U_1509),U_1507),U_1508))
          | ~ hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less(U_1509),U_1508),U_1507)) )
      | ~ preorder(U_1509) ),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

fof(f_391_3,plain,
    ! [U_1507,U_1509,U_1508] :
      ( ~ hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less(U_1509),U_1507),U_1508))
      | ~ hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less(U_1509),U_1508),U_1507))
      | ~ preorder(U_1509) ),
    inference(definitional_conversion,[status(esa)],[f_391_2]) ).

cnf(f_391_4,plain,
    ( ~ hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less(U_1509),U_1507),U_1508))
    | ~ hBOOL(hAPP(U_1509,bool,hAPP(U_1509,fun(U_1509,bool),ord_less(U_1509),U_1508),U_1507))
    | ~ preorder(U_1509) ),
    inference(clausify,[status(thm)],[f_391_3]) ).

fof(f_392_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ti(X_a,X) != ti(X_a,Y)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_339_order__less__imp__not__eq]) ).

fof(f_392_2,plain,
    ! [U_1512] :
      ( ! [U_1511,U_1510] :
          ( ti(U_1512,U_1511) != ti(U_1512,U_1510)
          | ~ hBOOL(hAPP(U_1512,bool,hAPP(U_1512,fun(U_1512,bool),ord_less(U_1512),U_1511),U_1510)) )
      | ~ order(U_1512) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ! [U_1511,U_1510,U_1512] :
      ( ti(U_1512,U_1511) != ti(U_1512,U_1510)
      | ~ hBOOL(hAPP(U_1512,bool,hAPP(U_1512,fun(U_1512,bool),ord_less(U_1512),U_1511),U_1510))
      | ~ order(U_1512) ),
    inference(definitional_conversion,[status(esa)],[f_392_2]) ).

cnf(f_392_4,plain,
    ( ti(U_1512,U_1511) != ti(U_1512,U_1510)
    | ~ hBOOL(hAPP(U_1512,bool,hAPP(U_1512,fun(U_1512,bool),ord_less(U_1512),U_1511),U_1510))
    | ~ order(U_1512) ),
    inference(clausify,[status(thm)],[f_392_3]) ).

fof(f_393_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ti(X_a,Y) != ti(X_a,X)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_340_order__less__imp__not__eq2]) ).

fof(f_393_2,plain,
    ! [U_1515] :
      ( ! [U_1514,U_1513] :
          ( ti(U_1515,U_1513) != ti(U_1515,U_1514)
          | ~ hBOOL(hAPP(U_1515,bool,hAPP(U_1515,fun(U_1515,bool),ord_less(U_1515),U_1514),U_1513)) )
      | ~ order(U_1515) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

fof(f_393_3,plain,
    ! [U_1513,U_1514,U_1515] :
      ( ti(U_1515,U_1513) != ti(U_1515,U_1514)
      | ~ hBOOL(hAPP(U_1515,bool,hAPP(U_1515,fun(U_1515,bool),ord_less(U_1515),U_1514),U_1513))
      | ~ order(U_1515) ),
    inference(definitional_conversion,[status(esa)],[f_393_2]) ).

cnf(f_393_4,plain,
    ( ti(U_1515,U_1513) != ti(U_1515,U_1514)
    | ~ hBOOL(hAPP(U_1515,bool,hAPP(U_1515,fun(U_1515,bool),ord_less(U_1515),U_1514),U_1513))
    | ~ order(U_1515) ),
    inference(clausify,[status(thm)],[f_393_3]) ).

fof(f_394_1,plain,
    ! [X_b] :
      ( ! [Pa,X_1,Y_1] :
          ( hBOOL(Pa)
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) )
      | ~ preorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_341_order__less__imp__triv]) ).

fof(f_394_2,plain,
    ! [U_1519] :
      ( ! [U_1518,U_1517,U_1516] :
          ( hBOOL(U_1518)
          | ~ hBOOL(hAPP(U_1519,bool,hAPP(U_1519,fun(U_1519,bool),ord_less(U_1519),U_1516),U_1517))
          | ~ hBOOL(hAPP(U_1519,bool,hAPP(U_1519,fun(U_1519,bool),ord_less(U_1519),U_1517),U_1516)) )
      | ~ preorder(U_1519) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

fof(f_394_3,plain,
    ! [U_1517,U_1518,U_1516,U_1519] :
      ( hBOOL(U_1518)
      | ~ hBOOL(hAPP(U_1519,bool,hAPP(U_1519,fun(U_1519,bool),ord_less(U_1519),U_1516),U_1517))
      | ~ hBOOL(hAPP(U_1519,bool,hAPP(U_1519,fun(U_1519,bool),ord_less(U_1519),U_1517),U_1516))
      | ~ preorder(U_1519) ),
    inference(definitional_conversion,[status(esa)],[f_394_2]) ).

cnf(f_394_4,plain,
    ( hBOOL(U_1518)
    | ~ hBOOL(hAPP(U_1519,bool,hAPP(U_1519,fun(U_1519,bool),ord_less(U_1519),U_1516),U_1517))
    | ~ hBOOL(hAPP(U_1519,bool,hAPP(U_1519,fun(U_1519,bool),ord_less(U_1519),U_1517),U_1516))
    | ~ preorder(U_1519) ),
    inference(clausify,[status(thm)],[f_394_3]) ).

fof(f_395_1,plain,
    ! [X_a] :
      ( ! [A_1,B_1] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_342_order__less__asym_H]) ).

fof(f_395_2,plain,
    ! [U_1522] :
      ( ! [U_1521,U_1520] :
          ( ~ hBOOL(hAPP(U_1522,bool,hAPP(U_1522,fun(U_1522,bool),ord_less(U_1522),U_1520),U_1521))
          | ~ hBOOL(hAPP(U_1522,bool,hAPP(U_1522,fun(U_1522,bool),ord_less(U_1522),U_1521),U_1520)) )
      | ~ preorder(U_1522) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

fof(f_395_3,plain,
    ! [U_1521,U_1522,U_1520] :
      ( ~ hBOOL(hAPP(U_1522,bool,hAPP(U_1522,fun(U_1522,bool),ord_less(U_1522),U_1520),U_1521))
      | ~ hBOOL(hAPP(U_1522,bool,hAPP(U_1522,fun(U_1522,bool),ord_less(U_1522),U_1521),U_1520))
      | ~ preorder(U_1522) ),
    inference(definitional_conversion,[status(esa)],[f_395_2]) ).

cnf(f_395_4,plain,
    ( ~ hBOOL(hAPP(U_1522,bool,hAPP(U_1522,fun(U_1522,bool),ord_less(U_1522),U_1520),U_1521))
    | ~ hBOOL(hAPP(U_1522,bool,hAPP(U_1522,fun(U_1522,bool),ord_less(U_1522),U_1521),U_1520))
    | ~ preorder(U_1522) ),
    inference(clausify,[status(thm)],[f_395_3]) ).

fof(f_396_1,plain,
    ! [X_a] :
      ( ! [B_1,A_1] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_343_xt1_I9_J]) ).

fof(f_396_2,plain,
    ! [U_1525] :
      ( ! [U_1524,U_1523] :
          ( ~ hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less(U_1525),U_1523),U_1524))
          | ~ hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less(U_1525),U_1524),U_1523)) )
      | ~ order(U_1525) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

fof(f_396_3,plain,
    ! [U_1524,U_1523,U_1525] :
      ( ~ hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less(U_1525),U_1523),U_1524))
      | ~ hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less(U_1525),U_1524),U_1523))
      | ~ order(U_1525) ),
    inference(definitional_conversion,[status(esa)],[f_396_2]) ).

cnf(f_396_4,plain,
    ( ~ hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less(U_1525),U_1523),U_1524))
    | ~ hBOOL(hAPP(U_1525,bool,hAPP(U_1525,fun(U_1525,bool),ord_less(U_1525),U_1524),U_1523))
    | ~ order(U_1525) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

fof(f_397_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C))
          | A_1 != B_1 )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_344_ord__eq__less__trans]) ).

fof(f_397_2,plain,
    ! [U_1529] :
      ( ! [U_1528,U_1527,U_1526] :
          ( hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less(U_1529),U_1527),U_1528))
          | ~ hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less(U_1529),U_1526),U_1528))
          | U_1527 != U_1526 )
      | ~ ord(U_1529) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

fof(f_397_3,plain,
    ! [U_1529,U_1526,U_1527,U_1528] :
      ( hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less(U_1529),U_1527),U_1528))
      | ~ hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less(U_1529),U_1526),U_1528))
      | U_1527 != U_1526
      | ~ ord(U_1529) ),
    inference(definitional_conversion,[status(esa)],[f_397_2]) ).

cnf(f_397_4,plain,
    ( hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less(U_1529),U_1527),U_1528))
    | ~ hBOOL(hAPP(U_1529,bool,hAPP(U_1529,fun(U_1529,bool),ord_less(U_1529),U_1526),U_1528))
    | U_1527 != U_1526
    | ~ ord(U_1529) ),
    inference(clausify,[status(thm)],[f_397_3]) ).

fof(f_398_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B_1))
          | ti(X_a,A_1) != ti(X_a,B_1) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_345_xt1_I1_J]) ).

fof(f_398_2,plain,
    ! [U_1533] :
      ( ! [U_1532,U_1531,U_1530] :
          ( hBOOL(hAPP(U_1533,bool,hAPP(U_1533,fun(U_1533,bool),ord_less(U_1533),U_1532),U_1531))
          | ~ hBOOL(hAPP(U_1533,bool,hAPP(U_1533,fun(U_1533,bool),ord_less(U_1533),U_1532),U_1530))
          | ti(U_1533,U_1531) != ti(U_1533,U_1530) )
      | ~ order(U_1533) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

fof(f_398_3,plain,
    ! [U_1531,U_1533,U_1532,U_1530] :
      ( hBOOL(hAPP(U_1533,bool,hAPP(U_1533,fun(U_1533,bool),ord_less(U_1533),U_1532),U_1531))
      | ~ hBOOL(hAPP(U_1533,bool,hAPP(U_1533,fun(U_1533,bool),ord_less(U_1533),U_1532),U_1530))
      | ti(U_1533,U_1531) != ti(U_1533,U_1530)
      | ~ order(U_1533) ),
    inference(definitional_conversion,[status(esa)],[f_398_2]) ).

cnf(f_398_4,plain,
    ( hBOOL(hAPP(U_1533,bool,hAPP(U_1533,fun(U_1533,bool),ord_less(U_1533),U_1532),U_1531))
    | ~ hBOOL(hAPP(U_1533,bool,hAPP(U_1533,fun(U_1533,bool),ord_less(U_1533),U_1532),U_1530))
    | ti(U_1533,U_1531) != ti(U_1533,U_1530)
    | ~ order(U_1533) ),
    inference(clausify,[status(thm)],[f_398_3]) ).

fof(f_399_1,plain,
    ! [X_a] :
      ( ! [C,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))
          | B_1 != C
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) )
      | ~ ord(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_346_ord__less__eq__trans]) ).

fof(f_399_2,plain,
    ! [U_1537] :
      ( ! [U_1536,U_1535,U_1534] :
          ( hBOOL(hAPP(U_1537,bool,hAPP(U_1537,fun(U_1537,bool),ord_less(U_1537),U_1535),U_1536))
          | U_1534 != U_1536
          | ~ hBOOL(hAPP(U_1537,bool,hAPP(U_1537,fun(U_1537,bool),ord_less(U_1537),U_1535),U_1534)) )
      | ~ ord(U_1537) ),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

fof(f_399_3,plain,
    ! [U_1537,U_1536,U_1535,U_1534] :
      ( hBOOL(hAPP(U_1537,bool,hAPP(U_1537,fun(U_1537,bool),ord_less(U_1537),U_1535),U_1536))
      | U_1534 != U_1536
      | ~ hBOOL(hAPP(U_1537,bool,hAPP(U_1537,fun(U_1537,bool),ord_less(U_1537),U_1535),U_1534))
      | ~ ord(U_1537) ),
    inference(definitional_conversion,[status(esa)],[f_399_2]) ).

cnf(f_399_4,plain,
    ( hBOOL(hAPP(U_1537,bool,hAPP(U_1537,fun(U_1537,bool),ord_less(U_1537),U_1535),U_1536))
    | U_1534 != U_1536
    | ~ hBOOL(hAPP(U_1537,bool,hAPP(U_1537,fun(U_1537,bool),ord_less(U_1537),U_1535),U_1534))
    | ~ ord(U_1537) ),
    inference(clausify,[status(thm)],[f_399_3]) ).

fof(f_400_1,plain,
    ! [X_a] :
      ( ! [C,B_1,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))
          | ti(X_a,B_1) != ti(X_a,C)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_347_xt1_I2_J]) ).

fof(f_400_2,plain,
    ! [U_1541] :
      ( ! [U_1540,U_1539,U_1538] :
          ( hBOOL(hAPP(U_1541,bool,hAPP(U_1541,fun(U_1541,bool),ord_less(U_1541),U_1540),U_1538))
          | ti(U_1541,U_1539) != ti(U_1541,U_1540)
          | ~ hBOOL(hAPP(U_1541,bool,hAPP(U_1541,fun(U_1541,bool),ord_less(U_1541),U_1539),U_1538)) )
      | ~ order(U_1541) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

fof(f_400_3,plain,
    ! [U_1540,U_1539,U_1538,U_1541] :
      ( hBOOL(hAPP(U_1541,bool,hAPP(U_1541,fun(U_1541,bool),ord_less(U_1541),U_1540),U_1538))
      | ti(U_1541,U_1539) != ti(U_1541,U_1540)
      | ~ hBOOL(hAPP(U_1541,bool,hAPP(U_1541,fun(U_1541,bool),ord_less(U_1541),U_1539),U_1538))
      | ~ order(U_1541) ),
    inference(definitional_conversion,[status(esa)],[f_400_2]) ).

cnf(f_400_4,plain,
    ( hBOOL(hAPP(U_1541,bool,hAPP(U_1541,fun(U_1541,bool),ord_less(U_1541),U_1540),U_1538))
    | ti(U_1541,U_1539) != ti(U_1541,U_1540)
    | ~ hBOOL(hAPP(U_1541,bool,hAPP(U_1541,fun(U_1541,bool),ord_less(U_1541),U_1539),U_1538))
    | ~ order(U_1541) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

fof(f_401_1,plain,
    ! [X_a] :
      ( ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_348_order__less__trans]) ).

fof(f_401_2,plain,
    ! [U_1545] :
      ( ! [U_1544,U_1543,U_1542] :
          ( hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less(U_1545),U_1543),U_1544))
          | ~ hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less(U_1545),U_1542),U_1544))
          | ~ hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less(U_1545),U_1543),U_1542)) )
      | ~ preorder(U_1545) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

fof(f_401_3,plain,
    ! [U_1545,U_1543,U_1542,U_1544] :
      ( hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less(U_1545),U_1543),U_1544))
      | ~ hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less(U_1545),U_1542),U_1544))
      | ~ hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less(U_1545),U_1543),U_1542))
      | ~ preorder(U_1545) ),
    inference(definitional_conversion,[status(esa)],[f_401_2]) ).

cnf(f_401_4,plain,
    ( hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less(U_1545),U_1543),U_1544))
    | ~ hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less(U_1545),U_1542),U_1544))
    | ~ hBOOL(hAPP(U_1545,bool,hAPP(U_1545,fun(U_1545,bool),ord_less(U_1545),U_1543),U_1542))
    | ~ preorder(U_1545) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

fof(f_402_1,plain,
    ! [X_a] :
      ( ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_349_xt1_I10_J]) ).

fof(f_402_2,plain,
    ! [U_1549] :
      ( ! [U_1548,U_1547,U_1546] :
          ( hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1548),U_1546))
          | ~ hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1548),U_1547))
          | ~ hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1547),U_1546)) )
      | ~ order(U_1549) ),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

fof(f_402_3,plain,
    ! [U_1547,U_1546,U_1549,U_1548] :
      ( hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1548),U_1546))
      | ~ hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1548),U_1547))
      | ~ hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1547),U_1546))
      | ~ order(U_1549) ),
    inference(definitional_conversion,[status(esa)],[f_402_2]) ).

cnf(f_402_4,plain,
    ( hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1548),U_1546))
    | ~ hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1548),U_1547))
    | ~ hBOOL(hAPP(U_1549,bool,hAPP(U_1549,fun(U_1549,bool),ord_less(U_1549),U_1547),U_1546))
    | ~ order(U_1549) ),
    inference(clausify,[status(thm)],[f_402_3]) ).

fof(f_403_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_350_order__less__asym]) ).

fof(f_403_2,plain,
    ! [U_1552] :
      ( ! [U_1551,U_1550] :
          ( ~ hBOOL(hAPP(U_1552,bool,hAPP(U_1552,fun(U_1552,bool),ord_less(U_1552),U_1550),U_1551))
          | ~ hBOOL(hAPP(U_1552,bool,hAPP(U_1552,fun(U_1552,bool),ord_less(U_1552),U_1551),U_1550)) )
      | ~ preorder(U_1552) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

fof(f_403_3,plain,
    ! [U_1551,U_1550,U_1552] :
      ( ~ hBOOL(hAPP(U_1552,bool,hAPP(U_1552,fun(U_1552,bool),ord_less(U_1552),U_1550),U_1551))
      | ~ hBOOL(hAPP(U_1552,bool,hAPP(U_1552,fun(U_1552,bool),ord_less(U_1552),U_1551),U_1550))
      | ~ preorder(U_1552) ),
    inference(definitional_conversion,[status(esa)],[f_403_2]) ).

cnf(f_403_4,plain,
    ( ~ hBOOL(hAPP(U_1552,bool,hAPP(U_1552,fun(U_1552,bool),ord_less(U_1552),U_1550),U_1551))
    | ~ hBOOL(hAPP(U_1552,bool,hAPP(U_1552,fun(U_1552,bool),ord_less(U_1552),U_1551),U_1550))
    | ~ preorder(U_1552) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

fof(f_404_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | ti(X_a,X) = ti(X_a,Y)
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_351_linorder__cases]) ).

fof(f_404_2,plain,
    ! [U_1555] :
      ( ! [U_1554,U_1553] :
          ( hBOOL(hAPP(U_1555,bool,hAPP(U_1555,fun(U_1555,bool),ord_less(U_1555),U_1553),U_1554))
          | ti(U_1555,U_1554) = ti(U_1555,U_1553)
          | hBOOL(hAPP(U_1555,bool,hAPP(U_1555,fun(U_1555,bool),ord_less(U_1555),U_1554),U_1553)) )
      | ~ linorder(U_1555) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

fof(f_404_3,plain,
    ! [U_1553,U_1554,U_1555] :
      ( hBOOL(hAPP(U_1555,bool,hAPP(U_1555,fun(U_1555,bool),ord_less(U_1555),U_1553),U_1554))
      | ti(U_1555,U_1554) = ti(U_1555,U_1553)
      | hBOOL(hAPP(U_1555,bool,hAPP(U_1555,fun(U_1555,bool),ord_less(U_1555),U_1554),U_1553))
      | ~ linorder(U_1555) ),
    inference(definitional_conversion,[status(esa)],[f_404_2]) ).

cnf(f_404_4,plain,
    ( hBOOL(hAPP(U_1555,bool,hAPP(U_1555,fun(U_1555,bool),ord_less(U_1555),U_1553),U_1554))
    | ti(U_1555,U_1554) = ti(U_1555,U_1553)
    | hBOOL(hAPP(U_1555,bool,hAPP(U_1555,fun(U_1555,bool),ord_less(U_1555),U_1554),U_1553))
    | ~ linorder(U_1555) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

fof(f_405_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_352_termination__basic__simps_I5_J]) ).

fof(f_405_2,plain,
    ! [U_1557,U_1556] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1557),U_1556))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1557),U_1556)) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

fof(f_405_3,plain,
    ! [U_1556,U_1557] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1557),U_1556))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1557),U_1556)) ),
    inference(definitional_conversion,[status(esa)],[f_405_2]) ).

cnf(f_405_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1557),U_1556))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1557),U_1556)) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

fof(f_406_1,plain,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)),
    inference(fof_nnf,[status(thm)],[fact_353_less__not__refl]) ).

fof(f_406_2,plain,
    ! [U_1558] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1558),U_1558)),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ! [U_1558] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1558),U_1558)),
    inference(definitional_conversion,[status(esa)],[f_406_2]) ).

cnf(f_406_4,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1558),U_1558)),
    inference(clausify,[status(thm)],[f_406_3]) ).

fof(f_407_1,plain,
    ! [M_1,Na] :
      ( ( M_1 != Na
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
        | M_1 = Na ) ),
    inference(fof_nnf,[status(thm)],[fact_354_nat__neq__iff]) ).

fof(f_407_2,plain,
    ! [U_1560,U_1559] :
      ( ( U_1560 != U_1559
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1559),U_1560))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1560),U_1559)) ) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1559),U_1560))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1560),U_1559))
        | U_1560 = U_1559 ) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ( ! [U_1564,U_1562] :
        ( U_1564 != U_1562
        | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1562),U_1564))
          & ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1564),U_1562)) ) )
    & ! [U_1563,U_1561] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1561),U_1563))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1563),U_1561))
        | U_1563 = U_1561 ) ),
    inference(miniscope,[status(thm)],[f_407_2]) ).

fof(f_407_4,plain,
    ( ! [U_1564,U_1562] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1562),U_1564))
        | ~ sP76(U_1564,U_1562) )
    & ! [U_1564,U_1562] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1564),U_1562))
        | ~ sP76(U_1564,U_1562) )
    & ! [U_1564,U_1562] :
        ( U_1564 != U_1562
        | sP76(U_1564,U_1562) )
    & ! [U_1561,U_1563] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1561),U_1563))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1563),U_1561))
        | U_1563 = U_1561 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76])],[f_407_3]) ).

cnf(f_407_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1561),U_1563))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1563),U_1561))
    | U_1563 = U_1561 ),
    inference(clausify,[status(thm)],[f_407_4]) ).

cnf(f_407_6,plain,
    ( U_1564 != U_1562
    | sP76(U_1564,U_1562) ),
    inference(clausify,[status(thm)],[f_407_4]) ).

cnf(f_407_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1564),U_1562))
    | ~ sP76(U_1564,U_1562) ),
    inference(clausify,[status(thm)],[f_407_4]) ).

cnf(f_407_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1562),U_1564))
    | ~ sP76(U_1564,U_1562) ),
    inference(clausify,[status(thm)],[f_407_4]) ).

fof(f_408_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y))
      | X = Y ),
    inference(fof_nnf,[status(thm)],[fact_355_linorder__neqE__nat]) ).

fof(f_408_2,plain,
    ! [U_1566,U_1565] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1565),U_1566))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1566),U_1565))
      | U_1566 = U_1565 ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

fof(f_408_3,plain,
    ! [U_1565,U_1566] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1565),U_1566))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1566),U_1565))
      | U_1566 = U_1565 ),
    inference(definitional_conversion,[status(esa)],[f_408_2]) ).

cnf(f_408_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1565),U_1566))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1566),U_1565))
    | U_1566 = U_1565 ),
    inference(clausify,[status(thm)],[f_408_3]) ).

fof(f_409_1,plain,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N)),
    inference(fof_nnf,[status(thm)],[fact_356_less__irrefl__nat]) ).

fof(f_409_2,plain,
    ! [U_1567] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1567),U_1567)),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

fof(f_409_3,plain,
    ! [U_1567] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1567),U_1567)),
    inference(definitional_conversion,[status(esa)],[f_409_2]) ).

cnf(f_409_4,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1567),U_1567)),
    inference(clausify,[status(thm)],[f_409_3]) ).

fof(f_410_1,plain,
    ! [N,M] :
      ( M != N
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) ),
    inference(fof_nnf,[status(thm)],[fact_357_less__not__refl2]) ).

fof(f_410_2,plain,
    ! [U_1569,U_1568] :
      ( U_1568 != U_1569
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1569),U_1568)) ),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

fof(f_410_3,plain,
    ! [U_1569,U_1568] :
      ( U_1568 != U_1569
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1569),U_1568)) ),
    inference(definitional_conversion,[status(esa)],[f_410_2]) ).

cnf(f_410_4,plain,
    ( U_1568 != U_1569
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1569),U_1568)) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

fof(f_411_1,plain,
    ! [S,T_3] :
      ( S != T_3
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) ),
    inference(fof_nnf,[status(thm)],[fact_358_less__not__refl3]) ).

fof(f_411_2,plain,
    ! [U_1571,U_1570] :
      ( U_1571 != U_1570
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1571),U_1570)) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

fof(f_411_3,plain,
    ! [U_1571,U_1570] :
      ( U_1571 != U_1570
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1571),U_1570)) ),
    inference(definitional_conversion,[status(esa)],[f_411_2]) ).

cnf(f_411_4,plain,
    ( U_1571 != U_1570
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1571),U_1570)) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

fof(f_412_1,plain,
    ! [Pa,M_1,Na] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_1))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_1))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1)) )
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_1))
        & M_1 = Na )
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,Na),M_1))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_359_nat__less__cases]) ).

fof(f_412_2,plain,
    ! [U_1574,U_1573,U_1572] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1574,U_1572),U_1573))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1574,U_1572),U_1573))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1572),U_1573)) )
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1574,U_1572),U_1573))
        & U_1573 = U_1572 )
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1574,U_1572),U_1573))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1573),U_1572)) ) ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

fof(f_412_3,plain,
    ( ! [U_1573,U_1574,U_1572] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1574,U_1572),U_1573))
        | ~ sP79(U_1573,U_1574,U_1572) )
    & ! [U_1573,U_1574,U_1572] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1572),U_1573))
        | ~ sP79(U_1573,U_1574,U_1572) )
    & ! [U_1573,U_1574,U_1572] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1574,U_1572),U_1573))
        | ~ sP78(U_1573,U_1574,U_1572) )
    & ! [U_1573,U_1574,U_1572] :
        ( U_1573 = U_1572
        | ~ sP78(U_1573,U_1574,U_1572) )
    & ! [U_1573,U_1574,U_1572] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1574,U_1572),U_1573))
        | ~ sP77(U_1573,U_1574,U_1572) )
    & ! [U_1573,U_1574,U_1572] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1573),U_1572))
        | ~ sP77(U_1573,U_1574,U_1572) )
    & ! [U_1573,U_1574,U_1572] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1574,U_1572),U_1573))
        | sP79(U_1573,U_1574,U_1572)
        | sP78(U_1573,U_1574,U_1572)
        | sP77(U_1573,U_1574,U_1572) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77,sP78,sP79])],[f_412_2]) ).

cnf(f_412_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1574,U_1572),U_1573))
    | sP79(U_1573,U_1574,U_1572)
    | sP78(U_1573,U_1574,U_1572)
    | sP77(U_1573,U_1574,U_1572) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

cnf(f_412_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1573),U_1572))
    | ~ sP77(U_1573,U_1574,U_1572) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

cnf(f_412_6,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1574,U_1572),U_1573))
    | ~ sP77(U_1573,U_1574,U_1572) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

cnf(f_412_7,plain,
    ( U_1573 = U_1572
    | ~ sP78(U_1573,U_1574,U_1572) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

cnf(f_412_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1574,U_1572),U_1573))
    | ~ sP78(U_1573,U_1574,U_1572) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

cnf(f_412_9,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1572),U_1573))
    | ~ sP79(U_1573,U_1574,U_1572) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

cnf(f_412_10,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),U_1574,U_1572),U_1573))
    | ~ sP79(U_1573,U_1574,U_1572) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

fof(f_413_1,plain,
    ! [X_a] :
      ( ! [A_1] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),bot_bot(X_a)))
      | ~ bot(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_360_not__less__bot]) ).

fof(f_413_2,plain,
    ! [U_1576] :
      ( ! [U_1575] : ~ hBOOL(hAPP(U_1576,bool,hAPP(U_1576,fun(U_1576,bool),ord_less(U_1576),U_1575),bot_bot(U_1576)))
      | ~ bot(U_1576) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ! [U_1576,U_1575] :
      ( ~ hBOOL(hAPP(U_1576,bool,hAPP(U_1576,fun(U_1576,bool),ord_less(U_1576),U_1575),bot_bot(U_1576)))
      | ~ bot(U_1576) ),
    inference(definitional_conversion,[status(esa)],[f_413_2]) ).

cnf(f_413_4,plain,
    ( ~ hBOOL(hAPP(U_1576,bool,hAPP(U_1576,fun(U_1576,bool),ord_less(U_1576),U_1575),bot_bot(U_1576)))
    | ~ bot(U_1576) ),
    inference(clausify,[status(thm)],[f_413_3]) ).

fof(f_414_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( ti(X_b,A_2) != bot_bot(X_b)
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),bot_bot(X_b)),A_2)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),bot_bot(X_b)),A_2))
            | ti(X_b,A_2) = bot_bot(X_b) ) )
      | ~ bot(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_361_bot__less]) ).

fof(f_414_2,plain,
    ! [U_1578] :
      ( ! [U_1577] :
          ( ( ti(U_1578,U_1577) != bot_bot(U_1578)
            | ~ hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less(U_1578),bot_bot(U_1578)),U_1577)) )
          & ( hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less(U_1578),bot_bot(U_1578)),U_1577))
            | ti(U_1578,U_1577) = bot_bot(U_1578) ) )
      | ~ bot(U_1578) ),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

fof(f_414_3,plain,
    ! [U_1578] :
      ( ( ! [U_1580] :
            ( ti(U_1578,U_1580) != bot_bot(U_1578)
            | ~ hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less(U_1578),bot_bot(U_1578)),U_1580)) )
        & ! [U_1579] :
            ( hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less(U_1578),bot_bot(U_1578)),U_1579))
            | ti(U_1578,U_1579) = bot_bot(U_1578) ) )
      | ~ bot(U_1578) ),
    inference(miniscope,[status(thm)],[f_414_2]) ).

fof(f_414_4,plain,
    ( ! [U_1579,U_1578,U_1580] :
        ( ti(U_1578,U_1580) != bot_bot(U_1578)
        | ~ hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less(U_1578),bot_bot(U_1578)),U_1580))
        | ~ sP80(U_1579,U_1578,U_1580) )
    & ! [U_1579,U_1578,U_1580] :
        ( hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less(U_1578),bot_bot(U_1578)),U_1579))
        | ti(U_1578,U_1579) = bot_bot(U_1578)
        | ~ sP80(U_1579,U_1578,U_1580) )
    & ! [U_1579,U_1578,U_1580] :
        ( sP80(U_1579,U_1578,U_1580)
        | ~ bot(U_1578) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_414_3]) ).

cnf(f_414_5,plain,
    ( sP80(U_1579,U_1578,U_1580)
    | ~ bot(U_1578) ),
    inference(clausify,[status(thm)],[f_414_4]) ).

cnf(f_414_6,plain,
    ( hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less(U_1578),bot_bot(U_1578)),U_1579))
    | ti(U_1578,U_1579) = bot_bot(U_1578)
    | ~ sP80(U_1579,U_1578,U_1580) ),
    inference(clausify,[status(thm)],[f_414_4]) ).

cnf(f_414_7,plain,
    ( ti(U_1578,U_1580) != bot_bot(U_1578)
    | ~ hBOOL(hAPP(U_1578,bool,hAPP(U_1578,fun(U_1578,bool),ord_less(U_1578),bot_bot(U_1578)),U_1580))
    | ~ sP80(U_1579,U_1578,U_1580) ),
    inference(clausify,[status(thm)],[f_414_4]) ).

fof(f_415_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_1] :
          ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) ) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_362_linorder__not__less]) ).

fof(f_415_2,plain,
    ! [U_1583] :
      ( ! [U_1582,U_1581] :
          ( ( ~ hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less(U_1583),U_1582),U_1581))
            | ~ hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less_eq(U_1583),U_1581),U_1582)) )
          & ( hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less_eq(U_1583),U_1581),U_1582))
            | hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less(U_1583),U_1582),U_1581)) ) )
      | ~ linorder(U_1583) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

fof(f_415_3,plain,
    ! [U_1583] :
      ( ( ! [U_1587,U_1585] :
            ( ~ hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less(U_1583),U_1587),U_1585))
            | ~ hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less_eq(U_1583),U_1585),U_1587)) )
        & ! [U_1586,U_1584] :
            ( hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less_eq(U_1583),U_1584),U_1586))
            | hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less(U_1583),U_1586),U_1584)) ) )
      | ~ linorder(U_1583) ),
    inference(miniscope,[status(thm)],[f_415_2]) ).

fof(f_415_4,plain,
    ( ! [U_1585,U_1583,U_1587,U_1584,U_1586] :
        ( ~ hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less(U_1583),U_1587),U_1585))
        | ~ hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less_eq(U_1583),U_1585),U_1587))
        | ~ sP81(U_1585,U_1583,U_1587,U_1584,U_1586) )
    & ! [U_1585,U_1583,U_1587,U_1584,U_1586] :
        ( hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less_eq(U_1583),U_1584),U_1586))
        | hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less(U_1583),U_1586),U_1584))
        | ~ sP81(U_1585,U_1583,U_1587,U_1584,U_1586) )
    & ! [U_1585,U_1583,U_1587,U_1584,U_1586] :
        ( sP81(U_1585,U_1583,U_1587,U_1584,U_1586)
        | ~ linorder(U_1583) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81])],[f_415_3]) ).

cnf(f_415_5,plain,
    ( sP81(U_1585,U_1583,U_1587,U_1584,U_1586)
    | ~ linorder(U_1583) ),
    inference(clausify,[status(thm)],[f_415_4]) ).

cnf(f_415_6,plain,
    ( hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less_eq(U_1583),U_1584),U_1586))
    | hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less(U_1583),U_1586),U_1584))
    | ~ sP81(U_1585,U_1583,U_1587,U_1584,U_1586) ),
    inference(clausify,[status(thm)],[f_415_4]) ).

cnf(f_415_7,plain,
    ( ~ hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less(U_1583),U_1587),U_1585))
    | ~ hBOOL(hAPP(U_1583,bool,hAPP(U_1583,fun(U_1583,bool),ord_less_eq(U_1583),U_1585),U_1587))
    | ~ sP81(U_1585,U_1583,U_1587,U_1584,U_1586) ),
    inference(clausify,[status(thm)],[f_415_4]) ).

fof(f_416_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_1] :
          ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_1))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) ) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_363_linorder__not__le]) ).

fof(f_416_2,plain,
    ! [U_1590] :
      ( ! [U_1589,U_1588] :
          ( ( ~ hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less_eq(U_1590),U_1589),U_1588))
            | ~ hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less(U_1590),U_1588),U_1589)) )
          & ( hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less(U_1590),U_1588),U_1589))
            | hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less_eq(U_1590),U_1589),U_1588)) ) )
      | ~ linorder(U_1590) ),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

fof(f_416_3,plain,
    ! [U_1590] :
      ( ( ! [U_1594,U_1592] :
            ( ~ hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less_eq(U_1590),U_1594),U_1592))
            | ~ hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less(U_1590),U_1592),U_1594)) )
        & ! [U_1593,U_1591] :
            ( hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less(U_1590),U_1591),U_1593))
            | hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less_eq(U_1590),U_1593),U_1591)) ) )
      | ~ linorder(U_1590) ),
    inference(miniscope,[status(thm)],[f_416_2]) ).

fof(f_416_4,plain,
    ( ! [U_1590,U_1592,U_1591,U_1594,U_1593] :
        ( ~ hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less_eq(U_1590),U_1594),U_1592))
        | ~ hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less(U_1590),U_1592),U_1594))
        | ~ sP82(U_1590,U_1592,U_1591,U_1594,U_1593) )
    & ! [U_1590,U_1592,U_1591,U_1594,U_1593] :
        ( hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less(U_1590),U_1591),U_1593))
        | hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less_eq(U_1590),U_1593),U_1591))
        | ~ sP82(U_1590,U_1592,U_1591,U_1594,U_1593) )
    & ! [U_1590,U_1592,U_1591,U_1594,U_1593] :
        ( sP82(U_1590,U_1592,U_1591,U_1594,U_1593)
        | ~ linorder(U_1590) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82])],[f_416_3]) ).

cnf(f_416_5,plain,
    ( sP82(U_1590,U_1592,U_1591,U_1594,U_1593)
    | ~ linorder(U_1590) ),
    inference(clausify,[status(thm)],[f_416_4]) ).

cnf(f_416_6,plain,
    ( hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less(U_1590),U_1591),U_1593))
    | hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less_eq(U_1590),U_1593),U_1591))
    | ~ sP82(U_1590,U_1592,U_1591,U_1594,U_1593) ),
    inference(clausify,[status(thm)],[f_416_4]) ).

cnf(f_416_7,plain,
    ( ~ hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less_eq(U_1590),U_1594),U_1592))
    | ~ hBOOL(hAPP(U_1590,bool,hAPP(U_1590,fun(U_1590,bool),ord_less(U_1590),U_1592),U_1594))
    | ~ sP82(U_1590,U_1592,U_1591,U_1594,U_1593) ),
    inference(clausify,[status(thm)],[f_416_4]) ).

fof(f_417_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_364_linorder__le__less__linear]) ).

fof(f_417_2,plain,
    ! [U_1597] :
      ( ! [U_1596,U_1595] :
          ( hBOOL(hAPP(U_1597,bool,hAPP(U_1597,fun(U_1597,bool),ord_less(U_1597),U_1595),U_1596))
          | hBOOL(hAPP(U_1597,bool,hAPP(U_1597,fun(U_1597,bool),ord_less_eq(U_1597),U_1596),U_1595)) )
      | ~ linorder(U_1597) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

fof(f_417_3,plain,
    ! [U_1596,U_1595,U_1597] :
      ( hBOOL(hAPP(U_1597,bool,hAPP(U_1597,fun(U_1597,bool),ord_less(U_1597),U_1595),U_1596))
      | hBOOL(hAPP(U_1597,bool,hAPP(U_1597,fun(U_1597,bool),ord_less_eq(U_1597),U_1596),U_1595))
      | ~ linorder(U_1597) ),
    inference(definitional_conversion,[status(esa)],[f_417_2]) ).

cnf(f_417_4,plain,
    ( hBOOL(hAPP(U_1597,bool,hAPP(U_1597,fun(U_1597,bool),ord_less(U_1597),U_1595),U_1596))
    | hBOOL(hAPP(U_1597,bool,hAPP(U_1597,fun(U_1597,bool),ord_less_eq(U_1597),U_1596),U_1595))
    | ~ linorder(U_1597) ),
    inference(clausify,[status(thm)],[f_417_3]) ).

fof(f_418_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_1] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
            | ti(X_b,X_1) = ti(X_b,Y_1)
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) )
          & ( ( ti(X_b,X_1) != ti(X_b,Y_1)
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) )
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) ) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_365_order__less__le]) ).

fof(f_418_2,plain,
    ! [U_1600] :
      ( ! [U_1599,U_1598] :
          ( ( hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less(U_1600),U_1599),U_1598))
            | ti(U_1600,U_1599) = ti(U_1600,U_1598)
            | ~ hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less_eq(U_1600),U_1599),U_1598)) )
          & ( ( ti(U_1600,U_1599) != ti(U_1600,U_1598)
              & hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less_eq(U_1600),U_1599),U_1598)) )
            | ~ hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less(U_1600),U_1599),U_1598)) ) )
      | ~ order(U_1600) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

fof(f_418_3,plain,
    ! [U_1600] :
      ( ( ! [U_1604,U_1602] :
            ( hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less(U_1600),U_1604),U_1602))
            | ti(U_1600,U_1604) = ti(U_1600,U_1602)
            | ~ hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less_eq(U_1600),U_1604),U_1602)) )
        & ! [U_1603,U_1601] :
            ( ( ti(U_1600,U_1603) != ti(U_1600,U_1601)
              & hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less_eq(U_1600),U_1603),U_1601)) )
            | ~ hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less(U_1600),U_1603),U_1601)) ) )
      | ~ order(U_1600) ),
    inference(miniscope,[status(thm)],[f_418_2]) ).

fof(f_418_4,plain,
    ( ! [U_1600,U_1601,U_1603] :
        ( ti(U_1600,U_1603) != ti(U_1600,U_1601)
        | ~ sP83(U_1600,U_1601,U_1603) )
    & ! [U_1600,U_1601,U_1603] :
        ( hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less_eq(U_1600),U_1603),U_1601))
        | ~ sP83(U_1600,U_1601,U_1603) )
    & ! [U_1600,U_1602,U_1601,U_1603,U_1604] :
        ( hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less(U_1600),U_1604),U_1602))
        | ti(U_1600,U_1604) = ti(U_1600,U_1602)
        | ~ hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less_eq(U_1600),U_1604),U_1602))
        | ~ sP84(U_1600,U_1602,U_1601,U_1603,U_1604) )
    & ! [U_1600,U_1602,U_1601,U_1603,U_1604] :
        ( sP83(U_1600,U_1601,U_1603)
        | ~ hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less(U_1600),U_1603),U_1601))
        | ~ sP84(U_1600,U_1602,U_1601,U_1603,U_1604) )
    & ! [U_1600,U_1602,U_1601,U_1603,U_1604] :
        ( sP84(U_1600,U_1602,U_1601,U_1603,U_1604)
        | ~ order(U_1600) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83,sP84])],[f_418_3]) ).

cnf(f_418_5,plain,
    ( sP84(U_1600,U_1602,U_1601,U_1603,U_1604)
    | ~ order(U_1600) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

cnf(f_418_6,plain,
    ( sP83(U_1600,U_1601,U_1603)
    | ~ hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less(U_1600),U_1603),U_1601))
    | ~ sP84(U_1600,U_1602,U_1601,U_1603,U_1604) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

cnf(f_418_7,plain,
    ( hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less(U_1600),U_1604),U_1602))
    | ti(U_1600,U_1604) = ti(U_1600,U_1602)
    | ~ hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less_eq(U_1600),U_1604),U_1602))
    | ~ sP84(U_1600,U_1602,U_1601,U_1603,U_1604) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

cnf(f_418_8,plain,
    ( hBOOL(hAPP(U_1600,bool,hAPP(U_1600,fun(U_1600,bool),ord_less_eq(U_1600),U_1603),U_1601))
    | ~ sP83(U_1600,U_1601,U_1603) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

cnf(f_418_9,plain,
    ( ti(U_1600,U_1603) != ti(U_1600,U_1601)
    | ~ sP83(U_1600,U_1601,U_1603) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

fof(f_419_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_1] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) )
          & ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) )
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) ) )
      | ~ preorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_366_less__le__not__le]) ).

fof(f_419_2,plain,
    ! [U_1607] :
      ( ! [U_1606,U_1605] :
          ( ( hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less(U_1607),U_1606),U_1605))
            | hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1605),U_1606))
            | ~ hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1606),U_1605)) )
          & ( ( ~ hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1605),U_1606))
              & hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1606),U_1605)) )
            | ~ hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less(U_1607),U_1606),U_1605)) ) )
      | ~ preorder(U_1607) ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

fof(f_419_3,plain,
    ! [U_1607] :
      ( ( ! [U_1611,U_1609] :
            ( hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less(U_1607),U_1611),U_1609))
            | hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1609),U_1611))
            | ~ hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1611),U_1609)) )
        & ! [U_1610,U_1608] :
            ( ( ~ hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1608),U_1610))
              & hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1610),U_1608)) )
            | ~ hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less(U_1607),U_1610),U_1608)) ) )
      | ~ preorder(U_1607) ),
    inference(miniscope,[status(thm)],[f_419_2]) ).

fof(f_419_4,plain,
    ( ! [U_1607,U_1608,U_1610] :
        ( ~ hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1608),U_1610))
        | ~ sP85(U_1607,U_1608,U_1610) )
    & ! [U_1607,U_1608,U_1610] :
        ( hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1610),U_1608))
        | ~ sP85(U_1607,U_1608,U_1610) )
    & ! [U_1609,U_1607,U_1608,U_1611,U_1610] :
        ( hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less(U_1607),U_1611),U_1609))
        | hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1609),U_1611))
        | ~ hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1611),U_1609))
        | ~ sP86(U_1609,U_1607,U_1608,U_1611,U_1610) )
    & ! [U_1609,U_1607,U_1608,U_1611,U_1610] :
        ( sP85(U_1607,U_1608,U_1610)
        | ~ hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less(U_1607),U_1610),U_1608))
        | ~ sP86(U_1609,U_1607,U_1608,U_1611,U_1610) )
    & ! [U_1609,U_1607,U_1608,U_1611,U_1610] :
        ( sP86(U_1609,U_1607,U_1608,U_1611,U_1610)
        | ~ preorder(U_1607) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85,sP86])],[f_419_3]) ).

cnf(f_419_5,plain,
    ( sP86(U_1609,U_1607,U_1608,U_1611,U_1610)
    | ~ preorder(U_1607) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

cnf(f_419_6,plain,
    ( sP85(U_1607,U_1608,U_1610)
    | ~ hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less(U_1607),U_1610),U_1608))
    | ~ sP86(U_1609,U_1607,U_1608,U_1611,U_1610) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

cnf(f_419_7,plain,
    ( hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less(U_1607),U_1611),U_1609))
    | hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1609),U_1611))
    | ~ hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1611),U_1609))
    | ~ sP86(U_1609,U_1607,U_1608,U_1611,U_1610) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

cnf(f_419_8,plain,
    ( hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1610),U_1608))
    | ~ sP85(U_1607,U_1608,U_1610) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

cnf(f_419_9,plain,
    ( ~ hBOOL(hAPP(U_1607,bool,hAPP(U_1607,fun(U_1607,bool),ord_less_eq(U_1607),U_1608),U_1610))
    | ~ sP85(U_1607,U_1608,U_1610) ),
    inference(clausify,[status(thm)],[f_419_4]) ).

fof(f_420_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_1] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1))
            | ( ti(X_b,X_1) != ti(X_b,Y_1)
              & ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) ) )
          & ( ti(X_b,X_1) = ti(X_b,Y_1)
            | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) ) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_367_order__le__less]) ).

fof(f_420_2,plain,
    ! [U_1614] :
      ( ! [U_1613,U_1612] :
          ( ( hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less_eq(U_1614),U_1613),U_1612))
            | ( ti(U_1614,U_1613) != ti(U_1614,U_1612)
              & ~ hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less(U_1614),U_1613),U_1612)) ) )
          & ( ti(U_1614,U_1613) = ti(U_1614,U_1612)
            | hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less(U_1614),U_1613),U_1612))
            | ~ hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less_eq(U_1614),U_1613),U_1612)) ) )
      | ~ order(U_1614) ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

fof(f_420_3,plain,
    ! [U_1614] :
      ( ( ! [U_1618,U_1616] :
            ( hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less_eq(U_1614),U_1618),U_1616))
            | ( ti(U_1614,U_1618) != ti(U_1614,U_1616)
              & ~ hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less(U_1614),U_1618),U_1616)) ) )
        & ! [U_1617,U_1615] :
            ( ti(U_1614,U_1617) = ti(U_1614,U_1615)
            | hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less(U_1614),U_1617),U_1615))
            | ~ hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less_eq(U_1614),U_1617),U_1615)) ) )
      | ~ order(U_1614) ),
    inference(miniscope,[status(thm)],[f_420_2]) ).

fof(f_420_4,plain,
    ( ! [U_1614,U_1616,U_1618] :
        ( ti(U_1614,U_1618) != ti(U_1614,U_1616)
        | ~ sP87(U_1614,U_1616,U_1618) )
    & ! [U_1614,U_1616,U_1618] :
        ( ~ hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less(U_1614),U_1618),U_1616))
        | ~ sP87(U_1614,U_1616,U_1618) )
    & ! [U_1615,U_1614,U_1616,U_1617,U_1618] :
        ( hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less_eq(U_1614),U_1618),U_1616))
        | sP87(U_1614,U_1616,U_1618)
        | ~ sP88(U_1615,U_1614,U_1616,U_1617,U_1618) )
    & ! [U_1615,U_1614,U_1616,U_1617,U_1618] :
        ( ti(U_1614,U_1617) = ti(U_1614,U_1615)
        | hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less(U_1614),U_1617),U_1615))
        | ~ hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less_eq(U_1614),U_1617),U_1615))
        | ~ sP88(U_1615,U_1614,U_1616,U_1617,U_1618) )
    & ! [U_1615,U_1614,U_1616,U_1617,U_1618] :
        ( sP88(U_1615,U_1614,U_1616,U_1617,U_1618)
        | ~ order(U_1614) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87,sP88])],[f_420_3]) ).

cnf(f_420_5,plain,
    ( sP88(U_1615,U_1614,U_1616,U_1617,U_1618)
    | ~ order(U_1614) ),
    inference(clausify,[status(thm)],[f_420_4]) ).

cnf(f_420_6,plain,
    ( ti(U_1614,U_1617) = ti(U_1614,U_1615)
    | hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less(U_1614),U_1617),U_1615))
    | ~ hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less_eq(U_1614),U_1617),U_1615))
    | ~ sP88(U_1615,U_1614,U_1616,U_1617,U_1618) ),
    inference(clausify,[status(thm)],[f_420_4]) ).

cnf(f_420_7,plain,
    ( hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less_eq(U_1614),U_1618),U_1616))
    | sP87(U_1614,U_1616,U_1618)
    | ~ sP88(U_1615,U_1614,U_1616,U_1617,U_1618) ),
    inference(clausify,[status(thm)],[f_420_4]) ).

cnf(f_420_8,plain,
    ( ~ hBOOL(hAPP(U_1614,bool,hAPP(U_1614,fun(U_1614,bool),ord_less(U_1614),U_1618),U_1616))
    | ~ sP87(U_1614,U_1616,U_1618) ),
    inference(clausify,[status(thm)],[f_420_4]) ).

cnf(f_420_9,plain,
    ( ti(U_1614,U_1618) != ti(U_1614,U_1616)
    | ~ sP87(U_1614,U_1616,U_1618) ),
    inference(clausify,[status(thm)],[f_420_4]) ).

fof(f_421_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_368_leI]) ).

fof(f_421_2,plain,
    ! [U_1621] :
      ( ! [U_1620,U_1619] :
          ( hBOOL(hAPP(U_1621,bool,hAPP(U_1621,fun(U_1621,bool),ord_less_eq(U_1621),U_1619),U_1620))
          | hBOOL(hAPP(U_1621,bool,hAPP(U_1621,fun(U_1621,bool),ord_less(U_1621),U_1620),U_1619)) )
      | ~ linorder(U_1621) ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

fof(f_421_3,plain,
    ! [U_1620,U_1621,U_1619] :
      ( hBOOL(hAPP(U_1621,bool,hAPP(U_1621,fun(U_1621,bool),ord_less_eq(U_1621),U_1619),U_1620))
      | hBOOL(hAPP(U_1621,bool,hAPP(U_1621,fun(U_1621,bool),ord_less(U_1621),U_1620),U_1619))
      | ~ linorder(U_1621) ),
    inference(definitional_conversion,[status(esa)],[f_421_2]) ).

cnf(f_421_4,plain,
    ( hBOOL(hAPP(U_1621,bool,hAPP(U_1621,fun(U_1621,bool),ord_less_eq(U_1621),U_1619),U_1620))
    | hBOOL(hAPP(U_1621,bool,hAPP(U_1621,fun(U_1621,bool),ord_less(U_1621),U_1620),U_1619))
    | ~ linorder(U_1621) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

fof(f_422_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_369_not__leE]) ).

fof(f_422_2,plain,
    ! [U_1624] :
      ( ! [U_1623,U_1622] :
          ( hBOOL(hAPP(U_1624,bool,hAPP(U_1624,fun(U_1624,bool),ord_less(U_1624),U_1622),U_1623))
          | hBOOL(hAPP(U_1624,bool,hAPP(U_1624,fun(U_1624,bool),ord_less_eq(U_1624),U_1623),U_1622)) )
      | ~ linorder(U_1624) ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

fof(f_422_3,plain,
    ! [U_1622,U_1624,U_1623] :
      ( hBOOL(hAPP(U_1624,bool,hAPP(U_1624,fun(U_1624,bool),ord_less(U_1624),U_1622),U_1623))
      | hBOOL(hAPP(U_1624,bool,hAPP(U_1624,fun(U_1624,bool),ord_less_eq(U_1624),U_1623),U_1622))
      | ~ linorder(U_1624) ),
    inference(definitional_conversion,[status(esa)],[f_422_2]) ).

cnf(f_422_4,plain,
    ( hBOOL(hAPP(U_1624,bool,hAPP(U_1624,fun(U_1624,bool),ord_less(U_1624),U_1622),U_1623))
    | hBOOL(hAPP(U_1624,bool,hAPP(U_1624,fun(U_1624,bool),ord_less_eq(U_1624),U_1623),U_1622))
    | ~ linorder(U_1624) ),
    inference(clausify,[status(thm)],[f_422_3]) ).

fof(f_423_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_1] :
          ( ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1))
              | ti(X_b,X_1) != ti(X_b,Y_1) )
            & ( ti(X_b,X_1) = ti(X_b,Y_1)
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) ) )
          | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_370_linorder__antisym__conv1]) ).

fof(f_423_2,plain,
    ! [U_1627] :
      ( ! [U_1626,U_1625] :
          ( ( ( hBOOL(hAPP(U_1627,bool,hAPP(U_1627,fun(U_1627,bool),ord_less_eq(U_1627),U_1626),U_1625))
              | ti(U_1627,U_1626) != ti(U_1627,U_1625) )
            & ( ti(U_1627,U_1626) = ti(U_1627,U_1625)
              | ~ hBOOL(hAPP(U_1627,bool,hAPP(U_1627,fun(U_1627,bool),ord_less_eq(U_1627),U_1626),U_1625)) ) )
          | hBOOL(hAPP(U_1627,bool,hAPP(U_1627,fun(U_1627,bool),ord_less(U_1627),U_1626),U_1625)) )
      | ~ linorder(U_1627) ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

fof(f_423_3,plain,
    ( ! [U_1625,U_1626,U_1627] :
        ( hBOOL(hAPP(U_1627,bool,hAPP(U_1627,fun(U_1627,bool),ord_less_eq(U_1627),U_1626),U_1625))
        | ti(U_1627,U_1626) != ti(U_1627,U_1625)
        | ~ sP89(U_1625,U_1626,U_1627) )
    & ! [U_1625,U_1626,U_1627] :
        ( ti(U_1627,U_1626) = ti(U_1627,U_1625)
        | ~ hBOOL(hAPP(U_1627,bool,hAPP(U_1627,fun(U_1627,bool),ord_less_eq(U_1627),U_1626),U_1625))
        | ~ sP89(U_1625,U_1626,U_1627) )
    & ! [U_1625,U_1626,U_1627] :
        ( sP89(U_1625,U_1626,U_1627)
        | hBOOL(hAPP(U_1627,bool,hAPP(U_1627,fun(U_1627,bool),ord_less(U_1627),U_1626),U_1625))
        | ~ linorder(U_1627) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_423_2]) ).

cnf(f_423_4,plain,
    ( sP89(U_1625,U_1626,U_1627)
    | hBOOL(hAPP(U_1627,bool,hAPP(U_1627,fun(U_1627,bool),ord_less(U_1627),U_1626),U_1625))
    | ~ linorder(U_1627) ),
    inference(clausify,[status(thm)],[f_423_3]) ).

cnf(f_423_5,plain,
    ( ti(U_1627,U_1626) = ti(U_1627,U_1625)
    | ~ hBOOL(hAPP(U_1627,bool,hAPP(U_1627,fun(U_1627,bool),ord_less_eq(U_1627),U_1626),U_1625))
    | ~ sP89(U_1625,U_1626,U_1627) ),
    inference(clausify,[status(thm)],[f_423_3]) ).

cnf(f_423_6,plain,
    ( hBOOL(hAPP(U_1627,bool,hAPP(U_1627,fun(U_1627,bool),ord_less_eq(U_1627),U_1626),U_1625))
    | ti(U_1627,U_1626) != ti(U_1627,U_1625)
    | ~ sP89(U_1625,U_1626,U_1627) ),
    inference(clausify,[status(thm)],[f_423_3]) ).

fof(f_424_1,plain,
    ! [X_a] :
      ( ! [A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1))
          | ti(X_a,A_1) = ti(X_a,B_1) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_371_order__neq__le__trans]) ).

fof(f_424_2,plain,
    ! [U_1630] :
      ( ! [U_1629,U_1628] :
          ( hBOOL(hAPP(U_1630,bool,hAPP(U_1630,fun(U_1630,bool),ord_less(U_1630),U_1629),U_1628))
          | ~ hBOOL(hAPP(U_1630,bool,hAPP(U_1630,fun(U_1630,bool),ord_less_eq(U_1630),U_1629),U_1628))
          | ti(U_1630,U_1629) = ti(U_1630,U_1628) )
      | ~ order(U_1630) ),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

fof(f_424_3,plain,
    ! [U_1630,U_1629,U_1628] :
      ( hBOOL(hAPP(U_1630,bool,hAPP(U_1630,fun(U_1630,bool),ord_less(U_1630),U_1629),U_1628))
      | ~ hBOOL(hAPP(U_1630,bool,hAPP(U_1630,fun(U_1630,bool),ord_less_eq(U_1630),U_1629),U_1628))
      | ti(U_1630,U_1629) = ti(U_1630,U_1628)
      | ~ order(U_1630) ),
    inference(definitional_conversion,[status(esa)],[f_424_2]) ).

cnf(f_424_4,plain,
    ( hBOOL(hAPP(U_1630,bool,hAPP(U_1630,fun(U_1630,bool),ord_less(U_1630),U_1629),U_1628))
    | ~ hBOOL(hAPP(U_1630,bool,hAPP(U_1630,fun(U_1630,bool),ord_less_eq(U_1630),U_1629),U_1628))
    | ti(U_1630,U_1629) = ti(U_1630,U_1628)
    | ~ order(U_1630) ),
    inference(clausify,[status(thm)],[f_424_3]) ).

fof(f_425_1,plain,
    ! [X_a] :
      ( ! [A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_1))
          | ti(X_a,A_1) = ti(X_a,B_1) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_372_xt1_I12_J]) ).

fof(f_425_2,plain,
    ! [U_1633] :
      ( ! [U_1632,U_1631] :
          ( hBOOL(hAPP(U_1633,bool,hAPP(U_1633,fun(U_1633,bool),ord_less(U_1633),U_1631),U_1632))
          | ~ hBOOL(hAPP(U_1633,bool,hAPP(U_1633,fun(U_1633,bool),ord_less_eq(U_1633),U_1631),U_1632))
          | ti(U_1633,U_1632) = ti(U_1633,U_1631) )
      | ~ order(U_1633) ),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

fof(f_425_3,plain,
    ! [U_1632,U_1631,U_1633] :
      ( hBOOL(hAPP(U_1633,bool,hAPP(U_1633,fun(U_1633,bool),ord_less(U_1633),U_1631),U_1632))
      | ~ hBOOL(hAPP(U_1633,bool,hAPP(U_1633,fun(U_1633,bool),ord_less_eq(U_1633),U_1631),U_1632))
      | ti(U_1633,U_1632) = ti(U_1633,U_1631)
      | ~ order(U_1633) ),
    inference(definitional_conversion,[status(esa)],[f_425_2]) ).

cnf(f_425_4,plain,
    ( hBOOL(hAPP(U_1633,bool,hAPP(U_1633,fun(U_1633,bool),ord_less(U_1633),U_1631),U_1632))
    | ~ hBOOL(hAPP(U_1633,bool,hAPP(U_1633,fun(U_1633,bool),ord_less_eq(U_1633),U_1631),U_1632))
    | ti(U_1633,U_1632) = ti(U_1633,U_1631)
    | ~ order(U_1633) ),
    inference(clausify,[status(thm)],[f_425_3]) ).

fof(f_426_1,plain,
    ! [X_a] :
      ( ! [Y,X] :
          ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_373_leD]) ).

fof(f_426_2,plain,
    ! [U_1636] :
      ( ! [U_1635,U_1634] :
          ( ~ hBOOL(hAPP(U_1636,bool,hAPP(U_1636,fun(U_1636,bool),ord_less(U_1636),U_1634),U_1635))
          | ~ hBOOL(hAPP(U_1636,bool,hAPP(U_1636,fun(U_1636,bool),ord_less_eq(U_1636),U_1635),U_1634)) )
      | ~ linorder(U_1636) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

fof(f_426_3,plain,
    ! [U_1634,U_1636,U_1635] :
      ( ~ hBOOL(hAPP(U_1636,bool,hAPP(U_1636,fun(U_1636,bool),ord_less(U_1636),U_1634),U_1635))
      | ~ hBOOL(hAPP(U_1636,bool,hAPP(U_1636,fun(U_1636,bool),ord_less_eq(U_1636),U_1635),U_1634))
      | ~ linorder(U_1636) ),
    inference(definitional_conversion,[status(esa)],[f_426_2]) ).

cnf(f_426_4,plain,
    ( ~ hBOOL(hAPP(U_1636,bool,hAPP(U_1636,fun(U_1636,bool),ord_less(U_1636),U_1634),U_1635))
    | ~ hBOOL(hAPP(U_1636,bool,hAPP(U_1636,fun(U_1636,bool),ord_less_eq(U_1636),U_1635),U_1634))
    | ~ linorder(U_1636) ),
    inference(clausify,[status(thm)],[f_426_3]) ).

fof(f_427_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_374_order__less__imp__le]) ).

fof(f_427_2,plain,
    ! [U_1639] :
      ( ! [U_1638,U_1637] :
          ( hBOOL(hAPP(U_1639,bool,hAPP(U_1639,fun(U_1639,bool),ord_less_eq(U_1639),U_1638),U_1637))
          | ~ hBOOL(hAPP(U_1639,bool,hAPP(U_1639,fun(U_1639,bool),ord_less(U_1639),U_1638),U_1637)) )
      | ~ preorder(U_1639) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

fof(f_427_3,plain,
    ! [U_1639,U_1637,U_1638] :
      ( hBOOL(hAPP(U_1639,bool,hAPP(U_1639,fun(U_1639,bool),ord_less_eq(U_1639),U_1638),U_1637))
      | ~ hBOOL(hAPP(U_1639,bool,hAPP(U_1639,fun(U_1639,bool),ord_less(U_1639),U_1638),U_1637))
      | ~ preorder(U_1639) ),
    inference(definitional_conversion,[status(esa)],[f_427_2]) ).

cnf(f_427_4,plain,
    ( hBOOL(hAPP(U_1639,bool,hAPP(U_1639,fun(U_1639,bool),ord_less_eq(U_1639),U_1638),U_1637))
    | ~ hBOOL(hAPP(U_1639,bool,hAPP(U_1639,fun(U_1639,bool),ord_less(U_1639),U_1638),U_1637))
    | ~ preorder(U_1639) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

fof(f_428_1,plain,
    ! [X_b] :
      ( ! [X_1,Y_1] :
          ( ( ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1))
              | ti(X_b,X_1) != ti(X_b,Y_1) )
            & ( ti(X_b,X_1) = ti(X_b,Y_1)
              | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_1)) ) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)) )
      | ~ linorder(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_375_linorder__antisym__conv2]) ).

fof(f_428_2,plain,
    ! [U_1642] :
      ( ! [U_1641,U_1640] :
          ( ( ( ~ hBOOL(hAPP(U_1642,bool,hAPP(U_1642,fun(U_1642,bool),ord_less(U_1642),U_1641),U_1640))
              | ti(U_1642,U_1641) != ti(U_1642,U_1640) )
            & ( ti(U_1642,U_1641) = ti(U_1642,U_1640)
              | hBOOL(hAPP(U_1642,bool,hAPP(U_1642,fun(U_1642,bool),ord_less(U_1642),U_1641),U_1640)) ) )
          | ~ hBOOL(hAPP(U_1642,bool,hAPP(U_1642,fun(U_1642,bool),ord_less_eq(U_1642),U_1641),U_1640)) )
      | ~ linorder(U_1642) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

fof(f_428_3,plain,
    ( ! [U_1640,U_1641,U_1642] :
        ( ~ hBOOL(hAPP(U_1642,bool,hAPP(U_1642,fun(U_1642,bool),ord_less(U_1642),U_1641),U_1640))
        | ti(U_1642,U_1641) != ti(U_1642,U_1640)
        | ~ sP90(U_1640,U_1641,U_1642) )
    & ! [U_1640,U_1641,U_1642] :
        ( ti(U_1642,U_1641) = ti(U_1642,U_1640)
        | hBOOL(hAPP(U_1642,bool,hAPP(U_1642,fun(U_1642,bool),ord_less(U_1642),U_1641),U_1640))
        | ~ sP90(U_1640,U_1641,U_1642) )
    & ! [U_1640,U_1641,U_1642] :
        ( sP90(U_1640,U_1641,U_1642)
        | ~ hBOOL(hAPP(U_1642,bool,hAPP(U_1642,fun(U_1642,bool),ord_less_eq(U_1642),U_1641),U_1640))
        | ~ linorder(U_1642) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_428_2]) ).

cnf(f_428_4,plain,
    ( sP90(U_1640,U_1641,U_1642)
    | ~ hBOOL(hAPP(U_1642,bool,hAPP(U_1642,fun(U_1642,bool),ord_less_eq(U_1642),U_1641),U_1640))
    | ~ linorder(U_1642) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

cnf(f_428_5,plain,
    ( ti(U_1642,U_1641) = ti(U_1642,U_1640)
    | hBOOL(hAPP(U_1642,bool,hAPP(U_1642,fun(U_1642,bool),ord_less(U_1642),U_1641),U_1640))
    | ~ sP90(U_1640,U_1641,U_1642) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

cnf(f_428_6,plain,
    ( ~ hBOOL(hAPP(U_1642,bool,hAPP(U_1642,fun(U_1642,bool),ord_less(U_1642),U_1641),U_1640))
    | ti(U_1642,U_1641) != ti(U_1642,U_1640)
    | ~ sP90(U_1640,U_1641,U_1642) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

fof(f_429_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( ti(X_a,X) = ti(X_a,Y)
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_376_order__le__imp__less__or__eq]) ).

fof(f_429_2,plain,
    ! [U_1645] :
      ( ! [U_1644,U_1643] :
          ( ti(U_1645,U_1644) = ti(U_1645,U_1643)
          | hBOOL(hAPP(U_1645,bool,hAPP(U_1645,fun(U_1645,bool),ord_less(U_1645),U_1644),U_1643))
          | ~ hBOOL(hAPP(U_1645,bool,hAPP(U_1645,fun(U_1645,bool),ord_less_eq(U_1645),U_1644),U_1643)) )
      | ~ order(U_1645) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

fof(f_429_3,plain,
    ! [U_1643,U_1644,U_1645] :
      ( ti(U_1645,U_1644) = ti(U_1645,U_1643)
      | hBOOL(hAPP(U_1645,bool,hAPP(U_1645,fun(U_1645,bool),ord_less(U_1645),U_1644),U_1643))
      | ~ hBOOL(hAPP(U_1645,bool,hAPP(U_1645,fun(U_1645,bool),ord_less_eq(U_1645),U_1644),U_1643))
      | ~ order(U_1645) ),
    inference(definitional_conversion,[status(esa)],[f_429_2]) ).

cnf(f_429_4,plain,
    ( ti(U_1645,U_1644) = ti(U_1645,U_1643)
    | hBOOL(hAPP(U_1645,bool,hAPP(U_1645,fun(U_1645,bool),ord_less(U_1645),U_1644),U_1643))
    | ~ hBOOL(hAPP(U_1645,bool,hAPP(U_1645,fun(U_1645,bool),ord_less_eq(U_1645),U_1644),U_1643))
    | ~ order(U_1645) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

fof(f_430_1,plain,
    ! [X_a] :
      ( ! [A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1))
          | ti(X_a,A_1) = ti(X_a,B_1)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_377_order__le__neq__trans]) ).

fof(f_430_2,plain,
    ! [U_1648] :
      ( ! [U_1647,U_1646] :
          ( hBOOL(hAPP(U_1648,bool,hAPP(U_1648,fun(U_1648,bool),ord_less(U_1648),U_1647),U_1646))
          | ti(U_1648,U_1647) = ti(U_1648,U_1646)
          | ~ hBOOL(hAPP(U_1648,bool,hAPP(U_1648,fun(U_1648,bool),ord_less_eq(U_1648),U_1647),U_1646)) )
      | ~ order(U_1648) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

fof(f_430_3,plain,
    ! [U_1647,U_1646,U_1648] :
      ( hBOOL(hAPP(U_1648,bool,hAPP(U_1648,fun(U_1648,bool),ord_less(U_1648),U_1647),U_1646))
      | ti(U_1648,U_1647) = ti(U_1648,U_1646)
      | ~ hBOOL(hAPP(U_1648,bool,hAPP(U_1648,fun(U_1648,bool),ord_less_eq(U_1648),U_1647),U_1646))
      | ~ order(U_1648) ),
    inference(definitional_conversion,[status(esa)],[f_430_2]) ).

cnf(f_430_4,plain,
    ( hBOOL(hAPP(U_1648,bool,hAPP(U_1648,fun(U_1648,bool),ord_less(U_1648),U_1647),U_1646))
    | ti(U_1648,U_1647) = ti(U_1648,U_1646)
    | ~ hBOOL(hAPP(U_1648,bool,hAPP(U_1648,fun(U_1648,bool),ord_less_eq(U_1648),U_1647),U_1646))
    | ~ order(U_1648) ),
    inference(clausify,[status(thm)],[f_430_3]) ).

fof(f_431_1,plain,
    ! [X_a] :
      ( ! [B_1,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_1))
          | ti(X_a,A_1) = ti(X_a,B_1)
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_1)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_378_xt1_I11_J]) ).

fof(f_431_2,plain,
    ! [U_1651] :
      ( ! [U_1650,U_1649] :
          ( hBOOL(hAPP(U_1651,bool,hAPP(U_1651,fun(U_1651,bool),ord_less(U_1651),U_1650),U_1649))
          | ti(U_1651,U_1649) = ti(U_1651,U_1650)
          | ~ hBOOL(hAPP(U_1651,bool,hAPP(U_1651,fun(U_1651,bool),ord_less_eq(U_1651),U_1650),U_1649)) )
      | ~ order(U_1651) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

fof(f_431_3,plain,
    ! [U_1650,U_1649,U_1651] :
      ( hBOOL(hAPP(U_1651,bool,hAPP(U_1651,fun(U_1651,bool),ord_less(U_1651),U_1650),U_1649))
      | ti(U_1651,U_1649) = ti(U_1651,U_1650)
      | ~ hBOOL(hAPP(U_1651,bool,hAPP(U_1651,fun(U_1651,bool),ord_less_eq(U_1651),U_1650),U_1649))
      | ~ order(U_1651) ),
    inference(definitional_conversion,[status(esa)],[f_431_2]) ).

cnf(f_431_4,plain,
    ( hBOOL(hAPP(U_1651,bool,hAPP(U_1651,fun(U_1651,bool),ord_less(U_1651),U_1650),U_1649))
    | ti(U_1651,U_1649) = ti(U_1651,U_1650)
    | ~ hBOOL(hAPP(U_1651,bool,hAPP(U_1651,fun(U_1651,bool),ord_less_eq(U_1651),U_1650),U_1649))
    | ~ order(U_1651) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

fof(f_432_1,plain,
    ! [X_a] :
      ( ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_379_order__less__le__trans]) ).

fof(f_432_2,plain,
    ! [U_1655] :
      ( ! [U_1654,U_1653,U_1652] :
          ( hBOOL(hAPP(U_1655,bool,hAPP(U_1655,fun(U_1655,bool),ord_less(U_1655),U_1653),U_1654))
          | ~ hBOOL(hAPP(U_1655,bool,hAPP(U_1655,fun(U_1655,bool),ord_less_eq(U_1655),U_1652),U_1654))
          | ~ hBOOL(hAPP(U_1655,bool,hAPP(U_1655,fun(U_1655,bool),ord_less(U_1655),U_1653),U_1652)) )
      | ~ preorder(U_1655) ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

fof(f_432_3,plain,
    ! [U_1652,U_1655,U_1653,U_1654] :
      ( hBOOL(hAPP(U_1655,bool,hAPP(U_1655,fun(U_1655,bool),ord_less(U_1655),U_1653),U_1654))
      | ~ hBOOL(hAPP(U_1655,bool,hAPP(U_1655,fun(U_1655,bool),ord_less_eq(U_1655),U_1652),U_1654))
      | ~ hBOOL(hAPP(U_1655,bool,hAPP(U_1655,fun(U_1655,bool),ord_less(U_1655),U_1653),U_1652))
      | ~ preorder(U_1655) ),
    inference(definitional_conversion,[status(esa)],[f_432_2]) ).

cnf(f_432_4,plain,
    ( hBOOL(hAPP(U_1655,bool,hAPP(U_1655,fun(U_1655,bool),ord_less(U_1655),U_1653),U_1654))
    | ~ hBOOL(hAPP(U_1655,bool,hAPP(U_1655,fun(U_1655,bool),ord_less_eq(U_1655),U_1652),U_1654))
    | ~ hBOOL(hAPP(U_1655,bool,hAPP(U_1655,fun(U_1655,bool),ord_less(U_1655),U_1653),U_1652))
    | ~ preorder(U_1655) ),
    inference(clausify,[status(thm)],[f_432_3]) ).

fof(f_433_1,plain,
    ! [X_a] :
      ( ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_380_xt1_I7_J]) ).

fof(f_433_2,plain,
    ! [U_1659] :
      ( ! [U_1658,U_1657,U_1656] :
          ( hBOOL(hAPP(U_1659,bool,hAPP(U_1659,fun(U_1659,bool),ord_less(U_1659),U_1658),U_1656))
          | ~ hBOOL(hAPP(U_1659,bool,hAPP(U_1659,fun(U_1659,bool),ord_less_eq(U_1659),U_1658),U_1657))
          | ~ hBOOL(hAPP(U_1659,bool,hAPP(U_1659,fun(U_1659,bool),ord_less(U_1659),U_1657),U_1656)) )
      | ~ order(U_1659) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

fof(f_433_3,plain,
    ! [U_1656,U_1657,U_1659,U_1658] :
      ( hBOOL(hAPP(U_1659,bool,hAPP(U_1659,fun(U_1659,bool),ord_less(U_1659),U_1658),U_1656))
      | ~ hBOOL(hAPP(U_1659,bool,hAPP(U_1659,fun(U_1659,bool),ord_less_eq(U_1659),U_1658),U_1657))
      | ~ hBOOL(hAPP(U_1659,bool,hAPP(U_1659,fun(U_1659,bool),ord_less(U_1659),U_1657),U_1656))
      | ~ order(U_1659) ),
    inference(definitional_conversion,[status(esa)],[f_433_2]) ).

cnf(f_433_4,plain,
    ( hBOOL(hAPP(U_1659,bool,hAPP(U_1659,fun(U_1659,bool),ord_less(U_1659),U_1658),U_1656))
    | ~ hBOOL(hAPP(U_1659,bool,hAPP(U_1659,fun(U_1659,bool),ord_less_eq(U_1659),U_1658),U_1657))
    | ~ hBOOL(hAPP(U_1659,bool,hAPP(U_1659,fun(U_1659,bool),ord_less(U_1659),U_1657),U_1656))
    | ~ order(U_1659) ),
    inference(clausify,[status(thm)],[f_433_3]) ).

fof(f_434_1,plain,
    ! [X_a] :
      ( ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) )
      | ~ preorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_381_order__le__less__trans]) ).

fof(f_434_2,plain,
    ! [U_1663] :
      ( ! [U_1662,U_1661,U_1660] :
          ( hBOOL(hAPP(U_1663,bool,hAPP(U_1663,fun(U_1663,bool),ord_less(U_1663),U_1661),U_1662))
          | ~ hBOOL(hAPP(U_1663,bool,hAPP(U_1663,fun(U_1663,bool),ord_less(U_1663),U_1660),U_1662))
          | ~ hBOOL(hAPP(U_1663,bool,hAPP(U_1663,fun(U_1663,bool),ord_less_eq(U_1663),U_1661),U_1660)) )
      | ~ preorder(U_1663) ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

fof(f_434_3,plain,
    ! [U_1660,U_1663,U_1661,U_1662] :
      ( hBOOL(hAPP(U_1663,bool,hAPP(U_1663,fun(U_1663,bool),ord_less(U_1663),U_1661),U_1662))
      | ~ hBOOL(hAPP(U_1663,bool,hAPP(U_1663,fun(U_1663,bool),ord_less(U_1663),U_1660),U_1662))
      | ~ hBOOL(hAPP(U_1663,bool,hAPP(U_1663,fun(U_1663,bool),ord_less_eq(U_1663),U_1661),U_1660))
      | ~ preorder(U_1663) ),
    inference(definitional_conversion,[status(esa)],[f_434_2]) ).

cnf(f_434_4,plain,
    ( hBOOL(hAPP(U_1663,bool,hAPP(U_1663,fun(U_1663,bool),ord_less(U_1663),U_1661),U_1662))
    | ~ hBOOL(hAPP(U_1663,bool,hAPP(U_1663,fun(U_1663,bool),ord_less(U_1663),U_1660),U_1662))
    | ~ hBOOL(hAPP(U_1663,bool,hAPP(U_1663,fun(U_1663,bool),ord_less_eq(U_1663),U_1661),U_1660))
    | ~ preorder(U_1663) ),
    inference(clausify,[status(thm)],[f_434_3]) ).

fof(f_435_1,plain,
    ! [X_a] :
      ( ! [Z,Y,X] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) )
      | ~ order(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_382_xt1_I8_J]) ).

fof(f_435_2,plain,
    ! [U_1667] :
      ( ! [U_1666,U_1665,U_1664] :
          ( hBOOL(hAPP(U_1667,bool,hAPP(U_1667,fun(U_1667,bool),ord_less(U_1667),U_1666),U_1664))
          | ~ hBOOL(hAPP(U_1667,bool,hAPP(U_1667,fun(U_1667,bool),ord_less(U_1667),U_1666),U_1665))
          | ~ hBOOL(hAPP(U_1667,bool,hAPP(U_1667,fun(U_1667,bool),ord_less_eq(U_1667),U_1665),U_1664)) )
      | ~ order(U_1667) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

fof(f_435_3,plain,
    ! [U_1664,U_1665,U_1667,U_1666] :
      ( hBOOL(hAPP(U_1667,bool,hAPP(U_1667,fun(U_1667,bool),ord_less(U_1667),U_1666),U_1664))
      | ~ hBOOL(hAPP(U_1667,bool,hAPP(U_1667,fun(U_1667,bool),ord_less(U_1667),U_1666),U_1665))
      | ~ hBOOL(hAPP(U_1667,bool,hAPP(U_1667,fun(U_1667,bool),ord_less_eq(U_1667),U_1665),U_1664))
      | ~ order(U_1667) ),
    inference(definitional_conversion,[status(esa)],[f_435_2]) ).

cnf(f_435_4,plain,
    ( hBOOL(hAPP(U_1667,bool,hAPP(U_1667,fun(U_1667,bool),ord_less(U_1667),U_1666),U_1664))
    | ~ hBOOL(hAPP(U_1667,bool,hAPP(U_1667,fun(U_1667,bool),ord_less(U_1667),U_1666),U_1665))
    | ~ hBOOL(hAPP(U_1667,bool,hAPP(U_1667,fun(U_1667,bool),ord_less_eq(U_1667),U_1665),U_1664))
    | ~ order(U_1667) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

fof(f_436_1,plain,
    ! [N_1] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_1))
        | ! [M_2] :
          ? [X_2] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_1)) ) )
      & ( ? [M_2] :
          ! [X_2] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_1)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_383_finite__nat__set__iff__bounded]) ).

fof(f_436_2,plain,
    ! [U_1672] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1672))
        | ! [U_1671] :
          ? [U_1670] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1670),U_1671))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1670),U_1672)) ) )
      & ( ? [U_1669] :
          ! [U_1668] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1668),U_1669))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1668),U_1672)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1672)) ) ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

fof(f_436_3,plain,
    ( ! [U_1674] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1674))
        | ! [U_1671] :
          ? [U_1670] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1670),U_1671))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1670),U_1674)) ) )
    & ! [U_1673] :
        ( ? [U_1669] :
          ! [U_1668] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1668),U_1669))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1668),U_1673)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1673)) ) ),
    inference(miniscope,[status(thm)],[f_436_2]) ).

fof(f_436_4,plain,
    ( ! [U_1674] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1674))
        | ! [U_1671] :
          ? [U_1670] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1670),U_1671))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1670),U_1674)) ) )
    & ! [U_1673] :
        ( ! [U_1668] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1668),sK45(U_1673)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1668),U_1673)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1673)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_1669,sK45(U_1673))],[f_436_3]) ).

fof(f_436_5,plain,
    ( ! [U_1674] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1674))
        | ! [U_1671] :
            ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK46(U_1674,U_1671)),U_1671))
            & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK46(U_1674,U_1671)),U_1674)) ) )
    & ! [U_1673] :
        ( ! [U_1668] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1668),sK45(U_1673)))
            | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1668),U_1673)) )
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1673)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_1670,sK46(U_1674,U_1671))],[f_436_4]) ).

fof(f_436_6,plain,
    ( ! [U_1671,U_1674] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK46(U_1674,U_1671)),U_1671))
        | ~ sP91(U_1671,U_1674) )
    & ! [U_1671,U_1674] :
        ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK46(U_1674,U_1671)),U_1674))
        | ~ sP91(U_1671,U_1674) )
    & ! [U_1671,U_1674] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1674))
        | sP91(U_1671,U_1674) )
    & ! [U_1668,U_1673] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1668),sK45(U_1673)))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1668),U_1673))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1673)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_436_5]) ).

cnf(f_436_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1668),sK45(U_1673)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1668),U_1673))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1673)) ),
    inference(clausify,[status(thm)],[f_436_6]) ).

cnf(f_436_8,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1674))
    | sP91(U_1671,U_1674) ),
    inference(clausify,[status(thm)],[f_436_6]) ).

cnf(f_436_9,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK46(U_1674,U_1671)),U_1674))
    | ~ sP91(U_1671,U_1674) ),
    inference(clausify,[status(thm)],[f_436_6]) ).

cnf(f_436_10,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK46(U_1674,U_1671)),U_1671))
    | ~ sP91(U_1671,U_1674) ),
    inference(clausify,[status(thm)],[f_436_6]) ).

fof(f_437_1,plain,
    ! [X_b,A_3,F,Na] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ti(fun(X_b,bool),A_3) != hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na))) ),
    inference(fof_nnf,[status(thm)],[fact_384_nat__seg__image__imp__finite]) ).

fof(f_437_2,plain,
    ! [U_1678,U_1677,U_1676,U_1675] :
      ( hBOOL(hAPP(fun(U_1678,bool),bool,finite_finite(U_1678),U_1677))
      | ti(fun(U_1678,bool),U_1677) != hAPP(fun(nat,bool),fun(U_1678,bool),hAPP(fun(nat,U_1678),fun(fun(nat,bool),fun(U_1678,bool)),image(nat,U_1678),U_1676),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1675))) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

fof(f_437_3,plain,
    ! [U_1678,U_1677] :
      ( ! [U_1676,U_1675] : ti(fun(U_1678,bool),U_1677) != hAPP(fun(nat,bool),fun(U_1678,bool),hAPP(fun(nat,U_1678),fun(fun(nat,bool),fun(U_1678,bool)),image(nat,U_1678),U_1676),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1675)))
      | hBOOL(hAPP(fun(U_1678,bool),bool,finite_finite(U_1678),U_1677)) ),
    inference(miniscope,[status(thm)],[f_437_2]) ).

fof(f_437_4,plain,
    ! [U_1677,U_1676,U_1678,U_1675] :
      ( ti(fun(U_1678,bool),U_1677) != hAPP(fun(nat,bool),fun(U_1678,bool),hAPP(fun(nat,U_1678),fun(fun(nat,bool),fun(U_1678,bool)),image(nat,U_1678),U_1676),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1675)))
      | hBOOL(hAPP(fun(U_1678,bool),bool,finite_finite(U_1678),U_1677)) ),
    inference(definitional_conversion,[status(esa)],[f_437_3]) ).

cnf(f_437_5,plain,
    ( ti(fun(U_1678,bool),U_1677) != hAPP(fun(nat,bool),fun(U_1678,bool),hAPP(fun(nat,U_1678),fun(fun(nat,bool),fun(U_1678,bool)),image(nat,U_1678),U_1676),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1675)))
    | hBOOL(hAPP(fun(U_1678,bool),bool,finite_finite(U_1678),U_1677)) ),
    inference(clausify,[status(thm)],[f_437_4]) ).

fof(f_438_1,plain,
    ! [Na] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),Na))) = Na,
    inference(fof_nnf,[status(thm)],[fact_385_card__Collect__less__nat]) ).

fof(f_438_2,plain,
    ! [U_1679] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1679))) = U_1679,
    inference(variable_rename,[status(thm)],[f_438_1]) ).

fof(f_438_3,plain,
    ! [U_1679] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1679))) = U_1679,
    inference(definitional_conversion,[status(esa)],[f_438_2]) ).

cnf(f_438_4,plain,
    hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1679))) = U_1679,
    inference(clausify,[status(thm)],[f_438_3]) ).

fof(f_439_1,plain,
    ! [Pa,I_1] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),Pa)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1))))),
    inference(fof_nnf,[status(thm)],[fact_386_finite__M__bounded__by__nat]) ).

fof(f_439_2,plain,
    ! [U_1681,U_1680] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),U_1681)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1680))))),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

fof(f_439_3,plain,
    ! [U_1680,U_1681] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),U_1681)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1680))))),
    inference(definitional_conversion,[status(esa)],[f_439_2]) ).

cnf(f_439_4,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),U_1681)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1680))))),
    inference(clausify,[status(thm)],[f_439_3]) ).

fof(f_440_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B_1)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_387_add__le__less__mono]) ).

fof(f_440_2,plain,
    ! [U_1686] :
      ( ! [U_1685,U_1684,U_1683,U_1682] :
          ( hBOOL(hAPP(U_1686,bool,hAPP(U_1686,fun(U_1686,bool),ord_less(U_1686),hAPP(U_1686,U_1686,hAPP(U_1686,fun(U_1686,U_1686),plus_plus(U_1686),U_1683),U_1685)),hAPP(U_1686,U_1686,hAPP(U_1686,fun(U_1686,U_1686),plus_plus(U_1686),U_1682),U_1684)))
          | ~ hBOOL(hAPP(U_1686,bool,hAPP(U_1686,fun(U_1686,bool),ord_less(U_1686),U_1685),U_1684))
          | ~ hBOOL(hAPP(U_1686,bool,hAPP(U_1686,fun(U_1686,bool),ord_less_eq(U_1686),U_1683),U_1682)) )
      | ~ ordere223160158up_add(U_1686) ),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

fof(f_440_3,plain,
    ! [U_1682,U_1686,U_1683,U_1684,U_1685] :
      ( hBOOL(hAPP(U_1686,bool,hAPP(U_1686,fun(U_1686,bool),ord_less(U_1686),hAPP(U_1686,U_1686,hAPP(U_1686,fun(U_1686,U_1686),plus_plus(U_1686),U_1683),U_1685)),hAPP(U_1686,U_1686,hAPP(U_1686,fun(U_1686,U_1686),plus_plus(U_1686),U_1682),U_1684)))
      | ~ hBOOL(hAPP(U_1686,bool,hAPP(U_1686,fun(U_1686,bool),ord_less(U_1686),U_1685),U_1684))
      | ~ hBOOL(hAPP(U_1686,bool,hAPP(U_1686,fun(U_1686,bool),ord_less_eq(U_1686),U_1683),U_1682))
      | ~ ordere223160158up_add(U_1686) ),
    inference(definitional_conversion,[status(esa)],[f_440_2]) ).

cnf(f_440_4,plain,
    ( hBOOL(hAPP(U_1686,bool,hAPP(U_1686,fun(U_1686,bool),ord_less(U_1686),hAPP(U_1686,U_1686,hAPP(U_1686,fun(U_1686,U_1686),plus_plus(U_1686),U_1683),U_1685)),hAPP(U_1686,U_1686,hAPP(U_1686,fun(U_1686,U_1686),plus_plus(U_1686),U_1682),U_1684)))
    | ~ hBOOL(hAPP(U_1686,bool,hAPP(U_1686,fun(U_1686,bool),ord_less(U_1686),U_1685),U_1684))
    | ~ hBOOL(hAPP(U_1686,bool,hAPP(U_1686,fun(U_1686,bool),ord_less_eq(U_1686),U_1683),U_1682))
    | ~ ordere223160158up_add(U_1686) ),
    inference(clausify,[status(thm)],[f_440_3]) ).

fof(f_441_1,plain,
    ! [X_a] :
      ( ! [C,D,A_1,B_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),D)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B_1)) )
      | ~ ordere223160158up_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_388_add__less__le__mono]) ).

fof(f_441_2,plain,
    ! [U_1691] :
      ( ! [U_1690,U_1689,U_1688,U_1687] :
          ( hBOOL(hAPP(U_1691,bool,hAPP(U_1691,fun(U_1691,bool),ord_less(U_1691),hAPP(U_1691,U_1691,hAPP(U_1691,fun(U_1691,U_1691),plus_plus(U_1691),U_1688),U_1690)),hAPP(U_1691,U_1691,hAPP(U_1691,fun(U_1691,U_1691),plus_plus(U_1691),U_1687),U_1689)))
          | ~ hBOOL(hAPP(U_1691,bool,hAPP(U_1691,fun(U_1691,bool),ord_less_eq(U_1691),U_1690),U_1689))
          | ~ hBOOL(hAPP(U_1691,bool,hAPP(U_1691,fun(U_1691,bool),ord_less(U_1691),U_1688),U_1687)) )
      | ~ ordere223160158up_add(U_1691) ),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

fof(f_441_3,plain,
    ! [U_1689,U_1691,U_1688,U_1687,U_1690] :
      ( hBOOL(hAPP(U_1691,bool,hAPP(U_1691,fun(U_1691,bool),ord_less(U_1691),hAPP(U_1691,U_1691,hAPP(U_1691,fun(U_1691,U_1691),plus_plus(U_1691),U_1688),U_1690)),hAPP(U_1691,U_1691,hAPP(U_1691,fun(U_1691,U_1691),plus_plus(U_1691),U_1687),U_1689)))
      | ~ hBOOL(hAPP(U_1691,bool,hAPP(U_1691,fun(U_1691,bool),ord_less_eq(U_1691),U_1690),U_1689))
      | ~ hBOOL(hAPP(U_1691,bool,hAPP(U_1691,fun(U_1691,bool),ord_less(U_1691),U_1688),U_1687))
      | ~ ordere223160158up_add(U_1691) ),
    inference(definitional_conversion,[status(esa)],[f_441_2]) ).

cnf(f_441_4,plain,
    ( hBOOL(hAPP(U_1691,bool,hAPP(U_1691,fun(U_1691,bool),ord_less(U_1691),hAPP(U_1691,U_1691,hAPP(U_1691,fun(U_1691,U_1691),plus_plus(U_1691),U_1688),U_1690)),hAPP(U_1691,U_1691,hAPP(U_1691,fun(U_1691,U_1691),plus_plus(U_1691),U_1687),U_1689)))
    | ~ hBOOL(hAPP(U_1691,bool,hAPP(U_1691,fun(U_1691,bool),ord_less_eq(U_1691),U_1690),U_1689))
    | ~ hBOOL(hAPP(U_1691,bool,hAPP(U_1691,fun(U_1691,bool),ord_less(U_1691),U_1688),U_1687))
    | ~ ordere223160158up_add(U_1691) ),
    inference(clausify,[status(thm)],[f_441_3]) ).

fof(f_442_1,plain,
    ! [I,M] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),M)))),
    inference(fof_nnf,[status(thm)],[fact_389_less__add__Suc1]) ).

fof(f_442_2,plain,
    ! [U_1693,U_1692] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1693),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1693),U_1692)))),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

fof(f_442_3,plain,
    ! [U_1692,U_1693] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1693),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1693),U_1692)))),
    inference(definitional_conversion,[status(esa)],[f_442_2]) ).

cnf(f_442_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1693),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1693),U_1692)))),
    inference(clausify,[status(thm)],[f_442_3]) ).

fof(f_443_1,plain,
    ! [I,M] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I)))),
    inference(fof_nnf,[status(thm)],[fact_390_less__add__Suc2]) ).

fof(f_443_2,plain,
    ! [U_1695,U_1694] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1695),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1694),U_1695)))),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

fof(f_443_3,plain,
    ! [U_1695,U_1694] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1695),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1694),U_1695)))),
    inference(definitional_conversion,[status(esa)],[f_443_2]) ).

cnf(f_443_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1695),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1694),U_1695)))),
    inference(clausify,[status(thm)],[f_443_3]) ).

fof(f_444_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
        | ! [K_1] : Na != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)) )
      & ( ? [K_1] : Na = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_391_less__iff__Suc__add]) ).

fof(f_444_2,plain,
    ! [U_1699,U_1698] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1699),U_1698))
        | ! [U_1697] : U_1698 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1699),U_1697)) )
      & ( ? [U_1696] : U_1698 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1699),U_1696))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1699),U_1698)) ) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

fof(f_444_3,plain,
    ( ! [U_1703,U_1701] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1703),U_1701))
        | ! [U_1697] : U_1701 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1703),U_1697)) )
    & ! [U_1702,U_1700] :
        ( ? [U_1696] : U_1700 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1702),U_1696))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1702),U_1700)) ) ),
    inference(miniscope,[status(thm)],[f_444_2]) ).

fof(f_444_4,plain,
    ( ! [U_1703,U_1701] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1703),U_1701))
        | ! [U_1697] : U_1701 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1703),U_1697)) )
    & ! [U_1702,U_1700] :
        ( U_1700 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1702),sK47(U_1702,U_1700)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1702),U_1700)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_1696,sK47(U_1702,U_1700))],[f_444_3]) ).

fof(f_444_5,plain,
    ( ! [U_1701,U_1697,U_1703] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1703),U_1701))
        | U_1701 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1703),U_1697)) )
    & ! [U_1700,U_1702] :
        ( U_1700 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1702),sK47(U_1702,U_1700)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1702),U_1700)) ) ),
    inference(definitional_conversion,[status(esa)],[f_444_4]) ).

cnf(f_444_6,plain,
    ( U_1700 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1702),sK47(U_1702,U_1700)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1702),U_1700)) ),
    inference(clausify,[status(thm)],[f_444_5]) ).

cnf(f_444_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1703),U_1701))
    | U_1701 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1703),U_1697)) ),
    inference(clausify,[status(thm)],[f_444_5]) ).

fof(f_445_1,plain,
    ! [Na,M_1] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_1)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_1))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_392_less__eq__Suc__le]) ).

fof(f_445_2,plain,
    ! [U_1705,U_1704] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1705),U_1704))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1705)),U_1704)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1705)),U_1704))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1705),U_1704)) ) ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

fof(f_445_3,plain,
    ( ! [U_1709,U_1707] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1709),U_1707))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1709)),U_1707)) )
    & ! [U_1708,U_1706] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1708)),U_1706))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1708),U_1706)) ) ),
    inference(miniscope,[status(thm)],[f_445_2]) ).

fof(f_445_4,plain,
    ( ! [U_1707,U_1709] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1709),U_1707))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1709)),U_1707)) )
    & ! [U_1706,U_1708] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1708)),U_1706))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1708),U_1706)) ) ),
    inference(definitional_conversion,[status(esa)],[f_445_3]) ).

cnf(f_445_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1708)),U_1706))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1708),U_1706)) ),
    inference(clausify,[status(thm)],[f_445_4]) ).

cnf(f_445_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1709),U_1707))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1709)),U_1707)) ),
    inference(clausify,[status(thm)],[f_445_4]) ).

fof(f_446_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,Na)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_393_less__Suc__eq__le]) ).

fof(f_446_2,plain,
    ! [U_1711,U_1710] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1711),hAPP(nat,nat,suc,U_1710)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1711),U_1710)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1711),U_1710))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1711),hAPP(nat,nat,suc,U_1710))) ) ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

fof(f_446_3,plain,
    ( ! [U_1715,U_1713] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1715),hAPP(nat,nat,suc,U_1713)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1715),U_1713)) )
    & ! [U_1714,U_1712] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1714),U_1712))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1714),hAPP(nat,nat,suc,U_1712))) ) ),
    inference(miniscope,[status(thm)],[f_446_2]) ).

fof(f_446_4,plain,
    ( ! [U_1715,U_1713] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1715),hAPP(nat,nat,suc,U_1713)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1715),U_1713)) )
    & ! [U_1712,U_1714] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1714),U_1712))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1714),hAPP(nat,nat,suc,U_1712))) ) ),
    inference(definitional_conversion,[status(esa)],[f_446_3]) ).

cnf(f_446_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1714),U_1712))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1714),hAPP(nat,nat,suc,U_1712))) ),
    inference(clausify,[status(thm)],[f_446_4]) ).

cnf(f_446_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1715),hAPP(nat,nat,suc,U_1713)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1715),U_1713)) ),
    inference(clausify,[status(thm)],[f_446_4]) ).

fof(f_447_1,plain,
    ! [M_1,Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_394_Suc__le__eq]) ).

fof(f_447_2,plain,
    ! [U_1717,U_1716] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1717)),U_1716))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1717),U_1716)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1717),U_1716))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1717)),U_1716)) ) ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

fof(f_447_3,plain,
    ( ! [U_1721,U_1719] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1721)),U_1719))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1721),U_1719)) )
    & ! [U_1720,U_1718] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1720),U_1718))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1720)),U_1718)) ) ),
    inference(miniscope,[status(thm)],[f_447_2]) ).

fof(f_447_4,plain,
    ( ! [U_1719,U_1721] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1721)),U_1719))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1721),U_1719)) )
    & ! [U_1720,U_1718] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1720),U_1718))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1720)),U_1718)) ) ),
    inference(definitional_conversion,[status(esa)],[f_447_3]) ).

cnf(f_447_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1720),U_1718))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1720)),U_1718)) ),
    inference(clausify,[status(thm)],[f_447_4]) ).

cnf(f_447_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1721)),U_1719))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1721),U_1719)) ),
    inference(clausify,[status(thm)],[f_447_4]) ).

fof(f_448_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_395_le__imp__less__Suc]) ).

fof(f_448_2,plain,
    ! [U_1723,U_1722] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1723),hAPP(nat,nat,suc,U_1722)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1723),U_1722)) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

fof(f_448_3,plain,
    ! [U_1722,U_1723] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1723),hAPP(nat,nat,suc,U_1722)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1723),U_1722)) ),
    inference(definitional_conversion,[status(esa)],[f_448_2]) ).

cnf(f_448_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1723),hAPP(nat,nat,suc,U_1722)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1723),U_1722)) ),
    inference(clausify,[status(thm)],[f_448_3]) ).

fof(f_449_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_396_Suc__leI]) ).

fof(f_449_2,plain,
    ! [U_1725,U_1724] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1725)),U_1724))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1725),U_1724)) ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

fof(f_449_3,plain,
    ! [U_1724,U_1725] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1725)),U_1724))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1725),U_1724)) ),
    inference(definitional_conversion,[status(esa)],[f_449_2]) ).

cnf(f_449_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1725)),U_1724))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1725),U_1724)) ),
    inference(clausify,[status(thm)],[f_449_3]) ).

fof(f_450_1,plain,
    ! [M_1,Na] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_1)))
          | Na != M_1 )
        & ( Na = M_1
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),hAPP(nat,nat,suc,M_1))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) ),
    inference(fof_nnf,[status(thm)],[fact_397_le__less__Suc__eq]) ).

fof(f_450_2,plain,
    ! [U_1727,U_1726] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1726),hAPP(nat,nat,suc,U_1727)))
          | U_1726 != U_1727 )
        & ( U_1726 = U_1727
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1726),hAPP(nat,nat,suc,U_1727))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1727),U_1726)) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

fof(f_450_3,plain,
    ( ! [U_1727,U_1726] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1726),hAPP(nat,nat,suc,U_1727)))
        | U_1726 != U_1727
        | ~ sP92(U_1727,U_1726) )
    & ! [U_1727,U_1726] :
        ( U_1726 = U_1727
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1726),hAPP(nat,nat,suc,U_1727)))
        | ~ sP92(U_1727,U_1726) )
    & ! [U_1727,U_1726] :
        ( sP92(U_1727,U_1726)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1727),U_1726)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92])],[f_450_2]) ).

cnf(f_450_4,plain,
    ( sP92(U_1727,U_1726)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1727),U_1726)) ),
    inference(clausify,[status(thm)],[f_450_3]) ).

cnf(f_450_5,plain,
    ( U_1726 = U_1727
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1726),hAPP(nat,nat,suc,U_1727)))
    | ~ sP92(U_1727,U_1726) ),
    inference(clausify,[status(thm)],[f_450_3]) ).

cnf(f_450_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1726),hAPP(nat,nat,suc,U_1727)))
    | U_1726 != U_1727
    | ~ sP92(U_1727,U_1726) ),
    inference(clausify,[status(thm)],[f_450_3]) ).

fof(f_451_1,plain,
    ! [M,N] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_398_Suc__le__lessD]) ).

fof(f_451_2,plain,
    ! [U_1729,U_1728] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1729),U_1728))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1729)),U_1728)) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

fof(f_451_3,plain,
    ! [U_1729,U_1728] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1729),U_1728))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1729)),U_1728)) ),
    inference(definitional_conversion,[status(esa)],[f_451_2]) ).

cnf(f_451_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1729),U_1728))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1729)),U_1728)) ),
    inference(clausify,[status(thm)],[f_451_3]) ).

fof(f_452_1,plain,
    ! [M,N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),hAPP(nat,nat,suc,M))),
    inference(fof_nnf,[status(thm)],[fact_399_diff__less__Suc]) ).

fof(f_452_2,plain,
    ! [U_1731,U_1730] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1731),U_1730)),hAPP(nat,nat,suc,U_1731))),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

fof(f_452_3,plain,
    ! [U_1730,U_1731] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1731),U_1730)),hAPP(nat,nat,suc,U_1731))),
    inference(definitional_conversion,[status(esa)],[f_452_2]) ).

cnf(f_452_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1731),U_1730)),hAPP(nat,nat,suc,U_1731))),
    inference(clausify,[status(thm)],[f_452_3]) ).

fof(f_453_1,plain,
    ! [M,N] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_400_add__diff__inverse]) ).

fof(f_453_2,plain,
    ! [U_1733,U_1732] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1732),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1733),U_1732)) = U_1733
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1733),U_1732)) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

fof(f_453_3,plain,
    ! [U_1733,U_1732] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1732),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1733),U_1732)) = U_1733
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1733),U_1732)) ),
    inference(definitional_conversion,[status(esa)],[f_453_2]) ).

cnf(f_453_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1732),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1733),U_1732)) = U_1733
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1733),U_1732)) ),
    inference(clausify,[status(thm)],[f_453_3]) ).

fof(f_454_1,plain,
    ! [I_1,J_1,K_2] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_2)),J_1)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_2)),J_1))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_401_less__diff__conv]) ).

fof(f_454_2,plain,
    ! [U_1736,U_1735,U_1734] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1736),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1735),U_1734)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1736),U_1734)),U_1735)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1736),U_1734)),U_1735))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1736),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1735),U_1734))) ) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

fof(f_454_3,plain,
    ( ! [U_1742,U_1740,U_1738] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1742),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1740),U_1738)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1742),U_1738)),U_1740)) )
    & ! [U_1741,U_1739,U_1737] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1741),U_1737)),U_1739))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1741),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1739),U_1737))) ) ),
    inference(miniscope,[status(thm)],[f_454_2]) ).

fof(f_454_4,plain,
    ( ! [U_1740,U_1738,U_1742] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1742),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1740),U_1738)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1742),U_1738)),U_1740)) )
    & ! [U_1739,U_1737,U_1741] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1741),U_1737)),U_1739))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1741),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1739),U_1737))) ) ),
    inference(definitional_conversion,[status(esa)],[f_454_3]) ).

cnf(f_454_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1741),U_1737)),U_1739))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1741),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1739),U_1737))) ),
    inference(clausify,[status(thm)],[f_454_4]) ).

cnf(f_454_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1742),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1740),U_1738)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1742),U_1738)),U_1740)) ),
    inference(clausify,[status(thm)],[f_454_4]) ).

fof(f_455_1,plain,
    ! [C,A_1,B_1] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B_1),C)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B_1)) ),
    inference(fof_nnf,[status(thm)],[fact_402_diff__less__mono]) ).

fof(f_455_2,plain,
    ! [U_1745,U_1744,U_1743] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1744),U_1745)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1743),U_1745)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1745),U_1744))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1744),U_1743)) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

fof(f_455_3,plain,
    ! [U_1743,U_1744,U_1745] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1744),U_1745)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1743),U_1745)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1745),U_1744))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1744),U_1743)) ),
    inference(definitional_conversion,[status(esa)],[f_455_2]) ).

cnf(f_455_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1744),U_1745)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1743),U_1745)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1745),U_1744))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1744),U_1743)) ),
    inference(clausify,[status(thm)],[f_455_3]) ).

fof(f_456_1,plain,
    ! [Na,K_2,M_1] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K_2)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),Na))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K_2))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),Na))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_2),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_403_less__diff__iff]) ).

fof(f_456_2,plain,
    ! [U_1748,U_1747,U_1746] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1746),U_1747)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1748),U_1747)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1746),U_1748)) )
        & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1746),U_1748))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1746),U_1747)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1748),U_1747))) ) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1747),U_1748))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1747),U_1746)) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

fof(f_456_3,plain,
    ( ! [U_1746,U_1747,U_1748] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1746),U_1747)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1748),U_1747)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1746),U_1748))
        | ~ sP93(U_1746,U_1747,U_1748) )
    & ! [U_1746,U_1747,U_1748] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1746),U_1748))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1746),U_1747)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1748),U_1747)))
        | ~ sP93(U_1746,U_1747,U_1748) )
    & ! [U_1746,U_1747,U_1748] :
        ( sP93(U_1746,U_1747,U_1748)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1747),U_1748))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1747),U_1746)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP93])],[f_456_2]) ).

cnf(f_456_4,plain,
    ( sP93(U_1746,U_1747,U_1748)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1747),U_1748))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1747),U_1746)) ),
    inference(clausify,[status(thm)],[f_456_3]) ).

cnf(f_456_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1746),U_1748))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1746),U_1747)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1748),U_1747)))
    | ~ sP93(U_1746,U_1747,U_1748) ),
    inference(clausify,[status(thm)],[f_456_3]) ).

cnf(f_456_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1746),U_1747)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1748),U_1747)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1746),U_1748))
    | ~ sP93(U_1746,U_1747,U_1748) ),
    inference(clausify,[status(thm)],[f_456_3]) ).

fof(f_457_1,plain,
    ! [X_2] : hAPP(nat,fun(nat,bool),ord_less(nat),X_2) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_2)),
    inference(fof_nnf,[status(thm)],[fact_404_less__eq__Suc__le__raw]) ).

fof(f_457_2,plain,
    ! [U_1749] : hAPP(nat,fun(nat,bool),ord_less(nat),U_1749) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1749)),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

fof(f_457_3,plain,
    ! [U_1749] : hAPP(nat,fun(nat,bool),ord_less(nat),U_1749) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1749)),
    inference(definitional_conversion,[status(esa)],[f_457_2]) ).

cnf(f_457_4,plain,
    hAPP(nat,fun(nat,bool),ord_less(nat),U_1749) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,U_1749)),
    inference(clausify,[status(thm)],[f_457_3]) ).

fof(f_458_1,plain,
    ! [M_1,K_2,F] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M_1)),K_2)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_2))))
      | ? [M_2,N_2] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_2)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_405_mono__nat__linear__lb]) ).

fof(f_458_2,plain,
    ! [U_1754,U_1753,U_1752] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,U_1752,U_1754)),U_1753)),hAPP(nat,nat,U_1752,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1754),U_1753))))
      | ? [U_1751,U_1750] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1752,U_1751)),hAPP(nat,nat,U_1752,U_1750)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1751),U_1750)) ) ),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

fof(f_458_3,plain,
    ! [U_1754,U_1753,U_1752] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,U_1752,U_1754)),U_1753)),hAPP(nat,nat,U_1752,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1754),U_1753))))
      | ? [U_1750] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1752,sK48(U_1754,U_1753,U_1752))),hAPP(nat,nat,U_1752,U_1750)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK48(U_1754,U_1753,U_1752)),U_1750)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_1751,sK48(U_1754,U_1753,U_1752))],[f_458_2]) ).

fof(f_458_4,plain,
    ! [U_1754,U_1753,U_1752] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,U_1752,U_1754)),U_1753)),hAPP(nat,nat,U_1752,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1754),U_1753))))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1752,sK48(U_1754,U_1753,U_1752))),hAPP(nat,nat,U_1752,sK49(U_1754,U_1753,U_1752))))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK48(U_1754,U_1753,U_1752)),sK49(U_1754,U_1753,U_1752))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_1750,sK49(U_1754,U_1753,U_1752))],[f_458_3]) ).

fof(f_458_5,plain,
    ( ! [U_1752,U_1753,U_1754] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1752,sK48(U_1754,U_1753,U_1752))),hAPP(nat,nat,U_1752,sK49(U_1754,U_1753,U_1752))))
        | ~ sP94(U_1752,U_1753,U_1754) )
    & ! [U_1752,U_1753,U_1754] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK48(U_1754,U_1753,U_1752)),sK49(U_1754,U_1753,U_1752)))
        | ~ sP94(U_1752,U_1753,U_1754) )
    & ! [U_1752,U_1753,U_1754] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,U_1752,U_1754)),U_1753)),hAPP(nat,nat,U_1752,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1754),U_1753))))
        | sP94(U_1752,U_1753,U_1754) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94])],[f_458_4]) ).

cnf(f_458_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,U_1752,U_1754)),U_1753)),hAPP(nat,nat,U_1752,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1754),U_1753))))
    | sP94(U_1752,U_1753,U_1754) ),
    inference(clausify,[status(thm)],[f_458_5]) ).

cnf(f_458_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK48(U_1754,U_1753,U_1752)),sK49(U_1754,U_1753,U_1752)))
    | ~ sP94(U_1752,U_1753,U_1754) ),
    inference(clausify,[status(thm)],[f_458_5]) ).

cnf(f_458_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1752,sK48(U_1754,U_1753,U_1752))),hAPP(nat,nat,U_1752,sK49(U_1754,U_1753,U_1752))))
    | ~ sP94(U_1752,U_1753,U_1754) ),
    inference(clausify,[status(thm)],[f_458_5]) ).

fof(f_459_1,plain,
    ! [Pa,I_1,J_1] :
      ( hBOOL(hAPP(nat,bool,Pa,I_1))
      | ? [I_2] :
          ( ~ hBOOL(hAPP(nat,bool,Pa,I_2))
          & hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,I_2)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) )
      | ~ hBOOL(hAPP(nat,bool,Pa,J_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_406_inc__induct]) ).

fof(f_459_2,plain,
    ! [U_1758,U_1757,U_1756] :
      ( hBOOL(hAPP(nat,bool,U_1758,U_1757))
      | ? [U_1755] :
          ( ~ hBOOL(hAPP(nat,bool,U_1758,U_1755))
          & hBOOL(hAPP(nat,bool,U_1758,hAPP(nat,nat,suc,U_1755)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1755),U_1756)) )
      | ~ hBOOL(hAPP(nat,bool,U_1758,U_1756))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1757),U_1756)) ),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

fof(f_459_3,plain,
    ! [U_1758,U_1757,U_1756] :
      ( hBOOL(hAPP(nat,bool,U_1758,U_1757))
      | ( ~ hBOOL(hAPP(nat,bool,U_1758,sK50(U_1758,U_1757,U_1756)))
        & hBOOL(hAPP(nat,bool,U_1758,hAPP(nat,nat,suc,sK50(U_1758,U_1757,U_1756))))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK50(U_1758,U_1757,U_1756)),U_1756)) )
      | ~ hBOOL(hAPP(nat,bool,U_1758,U_1756))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1757),U_1756)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_1755,sK50(U_1758,U_1757,U_1756))],[f_459_2]) ).

fof(f_459_4,plain,
    ( ! [U_1758,U_1756,U_1757] :
        ( ~ hBOOL(hAPP(nat,bool,U_1758,sK50(U_1758,U_1757,U_1756)))
        | ~ sP95(U_1758,U_1756,U_1757) )
    & ! [U_1758,U_1756,U_1757] :
        ( hBOOL(hAPP(nat,bool,U_1758,hAPP(nat,nat,suc,sK50(U_1758,U_1757,U_1756))))
        | ~ sP95(U_1758,U_1756,U_1757) )
    & ! [U_1758,U_1756,U_1757] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK50(U_1758,U_1757,U_1756)),U_1756))
        | ~ sP95(U_1758,U_1756,U_1757) )
    & ! [U_1758,U_1756,U_1757] :
        ( hBOOL(hAPP(nat,bool,U_1758,U_1757))
        | sP95(U_1758,U_1756,U_1757)
        | ~ hBOOL(hAPP(nat,bool,U_1758,U_1756))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1757),U_1756)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95])],[f_459_3]) ).

cnf(f_459_5,plain,
    ( hBOOL(hAPP(nat,bool,U_1758,U_1757))
    | sP95(U_1758,U_1756,U_1757)
    | ~ hBOOL(hAPP(nat,bool,U_1758,U_1756))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1757),U_1756)) ),
    inference(clausify,[status(thm)],[f_459_4]) ).

cnf(f_459_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK50(U_1758,U_1757,U_1756)),U_1756))
    | ~ sP95(U_1758,U_1756,U_1757) ),
    inference(clausify,[status(thm)],[f_459_4]) ).

cnf(f_459_7,plain,
    ( hBOOL(hAPP(nat,bool,U_1758,hAPP(nat,nat,suc,sK50(U_1758,U_1757,U_1756))))
    | ~ sP95(U_1758,U_1756,U_1757) ),
    inference(clausify,[status(thm)],[f_459_4]) ).

cnf(f_459_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,U_1758,sK50(U_1758,U_1757,U_1756)))
    | ~ sP95(U_1758,U_1756,U_1757) ),
    inference(clausify,[status(thm)],[f_459_4]) ).

fof(f_460_1,plain,
    ! [M,N] :
      ( ? [K_1] : N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_407_less__imp__Suc__add]) ).

fof(f_460_2,plain,
    ! [U_1761,U_1760] :
      ( ? [U_1759] : U_1760 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1761),U_1759))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1761),U_1760)) ),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

fof(f_460_3,plain,
    ! [U_1761,U_1760] :
      ( U_1760 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1761),sK51(U_1761,U_1760)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1761),U_1760)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_1759,sK51(U_1761,U_1760))],[f_460_2]) ).

fof(f_460_4,plain,
    ! [U_1761,U_1760] :
      ( U_1760 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1761),sK51(U_1761,U_1760)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1761),U_1760)) ),
    inference(definitional_conversion,[status(esa)],[f_460_3]) ).

cnf(f_460_5,plain,
    ( U_1760 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_1761),sK51(U_1761,U_1760)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1761),U_1760)) ),
    inference(clausify,[status(thm)],[f_460_4]) ).

fof(f_461_1,plain,
    ! [X_b,C_2,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_2),C_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_408_subset__psubset__trans]) ).

fof(f_461_2,plain,
    ! [U_1765,U_1764,U_1763,U_1762] :
      ( hBOOL(hAPP(fun(U_1765,bool),bool,hAPP(fun(U_1765,bool),fun(fun(U_1765,bool),bool),ord_less(fun(U_1765,bool)),U_1763),U_1764))
      | ~ hBOOL(hAPP(fun(U_1765,bool),bool,hAPP(fun(U_1765,bool),fun(fun(U_1765,bool),bool),ord_less(fun(U_1765,bool)),U_1762),U_1764))
      | ~ hBOOL(hAPP(fun(U_1765,bool),bool,hAPP(fun(U_1765,bool),fun(fun(U_1765,bool),bool),ord_less_eq(fun(U_1765,bool)),U_1763),U_1762)) ),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

fof(f_461_3,plain,
    ! [U_1763,U_1765,U_1762,U_1764] :
      ( hBOOL(hAPP(fun(U_1765,bool),bool,hAPP(fun(U_1765,bool),fun(fun(U_1765,bool),bool),ord_less(fun(U_1765,bool)),U_1763),U_1764))
      | ~ hBOOL(hAPP(fun(U_1765,bool),bool,hAPP(fun(U_1765,bool),fun(fun(U_1765,bool),bool),ord_less(fun(U_1765,bool)),U_1762),U_1764))
      | ~ hBOOL(hAPP(fun(U_1765,bool),bool,hAPP(fun(U_1765,bool),fun(fun(U_1765,bool),bool),ord_less_eq(fun(U_1765,bool)),U_1763),U_1762)) ),
    inference(definitional_conversion,[status(esa)],[f_461_2]) ).

cnf(f_461_4,plain,
    ( hBOOL(hAPP(fun(U_1765,bool),bool,hAPP(fun(U_1765,bool),fun(fun(U_1765,bool),bool),ord_less(fun(U_1765,bool)),U_1763),U_1764))
    | ~ hBOOL(hAPP(fun(U_1765,bool),bool,hAPP(fun(U_1765,bool),fun(fun(U_1765,bool),bool),ord_less(fun(U_1765,bool)),U_1762),U_1764))
    | ~ hBOOL(hAPP(fun(U_1765,bool),bool,hAPP(fun(U_1765,bool),fun(fun(U_1765,bool),bool),ord_less_eq(fun(U_1765,bool)),U_1763),U_1762)) ),
    inference(clausify,[status(thm)],[f_461_3]) ).

fof(f_462_1,plain,
    ! [X_b,C_2,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),C_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_409_psubset__subset__trans]) ).

fof(f_462_2,plain,
    ! [U_1769,U_1768,U_1767,U_1766] :
      ( hBOOL(hAPP(fun(U_1769,bool),bool,hAPP(fun(U_1769,bool),fun(fun(U_1769,bool),bool),ord_less(fun(U_1769,bool)),U_1767),U_1768))
      | ~ hBOOL(hAPP(fun(U_1769,bool),bool,hAPP(fun(U_1769,bool),fun(fun(U_1769,bool),bool),ord_less_eq(fun(U_1769,bool)),U_1766),U_1768))
      | ~ hBOOL(hAPP(fun(U_1769,bool),bool,hAPP(fun(U_1769,bool),fun(fun(U_1769,bool),bool),ord_less(fun(U_1769,bool)),U_1767),U_1766)) ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

fof(f_462_3,plain,
    ! [U_1767,U_1766,U_1769,U_1768] :
      ( hBOOL(hAPP(fun(U_1769,bool),bool,hAPP(fun(U_1769,bool),fun(fun(U_1769,bool),bool),ord_less(fun(U_1769,bool)),U_1767),U_1768))
      | ~ hBOOL(hAPP(fun(U_1769,bool),bool,hAPP(fun(U_1769,bool),fun(fun(U_1769,bool),bool),ord_less_eq(fun(U_1769,bool)),U_1766),U_1768))
      | ~ hBOOL(hAPP(fun(U_1769,bool),bool,hAPP(fun(U_1769,bool),fun(fun(U_1769,bool),bool),ord_less(fun(U_1769,bool)),U_1767),U_1766)) ),
    inference(definitional_conversion,[status(esa)],[f_462_2]) ).

cnf(f_462_4,plain,
    ( hBOOL(hAPP(fun(U_1769,bool),bool,hAPP(fun(U_1769,bool),fun(fun(U_1769,bool),bool),ord_less(fun(U_1769,bool)),U_1767),U_1768))
    | ~ hBOOL(hAPP(fun(U_1769,bool),bool,hAPP(fun(U_1769,bool),fun(fun(U_1769,bool),bool),ord_less_eq(fun(U_1769,bool)),U_1766),U_1768))
    | ~ hBOOL(hAPP(fun(U_1769,bool),bool,hAPP(fun(U_1769,bool),fun(fun(U_1769,bool),bool),ord_less(fun(U_1769,bool)),U_1767),U_1766)) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

fof(f_463_1,plain,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_410_psubset__imp__subset]) ).

fof(f_463_2,plain,
    ! [U_1772,U_1771,U_1770] :
      ( hBOOL(hAPP(fun(U_1772,bool),bool,hAPP(fun(U_1772,bool),fun(fun(U_1772,bool),bool),ord_less_eq(fun(U_1772,bool)),U_1771),U_1770))
      | ~ hBOOL(hAPP(fun(U_1772,bool),bool,hAPP(fun(U_1772,bool),fun(fun(U_1772,bool),bool),ord_less(fun(U_1772,bool)),U_1771),U_1770)) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

fof(f_463_3,plain,
    ! [U_1772,U_1771,U_1770] :
      ( hBOOL(hAPP(fun(U_1772,bool),bool,hAPP(fun(U_1772,bool),fun(fun(U_1772,bool),bool),ord_less_eq(fun(U_1772,bool)),U_1771),U_1770))
      | ~ hBOOL(hAPP(fun(U_1772,bool),bool,hAPP(fun(U_1772,bool),fun(fun(U_1772,bool),bool),ord_less(fun(U_1772,bool)),U_1771),U_1770)) ),
    inference(definitional_conversion,[status(esa)],[f_463_2]) ).

cnf(f_463_4,plain,
    ( hBOOL(hAPP(fun(U_1772,bool),bool,hAPP(fun(U_1772,bool),fun(fun(U_1772,bool),bool),ord_less_eq(fun(U_1772,bool)),U_1771),U_1770))
    | ~ hBOOL(hAPP(fun(U_1772,bool),bool,hAPP(fun(U_1772,bool),fun(fun(U_1772,bool),bool),ord_less(fun(U_1772,bool)),U_1771),U_1770)) ),
    inference(clausify,[status(thm)],[f_463_3]) ).

fof(f_464_1,plain,
    ! [X_b,A_3,B_2] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
        | ( ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_2)
          & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) ) )
      & ( ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)
        | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_411_subset__iff__psubset__eq]) ).

fof(f_464_2,plain,
    ! [U_1775,U_1774,U_1773] :
      ( ( hBOOL(hAPP(fun(U_1775,bool),bool,hAPP(fun(U_1775,bool),fun(fun(U_1775,bool),bool),ord_less_eq(fun(U_1775,bool)),U_1774),U_1773))
        | ( ti(fun(U_1775,bool),U_1774) != ti(fun(U_1775,bool),U_1773)
          & ~ hBOOL(hAPP(fun(U_1775,bool),bool,hAPP(fun(U_1775,bool),fun(fun(U_1775,bool),bool),ord_less(fun(U_1775,bool)),U_1774),U_1773)) ) )
      & ( ti(fun(U_1775,bool),U_1774) = ti(fun(U_1775,bool),U_1773)
        | hBOOL(hAPP(fun(U_1775,bool),bool,hAPP(fun(U_1775,bool),fun(fun(U_1775,bool),bool),ord_less(fun(U_1775,bool)),U_1774),U_1773))
        | ~ hBOOL(hAPP(fun(U_1775,bool),bool,hAPP(fun(U_1775,bool),fun(fun(U_1775,bool),bool),ord_less_eq(fun(U_1775,bool)),U_1774),U_1773)) ) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

fof(f_464_3,plain,
    ( ! [U_1781,U_1779,U_1777] :
        ( hBOOL(hAPP(fun(U_1781,bool),bool,hAPP(fun(U_1781,bool),fun(fun(U_1781,bool),bool),ord_less_eq(fun(U_1781,bool)),U_1779),U_1777))
        | ( ti(fun(U_1781,bool),U_1779) != ti(fun(U_1781,bool),U_1777)
          & ~ hBOOL(hAPP(fun(U_1781,bool),bool,hAPP(fun(U_1781,bool),fun(fun(U_1781,bool),bool),ord_less(fun(U_1781,bool)),U_1779),U_1777)) ) )
    & ! [U_1780,U_1778,U_1776] :
        ( ti(fun(U_1780,bool),U_1778) = ti(fun(U_1780,bool),U_1776)
        | hBOOL(hAPP(fun(U_1780,bool),bool,hAPP(fun(U_1780,bool),fun(fun(U_1780,bool),bool),ord_less(fun(U_1780,bool)),U_1778),U_1776))
        | ~ hBOOL(hAPP(fun(U_1780,bool),bool,hAPP(fun(U_1780,bool),fun(fun(U_1780,bool),bool),ord_less_eq(fun(U_1780,bool)),U_1778),U_1776)) ) ),
    inference(miniscope,[status(thm)],[f_464_2]) ).

fof(f_464_4,plain,
    ( ! [U_1777,U_1779,U_1781] :
        ( ti(fun(U_1781,bool),U_1779) != ti(fun(U_1781,bool),U_1777)
        | ~ sP96(U_1777,U_1779,U_1781) )
    & ! [U_1777,U_1779,U_1781] :
        ( ~ hBOOL(hAPP(fun(U_1781,bool),bool,hAPP(fun(U_1781,bool),fun(fun(U_1781,bool),bool),ord_less(fun(U_1781,bool)),U_1779),U_1777))
        | ~ sP96(U_1777,U_1779,U_1781) )
    & ! [U_1777,U_1779,U_1781] :
        ( hBOOL(hAPP(fun(U_1781,bool),bool,hAPP(fun(U_1781,bool),fun(fun(U_1781,bool),bool),ord_less_eq(fun(U_1781,bool)),U_1779),U_1777))
        | sP96(U_1777,U_1779,U_1781) )
    & ! [U_1776,U_1778,U_1780] :
        ( ti(fun(U_1780,bool),U_1778) = ti(fun(U_1780,bool),U_1776)
        | hBOOL(hAPP(fun(U_1780,bool),bool,hAPP(fun(U_1780,bool),fun(fun(U_1780,bool),bool),ord_less(fun(U_1780,bool)),U_1778),U_1776))
        | ~ hBOOL(hAPP(fun(U_1780,bool),bool,hAPP(fun(U_1780,bool),fun(fun(U_1780,bool),bool),ord_less_eq(fun(U_1780,bool)),U_1778),U_1776)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96])],[f_464_3]) ).

cnf(f_464_5,plain,
    ( ti(fun(U_1780,bool),U_1778) = ti(fun(U_1780,bool),U_1776)
    | hBOOL(hAPP(fun(U_1780,bool),bool,hAPP(fun(U_1780,bool),fun(fun(U_1780,bool),bool),ord_less(fun(U_1780,bool)),U_1778),U_1776))
    | ~ hBOOL(hAPP(fun(U_1780,bool),bool,hAPP(fun(U_1780,bool),fun(fun(U_1780,bool),bool),ord_less_eq(fun(U_1780,bool)),U_1778),U_1776)) ),
    inference(clausify,[status(thm)],[f_464_4]) ).

cnf(f_464_6,plain,
    ( hBOOL(hAPP(fun(U_1781,bool),bool,hAPP(fun(U_1781,bool),fun(fun(U_1781,bool),bool),ord_less_eq(fun(U_1781,bool)),U_1779),U_1777))
    | sP96(U_1777,U_1779,U_1781) ),
    inference(clausify,[status(thm)],[f_464_4]) ).

cnf(f_464_7,plain,
    ( ~ hBOOL(hAPP(fun(U_1781,bool),bool,hAPP(fun(U_1781,bool),fun(fun(U_1781,bool),bool),ord_less(fun(U_1781,bool)),U_1779),U_1777))
    | ~ sP96(U_1777,U_1779,U_1781) ),
    inference(clausify,[status(thm)],[f_464_4]) ).

cnf(f_464_8,plain,
    ( ti(fun(U_1781,bool),U_1779) != ti(fun(U_1781,bool),U_1777)
    | ~ sP96(U_1777,U_1779,U_1781) ),
    inference(clausify,[status(thm)],[f_464_4]) ).

fof(f_465_1,plain,
    ! [X_b,A_3,B_2] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
        | ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2)
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) )
      & ( ( ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_2)
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) )
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_412_psubset__eq]) ).

fof(f_465_2,plain,
    ! [U_1784,U_1783,U_1782] :
      ( ( hBOOL(hAPP(fun(U_1784,bool),bool,hAPP(fun(U_1784,bool),fun(fun(U_1784,bool),bool),ord_less(fun(U_1784,bool)),U_1783),U_1782))
        | ti(fun(U_1784,bool),U_1783) = ti(fun(U_1784,bool),U_1782)
        | ~ hBOOL(hAPP(fun(U_1784,bool),bool,hAPP(fun(U_1784,bool),fun(fun(U_1784,bool),bool),ord_less_eq(fun(U_1784,bool)),U_1783),U_1782)) )
      & ( ( ti(fun(U_1784,bool),U_1783) != ti(fun(U_1784,bool),U_1782)
          & hBOOL(hAPP(fun(U_1784,bool),bool,hAPP(fun(U_1784,bool),fun(fun(U_1784,bool),bool),ord_less_eq(fun(U_1784,bool)),U_1783),U_1782)) )
        | ~ hBOOL(hAPP(fun(U_1784,bool),bool,hAPP(fun(U_1784,bool),fun(fun(U_1784,bool),bool),ord_less(fun(U_1784,bool)),U_1783),U_1782)) ) ),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

fof(f_465_3,plain,
    ( ! [U_1790,U_1788,U_1786] :
        ( hBOOL(hAPP(fun(U_1790,bool),bool,hAPP(fun(U_1790,bool),fun(fun(U_1790,bool),bool),ord_less(fun(U_1790,bool)),U_1788),U_1786))
        | ti(fun(U_1790,bool),U_1788) = ti(fun(U_1790,bool),U_1786)
        | ~ hBOOL(hAPP(fun(U_1790,bool),bool,hAPP(fun(U_1790,bool),fun(fun(U_1790,bool),bool),ord_less_eq(fun(U_1790,bool)),U_1788),U_1786)) )
    & ! [U_1789,U_1787,U_1785] :
        ( ( ti(fun(U_1789,bool),U_1787) != ti(fun(U_1789,bool),U_1785)
          & hBOOL(hAPP(fun(U_1789,bool),bool,hAPP(fun(U_1789,bool),fun(fun(U_1789,bool),bool),ord_less_eq(fun(U_1789,bool)),U_1787),U_1785)) )
        | ~ hBOOL(hAPP(fun(U_1789,bool),bool,hAPP(fun(U_1789,bool),fun(fun(U_1789,bool),bool),ord_less(fun(U_1789,bool)),U_1787),U_1785)) ) ),
    inference(miniscope,[status(thm)],[f_465_2]) ).

fof(f_465_4,plain,
    ( ! [U_1785,U_1787,U_1789] :
        ( ti(fun(U_1789,bool),U_1787) != ti(fun(U_1789,bool),U_1785)
        | ~ sP97(U_1785,U_1787,U_1789) )
    & ! [U_1785,U_1787,U_1789] :
        ( hBOOL(hAPP(fun(U_1789,bool),bool,hAPP(fun(U_1789,bool),fun(fun(U_1789,bool),bool),ord_less_eq(fun(U_1789,bool)),U_1787),U_1785))
        | ~ sP97(U_1785,U_1787,U_1789) )
    & ! [U_1788,U_1786,U_1790] :
        ( hBOOL(hAPP(fun(U_1790,bool),bool,hAPP(fun(U_1790,bool),fun(fun(U_1790,bool),bool),ord_less(fun(U_1790,bool)),U_1788),U_1786))
        | ti(fun(U_1790,bool),U_1788) = ti(fun(U_1790,bool),U_1786)
        | ~ hBOOL(hAPP(fun(U_1790,bool),bool,hAPP(fun(U_1790,bool),fun(fun(U_1790,bool),bool),ord_less_eq(fun(U_1790,bool)),U_1788),U_1786)) )
    & ! [U_1785,U_1787,U_1789] :
        ( sP97(U_1785,U_1787,U_1789)
        | ~ hBOOL(hAPP(fun(U_1789,bool),bool,hAPP(fun(U_1789,bool),fun(fun(U_1789,bool),bool),ord_less(fun(U_1789,bool)),U_1787),U_1785)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP97])],[f_465_3]) ).

cnf(f_465_5,plain,
    ( sP97(U_1785,U_1787,U_1789)
    | ~ hBOOL(hAPP(fun(U_1789,bool),bool,hAPP(fun(U_1789,bool),fun(fun(U_1789,bool),bool),ord_less(fun(U_1789,bool)),U_1787),U_1785)) ),
    inference(clausify,[status(thm)],[f_465_4]) ).

cnf(f_465_6,plain,
    ( hBOOL(hAPP(fun(U_1790,bool),bool,hAPP(fun(U_1790,bool),fun(fun(U_1790,bool),bool),ord_less(fun(U_1790,bool)),U_1788),U_1786))
    | ti(fun(U_1790,bool),U_1788) = ti(fun(U_1790,bool),U_1786)
    | ~ hBOOL(hAPP(fun(U_1790,bool),bool,hAPP(fun(U_1790,bool),fun(fun(U_1790,bool),bool),ord_less_eq(fun(U_1790,bool)),U_1788),U_1786)) ),
    inference(clausify,[status(thm)],[f_465_4]) ).

cnf(f_465_7,plain,
    ( hBOOL(hAPP(fun(U_1789,bool),bool,hAPP(fun(U_1789,bool),fun(fun(U_1789,bool),bool),ord_less_eq(fun(U_1789,bool)),U_1787),U_1785))
    | ~ sP97(U_1785,U_1787,U_1789) ),
    inference(clausify,[status(thm)],[f_465_4]) ).

cnf(f_465_8,plain,
    ( ti(fun(U_1789,bool),U_1787) != ti(fun(U_1789,bool),U_1785)
    | ~ sP97(U_1785,U_1787,U_1789) ),
    inference(clausify,[status(thm)],[f_465_4]) ).

fof(f_466_1,plain,
    ! [X_b,A_3] : ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool)))),
    inference(fof_nnf,[status(thm)],[fact_413_not__psubset__empty]) ).

fof(f_466_2,plain,
    ! [U_1792,U_1791] : ~ hBOOL(hAPP(fun(U_1792,bool),bool,hAPP(fun(U_1792,bool),fun(fun(U_1792,bool),bool),ord_less(fun(U_1792,bool)),U_1791),bot_bot(fun(U_1792,bool)))),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

fof(f_466_3,plain,
    ! [U_1792,U_1791] : ~ hBOOL(hAPP(fun(U_1792,bool),bool,hAPP(fun(U_1792,bool),fun(fun(U_1792,bool),bool),ord_less(fun(U_1792,bool)),U_1791),bot_bot(fun(U_1792,bool)))),
    inference(definitional_conversion,[status(esa)],[f_466_2]) ).

cnf(f_466_4,plain,
    ~ hBOOL(hAPP(fun(U_1792,bool),bool,hAPP(fun(U_1792,bool),fun(fun(U_1792,bool),bool),ord_less(fun(U_1792,bool)),U_1791),bot_bot(fun(U_1792,bool)))),
    inference(clausify,[status(thm)],[f_466_3]) ).

fof(f_467_1,plain,
    ! [X_b,X_c] :
      ( ! [F,G] :
          ( ( hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less(fun(X_b,X_c)),F),G))
            | hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),G),F))
            | ~ hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) )
          & ( ( ~ hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),G),F))
              & hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) )
            | ~ hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less(fun(X_b,X_c)),F),G)) ) )
      | ~ ord(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_414_less__fun__def]) ).

fof(f_467_2,plain,
    ! [U_1796,U_1795] :
      ( ! [U_1794,U_1793] :
          ( ( hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less(fun(U_1796,U_1795)),U_1794),U_1793))
            | hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1793),U_1794))
            | ~ hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1794),U_1793)) )
          & ( ( ~ hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1793),U_1794))
              & hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1794),U_1793)) )
            | ~ hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less(fun(U_1796,U_1795)),U_1794),U_1793)) ) )
      | ~ ord(U_1795) ),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

fof(f_467_3,plain,
    ! [U_1796,U_1795] :
      ( ( ! [U_1800,U_1798] :
            ( hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less(fun(U_1796,U_1795)),U_1800),U_1798))
            | hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1798),U_1800))
            | ~ hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1800),U_1798)) )
        & ! [U_1799,U_1797] :
            ( ( ~ hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1797),U_1799))
              & hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1799),U_1797)) )
            | ~ hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less(fun(U_1796,U_1795)),U_1799),U_1797)) ) )
      | ~ ord(U_1795) ),
    inference(miniscope,[status(thm)],[f_467_2]) ).

fof(f_467_4,plain,
    ( ! [U_1795,U_1796,U_1797,U_1799] :
        ( ~ hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1797),U_1799))
        | ~ sP98(U_1795,U_1796,U_1797,U_1799) )
    & ! [U_1795,U_1796,U_1797,U_1799] :
        ( hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1799),U_1797))
        | ~ sP98(U_1795,U_1796,U_1797,U_1799) )
    & ! [U_1795,U_1800,U_1796,U_1798,U_1797,U_1799] :
        ( hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less(fun(U_1796,U_1795)),U_1800),U_1798))
        | hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1798),U_1800))
        | ~ hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1800),U_1798))
        | ~ sP99(U_1795,U_1800,U_1796,U_1798,U_1797,U_1799) )
    & ! [U_1795,U_1800,U_1796,U_1798,U_1797,U_1799] :
        ( sP98(U_1795,U_1796,U_1797,U_1799)
        | ~ hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less(fun(U_1796,U_1795)),U_1799),U_1797))
        | ~ sP99(U_1795,U_1800,U_1796,U_1798,U_1797,U_1799) )
    & ! [U_1795,U_1800,U_1796,U_1798,U_1797,U_1799] :
        ( sP99(U_1795,U_1800,U_1796,U_1798,U_1797,U_1799)
        | ~ ord(U_1795) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98,sP99])],[f_467_3]) ).

cnf(f_467_5,plain,
    ( sP99(U_1795,U_1800,U_1796,U_1798,U_1797,U_1799)
    | ~ ord(U_1795) ),
    inference(clausify,[status(thm)],[f_467_4]) ).

cnf(f_467_6,plain,
    ( sP98(U_1795,U_1796,U_1797,U_1799)
    | ~ hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less(fun(U_1796,U_1795)),U_1799),U_1797))
    | ~ sP99(U_1795,U_1800,U_1796,U_1798,U_1797,U_1799) ),
    inference(clausify,[status(thm)],[f_467_4]) ).

cnf(f_467_7,plain,
    ( hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less(fun(U_1796,U_1795)),U_1800),U_1798))
    | hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1798),U_1800))
    | ~ hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1800),U_1798))
    | ~ sP99(U_1795,U_1800,U_1796,U_1798,U_1797,U_1799) ),
    inference(clausify,[status(thm)],[f_467_4]) ).

cnf(f_467_8,plain,
    ( hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1799),U_1797))
    | ~ sP98(U_1795,U_1796,U_1797,U_1799) ),
    inference(clausify,[status(thm)],[f_467_4]) ).

cnf(f_467_9,plain,
    ( ~ hBOOL(hAPP(fun(U_1796,U_1795),bool,hAPP(fun(U_1796,U_1795),fun(fun(U_1796,U_1795),bool),ord_less_eq(fun(U_1796,U_1795)),U_1797),U_1799))
    | ~ sP98(U_1795,U_1796,U_1797,U_1799) ),
    inference(clausify,[status(thm)],[f_467_4]) ).

fof(f_468_1,plain,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_415_psubset__card__mono]) ).

fof(f_468_2,plain,
    ! [U_1803,U_1802,U_1801] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1803,bool),nat,finite_card(U_1803),U_1802)),hAPP(fun(U_1803,bool),nat,finite_card(U_1803),U_1801)))
      | ~ hBOOL(hAPP(fun(U_1803,bool),bool,hAPP(fun(U_1803,bool),fun(fun(U_1803,bool),bool),ord_less(fun(U_1803,bool)),U_1802),U_1801))
      | ~ hBOOL(hAPP(fun(U_1803,bool),bool,finite_finite(U_1803),U_1801)) ),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

fof(f_468_3,plain,
    ! [U_1803,U_1801,U_1802] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1803,bool),nat,finite_card(U_1803),U_1802)),hAPP(fun(U_1803,bool),nat,finite_card(U_1803),U_1801)))
      | ~ hBOOL(hAPP(fun(U_1803,bool),bool,hAPP(fun(U_1803,bool),fun(fun(U_1803,bool),bool),ord_less(fun(U_1803,bool)),U_1802),U_1801))
      | ~ hBOOL(hAPP(fun(U_1803,bool),bool,finite_finite(U_1803),U_1801)) ),
    inference(definitional_conversion,[status(esa)],[f_468_2]) ).

cnf(f_468_4,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1803,bool),nat,finite_card(U_1803),U_1802)),hAPP(fun(U_1803,bool),nat,finite_card(U_1803),U_1801)))
    | ~ hBOOL(hAPP(fun(U_1803,bool),bool,hAPP(fun(U_1803,bool),fun(fun(U_1803,bool),bool),ord_less(fun(U_1803,bool)),U_1802),U_1801))
    | ~ hBOOL(hAPP(fun(U_1803,bool),bool,finite_finite(U_1803),U_1801)) ),
    inference(clausify,[status(thm)],[f_468_3]) ).

fof(f_469_1,plain,
    ! [X_b,A_3,X_1,B_2] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2)))
        | ( ( ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
              & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) )
            | ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_2))
              & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ) )
          & ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) )
        | ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
          & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) ) )
      & ( ( ( ( ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
                | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) )
              & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))),B_2))
                | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) ) )
            | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) )
          & ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
            | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) ) )
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_416_psubset__insert__iff]) ).

fof(f_469_2,plain,
    ! [U_1807,U_1806,U_1805,U_1804] :
      ( ( hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(fun(U_1807,bool),fun(fun(U_1807,bool),bool),ord_less(fun(U_1807,bool)),U_1806),hAPP(fun(U_1807,bool),fun(U_1807,bool),hAPP(U_1807,fun(fun(U_1807,bool),fun(U_1807,bool)),insert(U_1807),U_1805),U_1804)))
        | ( ( ( ~ hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(fun(U_1807,bool),fun(fun(U_1807,bool),bool),ord_less_eq(fun(U_1807,bool)),U_1806),U_1804))
              & ~ hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(U_1807,fun(fun(U_1807,bool),bool),member(U_1807),U_1805),U_1806)) )
            | ( ~ hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(fun(U_1807,bool),fun(fun(U_1807,bool),bool),ord_less(fun(U_1807,bool)),hAPP(fun(U_1807,bool),fun(U_1807,bool),hAPP(fun(U_1807,bool),fun(fun(U_1807,bool),fun(U_1807,bool)),minus_minus(fun(U_1807,bool)),U_1806),hAPP(fun(U_1807,bool),fun(U_1807,bool),hAPP(U_1807,fun(fun(U_1807,bool),fun(U_1807,bool)),insert(U_1807),U_1805),bot_bot(fun(U_1807,bool))))),U_1804))
              & hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(U_1807,fun(fun(U_1807,bool),bool),member(U_1807),U_1805),U_1806)) ) )
          & ~ hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(U_1807,fun(fun(U_1807,bool),bool),member(U_1807),U_1805),U_1804)) )
        | ( ~ hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(fun(U_1807,bool),fun(fun(U_1807,bool),bool),ord_less(fun(U_1807,bool)),U_1806),U_1804))
          & hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(U_1807,fun(fun(U_1807,bool),bool),member(U_1807),U_1805),U_1804)) ) )
      & ( ( ( ( ( hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(fun(U_1807,bool),fun(fun(U_1807,bool),bool),ord_less_eq(fun(U_1807,bool)),U_1806),U_1804))
                | hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(U_1807,fun(fun(U_1807,bool),bool),member(U_1807),U_1805),U_1806)) )
              & ( hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(fun(U_1807,bool),fun(fun(U_1807,bool),bool),ord_less(fun(U_1807,bool)),hAPP(fun(U_1807,bool),fun(U_1807,bool),hAPP(fun(U_1807,bool),fun(fun(U_1807,bool),fun(U_1807,bool)),minus_minus(fun(U_1807,bool)),U_1806),hAPP(fun(U_1807,bool),fun(U_1807,bool),hAPP(U_1807,fun(fun(U_1807,bool),fun(U_1807,bool)),insert(U_1807),U_1805),bot_bot(fun(U_1807,bool))))),U_1804))
                | ~ hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(U_1807,fun(fun(U_1807,bool),bool),member(U_1807),U_1805),U_1806)) ) )
            | hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(U_1807,fun(fun(U_1807,bool),bool),member(U_1807),U_1805),U_1804)) )
          & ( hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(fun(U_1807,bool),fun(fun(U_1807,bool),bool),ord_less(fun(U_1807,bool)),U_1806),U_1804))
            | ~ hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(U_1807,fun(fun(U_1807,bool),bool),member(U_1807),U_1805),U_1804)) ) )
        | ~ hBOOL(hAPP(fun(U_1807,bool),bool,hAPP(fun(U_1807,bool),fun(fun(U_1807,bool),bool),ord_less(fun(U_1807,bool)),U_1806),hAPP(fun(U_1807,bool),fun(U_1807,bool),hAPP(U_1807,fun(fun(U_1807,bool),fun(U_1807,bool)),insert(U_1807),U_1805),U_1804))) ) ),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

fof(f_469_3,plain,
    ( ! [U_1815,U_1813,U_1811,U_1809] :
        ( hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),bool),ord_less(fun(U_1815,bool)),U_1813),hAPP(fun(U_1815,bool),fun(U_1815,bool),hAPP(U_1815,fun(fun(U_1815,bool),fun(U_1815,bool)),insert(U_1815),U_1811),U_1809)))
        | ( ( ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),bool),ord_less_eq(fun(U_1815,bool)),U_1813),U_1809))
              & ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(U_1815,fun(fun(U_1815,bool),bool),member(U_1815),U_1811),U_1813)) )
            | ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),bool),ord_less(fun(U_1815,bool)),hAPP(fun(U_1815,bool),fun(U_1815,bool),hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),fun(U_1815,bool)),minus_minus(fun(U_1815,bool)),U_1813),hAPP(fun(U_1815,bool),fun(U_1815,bool),hAPP(U_1815,fun(fun(U_1815,bool),fun(U_1815,bool)),insert(U_1815),U_1811),bot_bot(fun(U_1815,bool))))),U_1809))
              & hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(U_1815,fun(fun(U_1815,bool),bool),member(U_1815),U_1811),U_1813)) ) )
          & ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(U_1815,fun(fun(U_1815,bool),bool),member(U_1815),U_1811),U_1809)) )
        | ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),bool),ord_less(fun(U_1815,bool)),U_1813),U_1809))
          & hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(U_1815,fun(fun(U_1815,bool),bool),member(U_1815),U_1811),U_1809)) ) )
    & ! [U_1814,U_1812,U_1810,U_1808] :
        ( ( ( ( ( hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),bool),ord_less_eq(fun(U_1814,bool)),U_1812),U_1808))
                | hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(U_1814,fun(fun(U_1814,bool),bool),member(U_1814),U_1810),U_1812)) )
              & ( hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),bool),ord_less(fun(U_1814,bool)),hAPP(fun(U_1814,bool),fun(U_1814,bool),hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),fun(U_1814,bool)),minus_minus(fun(U_1814,bool)),U_1812),hAPP(fun(U_1814,bool),fun(U_1814,bool),hAPP(U_1814,fun(fun(U_1814,bool),fun(U_1814,bool)),insert(U_1814),U_1810),bot_bot(fun(U_1814,bool))))),U_1808))
                | ~ hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(U_1814,fun(fun(U_1814,bool),bool),member(U_1814),U_1810),U_1812)) ) )
            | hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(U_1814,fun(fun(U_1814,bool),bool),member(U_1814),U_1810),U_1808)) )
          & ( hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),bool),ord_less(fun(U_1814,bool)),U_1812),U_1808))
            | ~ hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(U_1814,fun(fun(U_1814,bool),bool),member(U_1814),U_1810),U_1808)) ) )
        | ~ hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),bool),ord_less(fun(U_1814,bool)),U_1812),hAPP(fun(U_1814,bool),fun(U_1814,bool),hAPP(U_1814,fun(fun(U_1814,bool),fun(U_1814,bool)),insert(U_1814),U_1810),U_1808))) ) ),
    inference(miniscope,[status(thm)],[f_469_2]) ).

fof(f_469_4,plain,
    ( ! [U_1811,U_1813,U_1815,U_1809] :
        ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),bool),ord_less_eq(fun(U_1815,bool)),U_1813),U_1809))
        | ~ sP104(U_1811,U_1813,U_1815,U_1809) )
    & ! [U_1811,U_1813,U_1815,U_1809] :
        ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(U_1815,fun(fun(U_1815,bool),bool),member(U_1815),U_1811),U_1813))
        | ~ sP104(U_1811,U_1813,U_1815,U_1809) )
    & ! [U_1811,U_1813,U_1815,U_1809] :
        ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),bool),ord_less(fun(U_1815,bool)),hAPP(fun(U_1815,bool),fun(U_1815,bool),hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),fun(U_1815,bool)),minus_minus(fun(U_1815,bool)),U_1813),hAPP(fun(U_1815,bool),fun(U_1815,bool),hAPP(U_1815,fun(fun(U_1815,bool),fun(U_1815,bool)),insert(U_1815),U_1811),bot_bot(fun(U_1815,bool))))),U_1809))
        | ~ sP103(U_1811,U_1813,U_1815,U_1809) )
    & ! [U_1811,U_1813,U_1815,U_1809] :
        ( hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(U_1815,fun(fun(U_1815,bool),bool),member(U_1815),U_1811),U_1813))
        | ~ sP103(U_1811,U_1813,U_1815,U_1809) )
    & ! [U_1811,U_1813,U_1815,U_1809] :
        ( sP104(U_1811,U_1813,U_1815,U_1809)
        | sP103(U_1811,U_1813,U_1815,U_1809)
        | ~ sP105(U_1811,U_1813,U_1815,U_1809) )
    & ! [U_1811,U_1813,U_1815,U_1809] :
        ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(U_1815,fun(fun(U_1815,bool),bool),member(U_1815),U_1811),U_1809))
        | ~ sP105(U_1811,U_1813,U_1815,U_1809) )
    & ! [U_1811,U_1813,U_1815,U_1809] :
        ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),bool),ord_less(fun(U_1815,bool)),U_1813),U_1809))
        | ~ sP102(U_1811,U_1813,U_1815,U_1809) )
    & ! [U_1811,U_1813,U_1815,U_1809] :
        ( hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(U_1815,fun(fun(U_1815,bool),bool),member(U_1815),U_1811),U_1809))
        | ~ sP102(U_1811,U_1813,U_1815,U_1809) )
    & ! [U_1812,U_1814,U_1808,U_1810] :
        ( hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),bool),ord_less_eq(fun(U_1814,bool)),U_1812),U_1808))
        | hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(U_1814,fun(fun(U_1814,bool),bool),member(U_1814),U_1810),U_1812))
        | ~ sP100(U_1812,U_1814,U_1808,U_1810) )
    & ! [U_1812,U_1814,U_1808,U_1810] :
        ( hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),bool),ord_less(fun(U_1814,bool)),hAPP(fun(U_1814,bool),fun(U_1814,bool),hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),fun(U_1814,bool)),minus_minus(fun(U_1814,bool)),U_1812),hAPP(fun(U_1814,bool),fun(U_1814,bool),hAPP(U_1814,fun(fun(U_1814,bool),fun(U_1814,bool)),insert(U_1814),U_1810),bot_bot(fun(U_1814,bool))))),U_1808))
        | ~ hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(U_1814,fun(fun(U_1814,bool),bool),member(U_1814),U_1810),U_1812))
        | ~ sP100(U_1812,U_1814,U_1808,U_1810) )
    & ! [U_1812,U_1814,U_1808,U_1810] :
        ( sP100(U_1812,U_1814,U_1808,U_1810)
        | hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(U_1814,fun(fun(U_1814,bool),bool),member(U_1814),U_1810),U_1808))
        | ~ sP101(U_1812,U_1814,U_1808,U_1810) )
    & ! [U_1812,U_1814,U_1808,U_1810] :
        ( hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),bool),ord_less(fun(U_1814,bool)),U_1812),U_1808))
        | ~ hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(U_1814,fun(fun(U_1814,bool),bool),member(U_1814),U_1810),U_1808))
        | ~ sP101(U_1812,U_1814,U_1808,U_1810) )
    & ! [U_1811,U_1813,U_1815,U_1809] :
        ( hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),bool),ord_less(fun(U_1815,bool)),U_1813),hAPP(fun(U_1815,bool),fun(U_1815,bool),hAPP(U_1815,fun(fun(U_1815,bool),fun(U_1815,bool)),insert(U_1815),U_1811),U_1809)))
        | sP105(U_1811,U_1813,U_1815,U_1809)
        | sP102(U_1811,U_1813,U_1815,U_1809) )
    & ! [U_1812,U_1814,U_1808,U_1810] :
        ( sP101(U_1812,U_1814,U_1808,U_1810)
        | ~ hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),bool),ord_less(fun(U_1814,bool)),U_1812),hAPP(fun(U_1814,bool),fun(U_1814,bool),hAPP(U_1814,fun(fun(U_1814,bool),fun(U_1814,bool)),insert(U_1814),U_1810),U_1808))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100,sP101,sP102,sP103,sP104,sP105])],[f_469_3]) ).

cnf(f_469_5,plain,
    ( sP101(U_1812,U_1814,U_1808,U_1810)
    | ~ hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),bool),ord_less(fun(U_1814,bool)),U_1812),hAPP(fun(U_1814,bool),fun(U_1814,bool),hAPP(U_1814,fun(fun(U_1814,bool),fun(U_1814,bool)),insert(U_1814),U_1810),U_1808))) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_6,plain,
    ( hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),bool),ord_less(fun(U_1815,bool)),U_1813),hAPP(fun(U_1815,bool),fun(U_1815,bool),hAPP(U_1815,fun(fun(U_1815,bool),fun(U_1815,bool)),insert(U_1815),U_1811),U_1809)))
    | sP105(U_1811,U_1813,U_1815,U_1809)
    | sP102(U_1811,U_1813,U_1815,U_1809) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_7,plain,
    ( hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),bool),ord_less(fun(U_1814,bool)),U_1812),U_1808))
    | ~ hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(U_1814,fun(fun(U_1814,bool),bool),member(U_1814),U_1810),U_1808))
    | ~ sP101(U_1812,U_1814,U_1808,U_1810) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_8,plain,
    ( sP100(U_1812,U_1814,U_1808,U_1810)
    | hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(U_1814,fun(fun(U_1814,bool),bool),member(U_1814),U_1810),U_1808))
    | ~ sP101(U_1812,U_1814,U_1808,U_1810) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_9,plain,
    ( hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),bool),ord_less(fun(U_1814,bool)),hAPP(fun(U_1814,bool),fun(U_1814,bool),hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),fun(U_1814,bool)),minus_minus(fun(U_1814,bool)),U_1812),hAPP(fun(U_1814,bool),fun(U_1814,bool),hAPP(U_1814,fun(fun(U_1814,bool),fun(U_1814,bool)),insert(U_1814),U_1810),bot_bot(fun(U_1814,bool))))),U_1808))
    | ~ hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(U_1814,fun(fun(U_1814,bool),bool),member(U_1814),U_1810),U_1812))
    | ~ sP100(U_1812,U_1814,U_1808,U_1810) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_10,plain,
    ( hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(fun(U_1814,bool),fun(fun(U_1814,bool),bool),ord_less_eq(fun(U_1814,bool)),U_1812),U_1808))
    | hBOOL(hAPP(fun(U_1814,bool),bool,hAPP(U_1814,fun(fun(U_1814,bool),bool),member(U_1814),U_1810),U_1812))
    | ~ sP100(U_1812,U_1814,U_1808,U_1810) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_11,plain,
    ( hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(U_1815,fun(fun(U_1815,bool),bool),member(U_1815),U_1811),U_1809))
    | ~ sP102(U_1811,U_1813,U_1815,U_1809) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_12,plain,
    ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),bool),ord_less(fun(U_1815,bool)),U_1813),U_1809))
    | ~ sP102(U_1811,U_1813,U_1815,U_1809) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_13,plain,
    ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(U_1815,fun(fun(U_1815,bool),bool),member(U_1815),U_1811),U_1809))
    | ~ sP105(U_1811,U_1813,U_1815,U_1809) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_14,plain,
    ( sP104(U_1811,U_1813,U_1815,U_1809)
    | sP103(U_1811,U_1813,U_1815,U_1809)
    | ~ sP105(U_1811,U_1813,U_1815,U_1809) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_15,plain,
    ( hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(U_1815,fun(fun(U_1815,bool),bool),member(U_1815),U_1811),U_1813))
    | ~ sP103(U_1811,U_1813,U_1815,U_1809) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_16,plain,
    ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),bool),ord_less(fun(U_1815,bool)),hAPP(fun(U_1815,bool),fun(U_1815,bool),hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),fun(U_1815,bool)),minus_minus(fun(U_1815,bool)),U_1813),hAPP(fun(U_1815,bool),fun(U_1815,bool),hAPP(U_1815,fun(fun(U_1815,bool),fun(U_1815,bool)),insert(U_1815),U_1811),bot_bot(fun(U_1815,bool))))),U_1809))
    | ~ sP103(U_1811,U_1813,U_1815,U_1809) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_17,plain,
    ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(U_1815,fun(fun(U_1815,bool),bool),member(U_1815),U_1811),U_1813))
    | ~ sP104(U_1811,U_1813,U_1815,U_1809) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

cnf(f_469_18,plain,
    ( ~ hBOOL(hAPP(fun(U_1815,bool),bool,hAPP(fun(U_1815,bool),fun(fun(U_1815,bool),bool),ord_less_eq(fun(U_1815,bool)),U_1813),U_1809))
    | ~ sP104(U_1811,U_1813,U_1815,U_1809) ),
    inference(clausify,[status(thm)],[f_469_4]) ).

fof(f_470_1,plain,
    ! [X_b,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_417_card__psubset]) ).

fof(f_470_2,plain,
    ! [U_1818,U_1817,U_1816] :
      ( hBOOL(hAPP(fun(U_1818,bool),bool,hAPP(fun(U_1818,bool),fun(fun(U_1818,bool),bool),ord_less(fun(U_1818,bool)),U_1817),U_1816))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1818,bool),nat,finite_card(U_1818),U_1817)),hAPP(fun(U_1818,bool),nat,finite_card(U_1818),U_1816)))
      | ~ hBOOL(hAPP(fun(U_1818,bool),bool,hAPP(fun(U_1818,bool),fun(fun(U_1818,bool),bool),ord_less_eq(fun(U_1818,bool)),U_1817),U_1816))
      | ~ hBOOL(hAPP(fun(U_1818,bool),bool,finite_finite(U_1818),U_1816)) ),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

fof(f_470_3,plain,
    ! [U_1816,U_1818,U_1817] :
      ( hBOOL(hAPP(fun(U_1818,bool),bool,hAPP(fun(U_1818,bool),fun(fun(U_1818,bool),bool),ord_less(fun(U_1818,bool)),U_1817),U_1816))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1818,bool),nat,finite_card(U_1818),U_1817)),hAPP(fun(U_1818,bool),nat,finite_card(U_1818),U_1816)))
      | ~ hBOOL(hAPP(fun(U_1818,bool),bool,hAPP(fun(U_1818,bool),fun(fun(U_1818,bool),bool),ord_less_eq(fun(U_1818,bool)),U_1817),U_1816))
      | ~ hBOOL(hAPP(fun(U_1818,bool),bool,finite_finite(U_1818),U_1816)) ),
    inference(definitional_conversion,[status(esa)],[f_470_2]) ).

cnf(f_470_4,plain,
    ( hBOOL(hAPP(fun(U_1818,bool),bool,hAPP(fun(U_1818,bool),fun(fun(U_1818,bool),bool),ord_less(fun(U_1818,bool)),U_1817),U_1816))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(U_1818,bool),nat,finite_card(U_1818),U_1817)),hAPP(fun(U_1818,bool),nat,finite_card(U_1818),U_1816)))
    | ~ hBOOL(hAPP(fun(U_1818,bool),bool,hAPP(fun(U_1818,bool),fun(fun(U_1818,bool),bool),ord_less_eq(fun(U_1818,bool)),U_1817),U_1816))
    | ~ hBOOL(hAPP(fun(U_1818,bool),bool,finite_finite(U_1818),U_1816)) ),
    inference(clausify,[status(thm)],[f_470_3]) ).

fof(f_471_1,plain,
    ! [X_b,A_3] :
      ( ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
        | ! [N_2,F_1] : ti(fun(X_b,bool),A_3) != hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F_1),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2))) )
      & ( ? [N_2,F_1] : ti(fun(X_b,bool),A_3) = hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F_1),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2)))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_418_finite__conv__nat__seg__image]) ).

fof(f_471_2,plain,
    ! [U_1824,U_1823] :
      ( ( hBOOL(hAPP(fun(U_1824,bool),bool,finite_finite(U_1824),U_1823))
        | ! [U_1822,U_1821] : ti(fun(U_1824,bool),U_1823) != hAPP(fun(nat,bool),fun(U_1824,bool),hAPP(fun(nat,U_1824),fun(fun(nat,bool),fun(U_1824,bool)),image(nat,U_1824),U_1821),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1822))) )
      & ( ? [U_1820,U_1819] : ti(fun(U_1824,bool),U_1823) = hAPP(fun(nat,bool),fun(U_1824,bool),hAPP(fun(nat,U_1824),fun(fun(nat,bool),fun(U_1824,bool)),image(nat,U_1824),U_1819),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1820)))
        | ~ hBOOL(hAPP(fun(U_1824,bool),bool,finite_finite(U_1824),U_1823)) ) ),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

fof(f_471_3,plain,
    ( ! [U_1828,U_1826] :
        ( hBOOL(hAPP(fun(U_1828,bool),bool,finite_finite(U_1828),U_1826))
        | ! [U_1822,U_1821] : ti(fun(U_1828,bool),U_1826) != hAPP(fun(nat,bool),fun(U_1828,bool),hAPP(fun(nat,U_1828),fun(fun(nat,bool),fun(U_1828,bool)),image(nat,U_1828),U_1821),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1822))) )
    & ! [U_1827,U_1825] :
        ( ? [U_1820,U_1819] : ti(fun(U_1827,bool),U_1825) = hAPP(fun(nat,bool),fun(U_1827,bool),hAPP(fun(nat,U_1827),fun(fun(nat,bool),fun(U_1827,bool)),image(nat,U_1827),U_1819),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1820)))
        | ~ hBOOL(hAPP(fun(U_1827,bool),bool,finite_finite(U_1827),U_1825)) ) ),
    inference(miniscope,[status(thm)],[f_471_2]) ).

fof(f_471_4,plain,
    ( ! [U_1828,U_1826] :
        ( hBOOL(hAPP(fun(U_1828,bool),bool,finite_finite(U_1828),U_1826))
        | ! [U_1822,U_1821] : ti(fun(U_1828,bool),U_1826) != hAPP(fun(nat,bool),fun(U_1828,bool),hAPP(fun(nat,U_1828),fun(fun(nat,bool),fun(U_1828,bool)),image(nat,U_1828),U_1821),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1822))) )
    & ! [U_1827,U_1825] :
        ( ? [U_1819] : ti(fun(U_1827,bool),U_1825) = hAPP(fun(nat,bool),fun(U_1827,bool),hAPP(fun(nat,U_1827),fun(fun(nat,bool),fun(U_1827,bool)),image(nat,U_1827),U_1819),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK52(U_1827,U_1825))))
        | ~ hBOOL(hAPP(fun(U_1827,bool),bool,finite_finite(U_1827),U_1825)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_1820,sK52(U_1827,U_1825))],[f_471_3]) ).

fof(f_471_5,plain,
    ( ! [U_1828,U_1826] :
        ( hBOOL(hAPP(fun(U_1828,bool),bool,finite_finite(U_1828),U_1826))
        | ! [U_1822,U_1821] : ti(fun(U_1828,bool),U_1826) != hAPP(fun(nat,bool),fun(U_1828,bool),hAPP(fun(nat,U_1828),fun(fun(nat,bool),fun(U_1828,bool)),image(nat,U_1828),U_1821),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1822))) )
    & ! [U_1827,U_1825] :
        ( ti(fun(U_1827,bool),U_1825) = hAPP(fun(nat,bool),fun(U_1827,bool),hAPP(fun(nat,U_1827),fun(fun(nat,bool),fun(U_1827,bool)),image(nat,U_1827),sK53(U_1827,U_1825)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK52(U_1827,U_1825))))
        | ~ hBOOL(hAPP(fun(U_1827,bool),bool,finite_finite(U_1827),U_1825)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_1819,sK53(U_1827,U_1825))],[f_471_4]) ).

fof(f_471_6,plain,
    ( ! [U_1828,U_1822,U_1826,U_1821] :
        ( hBOOL(hAPP(fun(U_1828,bool),bool,finite_finite(U_1828),U_1826))
        | ti(fun(U_1828,bool),U_1826) != hAPP(fun(nat,bool),fun(U_1828,bool),hAPP(fun(nat,U_1828),fun(fun(nat,bool),fun(U_1828,bool)),image(nat,U_1828),U_1821),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1822))) )
    & ! [U_1827,U_1825] :
        ( ti(fun(U_1827,bool),U_1825) = hAPP(fun(nat,bool),fun(U_1827,bool),hAPP(fun(nat,U_1827),fun(fun(nat,bool),fun(U_1827,bool)),image(nat,U_1827),sK53(U_1827,U_1825)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK52(U_1827,U_1825))))
        | ~ hBOOL(hAPP(fun(U_1827,bool),bool,finite_finite(U_1827),U_1825)) ) ),
    inference(definitional_conversion,[status(esa)],[f_471_5]) ).

cnf(f_471_7,plain,
    ( ti(fun(U_1827,bool),U_1825) = hAPP(fun(nat,bool),fun(U_1827,bool),hAPP(fun(nat,U_1827),fun(fun(nat,bool),fun(U_1827,bool)),image(nat,U_1827),sK53(U_1827,U_1825)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK52(U_1827,U_1825))))
    | ~ hBOOL(hAPP(fun(U_1827,bool),bool,finite_finite(U_1827),U_1825)) ),
    inference(clausify,[status(thm)],[f_471_6]) ).

cnf(f_471_8,plain,
    ( hBOOL(hAPP(fun(U_1828,bool),bool,finite_finite(U_1828),U_1826))
    | ti(fun(U_1828,bool),U_1826) != hAPP(fun(nat,bool),fun(U_1828,bool),hAPP(fun(nat,U_1828),fun(fun(nat,bool),fun(U_1828,bool)),image(nat,U_1828),U_1821),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),U_1822))) ),
    inference(clausify,[status(thm)],[f_471_6]) ).

fof(f_472_1,plain,
    ! [X_b] :
      ( ! [Na,N_3,F] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),N_3))
          | ? [N_2] : ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_2)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_2)))) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_419_lift__Suc__mono__less]) ).

fof(f_472_2,plain,
    ! [U_1833] :
      ( ! [U_1832,U_1831,U_1830] :
          ( hBOOL(hAPP(U_1833,bool,hAPP(U_1833,fun(U_1833,bool),ord_less(U_1833),hAPP(nat,U_1833,U_1830,U_1832)),hAPP(nat,U_1833,U_1830,U_1831)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1832),U_1831))
          | ? [U_1829] : ~ hBOOL(hAPP(U_1833,bool,hAPP(U_1833,fun(U_1833,bool),ord_less(U_1833),hAPP(nat,U_1833,U_1830,U_1829)),hAPP(nat,U_1833,U_1830,hAPP(nat,nat,suc,U_1829)))) )
      | ~ order(U_1833) ),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

fof(f_472_3,plain,
    ! [U_1833] :
      ( ! [U_1832,U_1831,U_1830] :
          ( hBOOL(hAPP(U_1833,bool,hAPP(U_1833,fun(U_1833,bool),ord_less(U_1833),hAPP(nat,U_1833,U_1830,U_1832)),hAPP(nat,U_1833,U_1830,U_1831)))
          | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1832),U_1831))
          | ~ hBOOL(hAPP(U_1833,bool,hAPP(U_1833,fun(U_1833,bool),ord_less(U_1833),hAPP(nat,U_1833,U_1830,sK54(U_1833,U_1832,U_1831,U_1830))),hAPP(nat,U_1833,U_1830,hAPP(nat,nat,suc,sK54(U_1833,U_1832,U_1831,U_1830))))) )
      | ~ order(U_1833) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_1829,sK54(U_1833,U_1832,U_1831,U_1830))],[f_472_2]) ).

fof(f_472_4,plain,
    ! [U_1830,U_1831,U_1833,U_1832] :
      ( hBOOL(hAPP(U_1833,bool,hAPP(U_1833,fun(U_1833,bool),ord_less(U_1833),hAPP(nat,U_1833,U_1830,U_1832)),hAPP(nat,U_1833,U_1830,U_1831)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1832),U_1831))
      | ~ hBOOL(hAPP(U_1833,bool,hAPP(U_1833,fun(U_1833,bool),ord_less(U_1833),hAPP(nat,U_1833,U_1830,sK54(U_1833,U_1832,U_1831,U_1830))),hAPP(nat,U_1833,U_1830,hAPP(nat,nat,suc,sK54(U_1833,U_1832,U_1831,U_1830)))))
      | ~ order(U_1833) ),
    inference(definitional_conversion,[status(esa)],[f_472_3]) ).

cnf(f_472_5,plain,
    ( hBOOL(hAPP(U_1833,bool,hAPP(U_1833,fun(U_1833,bool),ord_less(U_1833),hAPP(nat,U_1833,U_1830,U_1832)),hAPP(nat,U_1833,U_1830,U_1831)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1832),U_1831))
    | ~ hBOOL(hAPP(U_1833,bool,hAPP(U_1833,fun(U_1833,bool),ord_less(U_1833),hAPP(nat,U_1833,U_1830,sK54(U_1833,U_1832,U_1831,U_1830))),hAPP(nat,U_1833,U_1830,hAPP(nat,nat,suc,sK54(U_1833,U_1832,U_1831,U_1830)))))
    | ~ order(U_1833) ),
    inference(clausify,[status(thm)],[f_472_4]) ).

fof(f_473_1,plain,
    ! [X_b,C_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_3))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_420_psubsetD]) ).

fof(f_473_2,plain,
    ! [U_1837,U_1836,U_1835,U_1834] :
      ( hBOOL(hAPP(fun(U_1837,bool),bool,hAPP(U_1837,fun(fun(U_1837,bool),bool),member(U_1837),U_1836),U_1834))
      | ~ hBOOL(hAPP(fun(U_1837,bool),bool,hAPP(U_1837,fun(fun(U_1837,bool),bool),member(U_1837),U_1836),U_1835))
      | ~ hBOOL(hAPP(fun(U_1837,bool),bool,hAPP(fun(U_1837,bool),fun(fun(U_1837,bool),bool),ord_less(fun(U_1837,bool)),U_1835),U_1834)) ),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

fof(f_473_3,plain,
    ! [U_1836,U_1835,U_1837,U_1834] :
      ( hBOOL(hAPP(fun(U_1837,bool),bool,hAPP(U_1837,fun(fun(U_1837,bool),bool),member(U_1837),U_1836),U_1834))
      | ~ hBOOL(hAPP(fun(U_1837,bool),bool,hAPP(U_1837,fun(fun(U_1837,bool),bool),member(U_1837),U_1836),U_1835))
      | ~ hBOOL(hAPP(fun(U_1837,bool),bool,hAPP(fun(U_1837,bool),fun(fun(U_1837,bool),bool),ord_less(fun(U_1837,bool)),U_1835),U_1834)) ),
    inference(definitional_conversion,[status(esa)],[f_473_2]) ).

cnf(f_473_4,plain,
    ( hBOOL(hAPP(fun(U_1837,bool),bool,hAPP(U_1837,fun(fun(U_1837,bool),bool),member(U_1837),U_1836),U_1834))
    | ~ hBOOL(hAPP(fun(U_1837,bool),bool,hAPP(U_1837,fun(fun(U_1837,bool),bool),member(U_1837),U_1836),U_1835))
    | ~ hBOOL(hAPP(fun(U_1837,bool),bool,hAPP(fun(U_1837,bool),fun(fun(U_1837,bool),bool),ord_less(fun(U_1837,bool)),U_1835),U_1834)) ),
    inference(clausify,[status(thm)],[f_473_3]) ).

fof(f_474_1,plain,
    ! [X_b,C_2,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_2),C_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_421_psubset__trans]) ).

fof(f_474_2,plain,
    ! [U_1841,U_1840,U_1839,U_1838] :
      ( hBOOL(hAPP(fun(U_1841,bool),bool,hAPP(fun(U_1841,bool),fun(fun(U_1841,bool),bool),ord_less(fun(U_1841,bool)),U_1839),U_1840))
      | ~ hBOOL(hAPP(fun(U_1841,bool),bool,hAPP(fun(U_1841,bool),fun(fun(U_1841,bool),bool),ord_less(fun(U_1841,bool)),U_1838),U_1840))
      | ~ hBOOL(hAPP(fun(U_1841,bool),bool,hAPP(fun(U_1841,bool),fun(fun(U_1841,bool),bool),ord_less(fun(U_1841,bool)),U_1839),U_1838)) ),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

fof(f_474_3,plain,
    ! [U_1839,U_1841,U_1838,U_1840] :
      ( hBOOL(hAPP(fun(U_1841,bool),bool,hAPP(fun(U_1841,bool),fun(fun(U_1841,bool),bool),ord_less(fun(U_1841,bool)),U_1839),U_1840))
      | ~ hBOOL(hAPP(fun(U_1841,bool),bool,hAPP(fun(U_1841,bool),fun(fun(U_1841,bool),bool),ord_less(fun(U_1841,bool)),U_1838),U_1840))
      | ~ hBOOL(hAPP(fun(U_1841,bool),bool,hAPP(fun(U_1841,bool),fun(fun(U_1841,bool),bool),ord_less(fun(U_1841,bool)),U_1839),U_1838)) ),
    inference(definitional_conversion,[status(esa)],[f_474_2]) ).

cnf(f_474_4,plain,
    ( hBOOL(hAPP(fun(U_1841,bool),bool,hAPP(fun(U_1841,bool),fun(fun(U_1841,bool),bool),ord_less(fun(U_1841,bool)),U_1839),U_1840))
    | ~ hBOOL(hAPP(fun(U_1841,bool),bool,hAPP(fun(U_1841,bool),fun(fun(U_1841,bool),bool),ord_less(fun(U_1841,bool)),U_1838),U_1840))
    | ~ hBOOL(hAPP(fun(U_1841,bool),bool,hAPP(fun(U_1841,bool),fun(fun(U_1841,bool),bool),ord_less(fun(U_1841,bool)),U_1839),U_1838)) ),
    inference(clausify,[status(thm)],[f_474_3]) ).

fof(f_475_1,plain,
    ! [X_b] :
      ( ! [Na,M_1,F] :
          ( ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,M_1)))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1)) )
            & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Na),M_1))
              | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,M_1))) ) )
          | ? [N_2] : ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,F,N_2)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_2)))) )
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_422_lift__Suc__mono__less__iff]) ).

fof(f_475_2,plain,
    ! [U_1846] :
      ( ! [U_1845,U_1844,U_1843] :
          ( ( ( hBOOL(hAPP(U_1846,bool,hAPP(U_1846,fun(U_1846,bool),ord_less(U_1846),hAPP(nat,U_1846,U_1843,U_1845)),hAPP(nat,U_1846,U_1843,U_1844)))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1845),U_1844)) )
            & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1845),U_1844))
              | ~ hBOOL(hAPP(U_1846,bool,hAPP(U_1846,fun(U_1846,bool),ord_less(U_1846),hAPP(nat,U_1846,U_1843,U_1845)),hAPP(nat,U_1846,U_1843,U_1844))) ) )
          | ? [U_1842] : ~ hBOOL(hAPP(U_1846,bool,hAPP(U_1846,fun(U_1846,bool),ord_less(U_1846),hAPP(nat,U_1846,U_1843,U_1842)),hAPP(nat,U_1846,U_1843,hAPP(nat,nat,suc,U_1842)))) )
      | ~ order(U_1846) ),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

fof(f_475_3,plain,
    ! [U_1846] :
      ( ! [U_1845,U_1844,U_1843] :
          ( ( ( hBOOL(hAPP(U_1846,bool,hAPP(U_1846,fun(U_1846,bool),ord_less(U_1846),hAPP(nat,U_1846,U_1843,U_1845)),hAPP(nat,U_1846,U_1843,U_1844)))
              | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1845),U_1844)) )
            & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1845),U_1844))
              | ~ hBOOL(hAPP(U_1846,bool,hAPP(U_1846,fun(U_1846,bool),ord_less(U_1846),hAPP(nat,U_1846,U_1843,U_1845)),hAPP(nat,U_1846,U_1843,U_1844))) ) )
          | ~ hBOOL(hAPP(U_1846,bool,hAPP(U_1846,fun(U_1846,bool),ord_less(U_1846),hAPP(nat,U_1846,U_1843,sK55(U_1846,U_1845,U_1844,U_1843))),hAPP(nat,U_1846,U_1843,hAPP(nat,nat,suc,sK55(U_1846,U_1845,U_1844,U_1843))))) )
      | ~ order(U_1846) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_1842,sK55(U_1846,U_1845,U_1844,U_1843))],[f_475_2]) ).

fof(f_475_4,plain,
    ( ! [U_1843,U_1846,U_1844,U_1845] :
        ( hBOOL(hAPP(U_1846,bool,hAPP(U_1846,fun(U_1846,bool),ord_less(U_1846),hAPP(nat,U_1846,U_1843,U_1845)),hAPP(nat,U_1846,U_1843,U_1844)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1845),U_1844))
        | ~ sP106(U_1843,U_1846,U_1844,U_1845) )
    & ! [U_1843,U_1846,U_1844,U_1845] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1845),U_1844))
        | ~ hBOOL(hAPP(U_1846,bool,hAPP(U_1846,fun(U_1846,bool),ord_less(U_1846),hAPP(nat,U_1846,U_1843,U_1845)),hAPP(nat,U_1846,U_1843,U_1844)))
        | ~ sP106(U_1843,U_1846,U_1844,U_1845) )
    & ! [U_1843,U_1846,U_1844,U_1845] :
        ( sP106(U_1843,U_1846,U_1844,U_1845)
        | ~ hBOOL(hAPP(U_1846,bool,hAPP(U_1846,fun(U_1846,bool),ord_less(U_1846),hAPP(nat,U_1846,U_1843,sK55(U_1846,U_1845,U_1844,U_1843))),hAPP(nat,U_1846,U_1843,hAPP(nat,nat,suc,sK55(U_1846,U_1845,U_1844,U_1843)))))
        | ~ order(U_1846) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP106])],[f_475_3]) ).

cnf(f_475_5,plain,
    ( sP106(U_1843,U_1846,U_1844,U_1845)
    | ~ hBOOL(hAPP(U_1846,bool,hAPP(U_1846,fun(U_1846,bool),ord_less(U_1846),hAPP(nat,U_1846,U_1843,sK55(U_1846,U_1845,U_1844,U_1843))),hAPP(nat,U_1846,U_1843,hAPP(nat,nat,suc,sK55(U_1846,U_1845,U_1844,U_1843)))))
    | ~ order(U_1846) ),
    inference(clausify,[status(thm)],[f_475_4]) ).

cnf(f_475_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1845),U_1844))
    | ~ hBOOL(hAPP(U_1846,bool,hAPP(U_1846,fun(U_1846,bool),ord_less(U_1846),hAPP(nat,U_1846,U_1843,U_1845)),hAPP(nat,U_1846,U_1843,U_1844)))
    | ~ sP106(U_1843,U_1846,U_1844,U_1845) ),
    inference(clausify,[status(thm)],[f_475_4]) ).

cnf(f_475_7,plain,
    ( hBOOL(hAPP(U_1846,bool,hAPP(U_1846,fun(U_1846,bool),ord_less(U_1846),hAPP(nat,U_1846,U_1843,U_1845)),hAPP(nat,U_1846,U_1843,U_1844)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1845),U_1844))
    | ~ sP106(U_1843,U_1846,U_1844,U_1845) ),
    inference(clausify,[status(thm)],[f_475_4]) ).

fof(f_476_1,plain,
    ! [X_a] :
      ( ! [A_1] : hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_423_less__add__one]) ).

fof(f_476_2,plain,
    ! [U_1848] :
      ( ! [U_1847] : hBOOL(hAPP(U_1848,bool,hAPP(U_1848,fun(U_1848,bool),ord_less(U_1848),U_1847),hAPP(U_1848,U_1848,hAPP(U_1848,fun(U_1848,U_1848),plus_plus(U_1848),U_1847),one_one(U_1848))))
      | ~ linordered_semidom(U_1848) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

fof(f_476_3,plain,
    ! [U_1847,U_1848] :
      ( hBOOL(hAPP(U_1848,bool,hAPP(U_1848,fun(U_1848,bool),ord_less(U_1848),U_1847),hAPP(U_1848,U_1848,hAPP(U_1848,fun(U_1848,U_1848),plus_plus(U_1848),U_1847),one_one(U_1848))))
      | ~ linordered_semidom(U_1848) ),
    inference(definitional_conversion,[status(esa)],[f_476_2]) ).

cnf(f_476_4,plain,
    ( hBOOL(hAPP(U_1848,bool,hAPP(U_1848,fun(U_1848,bool),ord_less(U_1848),U_1847),hAPP(U_1848,U_1848,hAPP(U_1848,fun(U_1848,U_1848),plus_plus(U_1848),U_1847),one_one(U_1848))))
    | ~ linordered_semidom(U_1848) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

fof(f_477_1,plain,
    ! [X_a] :
      ( ! [X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))
          | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))
          | ti(X_a,X) = ti(X_a,Y) )
      | ~ linordered_idom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_424_linorder__neqE__linordered__idom]) ).

fof(f_477_2,plain,
    ! [U_1851] :
      ( ! [U_1850,U_1849] :
          ( hBOOL(hAPP(U_1851,bool,hAPP(U_1851,fun(U_1851,bool),ord_less(U_1851),U_1849),U_1850))
          | hBOOL(hAPP(U_1851,bool,hAPP(U_1851,fun(U_1851,bool),ord_less(U_1851),U_1850),U_1849))
          | ti(U_1851,U_1850) = ti(U_1851,U_1849) )
      | ~ linordered_idom(U_1851) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

fof(f_477_3,plain,
    ! [U_1849,U_1850,U_1851] :
      ( hBOOL(hAPP(U_1851,bool,hAPP(U_1851,fun(U_1851,bool),ord_less(U_1851),U_1849),U_1850))
      | hBOOL(hAPP(U_1851,bool,hAPP(U_1851,fun(U_1851,bool),ord_less(U_1851),U_1850),U_1849))
      | ti(U_1851,U_1850) = ti(U_1851,U_1849)
      | ~ linordered_idom(U_1851) ),
    inference(definitional_conversion,[status(esa)],[f_477_2]) ).

cnf(f_477_4,plain,
    ( hBOOL(hAPP(U_1851,bool,hAPP(U_1851,fun(U_1851,bool),ord_less(U_1851),U_1849),U_1850))
    | hBOOL(hAPP(U_1851,bool,hAPP(U_1851,fun(U_1851,bool),ord_less(U_1851),U_1850),U_1849))
    | ti(U_1851,U_1850) = ti(U_1851,U_1849)
    | ~ linordered_idom(U_1851) ),
    inference(clausify,[status(thm)],[f_477_3]) ).

fof(f_478_1,plain,
    ! [Na,N_1] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N_1))
      | ? [X_2] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),Na))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_425_bounded__nat__set__is__finite]) ).

fof(f_478_2,plain,
    ! [U_1854,U_1853] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1853))
      | ? [U_1852] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1852),U_1854))
          & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),U_1852),U_1853)) ) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

fof(f_478_3,plain,
    ! [U_1854,U_1853] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1853))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK56(U_1854,U_1853)),U_1854))
        & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK56(U_1854,U_1853)),U_1853)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_1852,sK56(U_1854,U_1853))],[f_478_2]) ).

fof(f_478_4,plain,
    ( ! [U_1853,U_1854] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK56(U_1854,U_1853)),U_1854))
        | ~ sP107(U_1853,U_1854) )
    & ! [U_1853,U_1854] :
        ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK56(U_1854,U_1853)),U_1853))
        | ~ sP107(U_1853,U_1854) )
    & ! [U_1853,U_1854] :
        ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1853))
        | sP107(U_1853,U_1854) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107])],[f_478_3]) ).

cnf(f_478_5,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),U_1853))
    | sP107(U_1853,U_1854) ),
    inference(clausify,[status(thm)],[f_478_4]) ).

cnf(f_478_6,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK56(U_1854,U_1853)),U_1853))
    | ~ sP107(U_1853,U_1854) ),
    inference(clausify,[status(thm)],[f_478_4]) ).

cnf(f_478_7,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK56(U_1854,U_1853)),U_1854))
    | ~ sP107(U_1853,U_1854) ),
    inference(clausify,[status(thm)],[f_478_4]) ).

fof(f_479_1,plain,
    ! [X_b,A_3,B_2] :
      ( ? [B_3] : hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),A_3)))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_426_psubset__imp__ex__mem]) ).

fof(f_479_2,plain,
    ! [U_1858,U_1857,U_1856] :
      ( ? [U_1855] : hBOOL(hAPP(fun(U_1858,bool),bool,hAPP(U_1858,fun(fun(U_1858,bool),bool),member(U_1858),U_1855),hAPP(fun(U_1858,bool),fun(U_1858,bool),hAPP(fun(U_1858,bool),fun(fun(U_1858,bool),fun(U_1858,bool)),minus_minus(fun(U_1858,bool)),U_1856),U_1857)))
      | ~ hBOOL(hAPP(fun(U_1858,bool),bool,hAPP(fun(U_1858,bool),fun(fun(U_1858,bool),bool),ord_less(fun(U_1858,bool)),U_1857),U_1856)) ),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

fof(f_479_3,plain,
    ! [U_1858,U_1857,U_1856] :
      ( hBOOL(hAPP(fun(U_1858,bool),bool,hAPP(U_1858,fun(fun(U_1858,bool),bool),member(U_1858),sK57(U_1858,U_1857,U_1856)),hAPP(fun(U_1858,bool),fun(U_1858,bool),hAPP(fun(U_1858,bool),fun(fun(U_1858,bool),fun(U_1858,bool)),minus_minus(fun(U_1858,bool)),U_1856),U_1857)))
      | ~ hBOOL(hAPP(fun(U_1858,bool),bool,hAPP(fun(U_1858,bool),fun(fun(U_1858,bool),bool),ord_less(fun(U_1858,bool)),U_1857),U_1856)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_1855,sK57(U_1858,U_1857,U_1856))],[f_479_2]) ).

fof(f_479_4,plain,
    ! [U_1858,U_1856,U_1857] :
      ( hBOOL(hAPP(fun(U_1858,bool),bool,hAPP(U_1858,fun(fun(U_1858,bool),bool),member(U_1858),sK57(U_1858,U_1857,U_1856)),hAPP(fun(U_1858,bool),fun(U_1858,bool),hAPP(fun(U_1858,bool),fun(fun(U_1858,bool),fun(U_1858,bool)),minus_minus(fun(U_1858,bool)),U_1856),U_1857)))
      | ~ hBOOL(hAPP(fun(U_1858,bool),bool,hAPP(fun(U_1858,bool),fun(fun(U_1858,bool),bool),ord_less(fun(U_1858,bool)),U_1857),U_1856)) ),
    inference(definitional_conversion,[status(esa)],[f_479_3]) ).

cnf(f_479_5,plain,
    ( hBOOL(hAPP(fun(U_1858,bool),bool,hAPP(U_1858,fun(fun(U_1858,bool),bool),member(U_1858),sK57(U_1858,U_1857,U_1856)),hAPP(fun(U_1858,bool),fun(U_1858,bool),hAPP(fun(U_1858,bool),fun(fun(U_1858,bool),fun(U_1858,bool)),minus_minus(fun(U_1858,bool)),U_1856),U_1857)))
    | ~ hBOOL(hAPP(fun(U_1858,bool),bool,hAPP(fun(U_1858,bool),fun(fun(U_1858,bool),bool),ord_less(fun(U_1858,bool)),U_1857),U_1856)) ),
    inference(clausify,[status(thm)],[f_479_4]) ).

fof(f_480_1,plain,
    ! [I_1,J_1,F] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1))
      | ? [I_2,J] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) ) ),
    inference(fof_nnf,[status(thm)],[fact_427_less__mono__imp__le__mono]) ).

fof(f_480_2,plain,
    ! [U_1863,U_1862,U_1861] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1861,U_1863)),hAPP(nat,nat,U_1861,U_1862)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1863),U_1862))
      | ? [U_1860,U_1859] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1861,U_1860)),hAPP(nat,nat,U_1861,U_1859)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1860),U_1859)) ) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

fof(f_480_3,plain,
    ! [U_1863,U_1862,U_1861] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1861,U_1863)),hAPP(nat,nat,U_1861,U_1862)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1863),U_1862))
      | ? [U_1859] :
          ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1861,sK58(U_1863,U_1862,U_1861))),hAPP(nat,nat,U_1861,U_1859)))
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK58(U_1863,U_1862,U_1861)),U_1859)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_1860,sK58(U_1863,U_1862,U_1861))],[f_480_2]) ).

fof(f_480_4,plain,
    ! [U_1863,U_1862,U_1861] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1861,U_1863)),hAPP(nat,nat,U_1861,U_1862)))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1863),U_1862))
      | ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1861,sK58(U_1863,U_1862,U_1861))),hAPP(nat,nat,U_1861,sK59(U_1863,U_1862,U_1861))))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK58(U_1863,U_1862,U_1861)),sK59(U_1863,U_1862,U_1861))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_1859,sK59(U_1863,U_1862,U_1861))],[f_480_3]) ).

fof(f_480_5,plain,
    ( ! [U_1861,U_1862,U_1863] :
        ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1861,sK58(U_1863,U_1862,U_1861))),hAPP(nat,nat,U_1861,sK59(U_1863,U_1862,U_1861))))
        | ~ sP108(U_1861,U_1862,U_1863) )
    & ! [U_1861,U_1862,U_1863] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK58(U_1863,U_1862,U_1861)),sK59(U_1863,U_1862,U_1861)))
        | ~ sP108(U_1861,U_1862,U_1863) )
    & ! [U_1861,U_1862,U_1863] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1861,U_1863)),hAPP(nat,nat,U_1861,U_1862)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1863),U_1862))
        | sP108(U_1861,U_1862,U_1863) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108])],[f_480_4]) ).

cnf(f_480_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,U_1861,U_1863)),hAPP(nat,nat,U_1861,U_1862)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_1863),U_1862))
    | sP108(U_1861,U_1862,U_1863) ),
    inference(clausify,[status(thm)],[f_480_5]) ).

cnf(f_480_7,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK58(U_1863,U_1862,U_1861)),sK59(U_1863,U_1862,U_1861)))
    | ~ sP108(U_1861,U_1862,U_1863) ),
    inference(clausify,[status(thm)],[f_480_5]) ).

cnf(f_480_8,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,U_1861,sK58(U_1863,U_1862,U_1861))),hAPP(nat,nat,U_1861,sK59(U_1863,U_1862,U_1861))))
    | ~ sP108(U_1861,U_1862,U_1863) ),
    inference(clausify,[status(thm)],[f_480_5]) ).

fof(f_481_1,plain,
    ! [I,K] :
      ( ? [J] :
          ( K = hAPP(nat,nat,suc,J)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I)),K)) ),
    inference(fof_nnf,[status(thm)],[fact_428_Suc__lessE]) ).

fof(f_481_2,plain,
    ! [U_1866,U_1865] :
      ( ? [U_1864] :
          ( U_1865 = hAPP(nat,nat,suc,U_1864)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1866),U_1864)) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1866)),U_1865)) ),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

fof(f_481_3,plain,
    ! [U_1866,U_1865] :
      ( ( U_1865 = hAPP(nat,nat,suc,sK60(U_1866,U_1865))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1866),sK60(U_1866,U_1865))) )
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1866)),U_1865)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_1864,sK60(U_1866,U_1865))],[f_481_2]) ).

fof(f_481_4,plain,
    ( ! [U_1866,U_1865] :
        ( U_1865 = hAPP(nat,nat,suc,sK60(U_1866,U_1865))
        | ~ sP109(U_1866,U_1865) )
    & ! [U_1866,U_1865] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1866),sK60(U_1866,U_1865)))
        | ~ sP109(U_1866,U_1865) )
    & ! [U_1866,U_1865] :
        ( sP109(U_1866,U_1865)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1866)),U_1865)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_481_3]) ).

cnf(f_481_5,plain,
    ( sP109(U_1866,U_1865)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,U_1866)),U_1865)) ),
    inference(clausify,[status(thm)],[f_481_4]) ).

cnf(f_481_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1866),sK60(U_1866,U_1865)))
    | ~ sP109(U_1866,U_1865) ),
    inference(clausify,[status(thm)],[f_481_4]) ).

cnf(f_481_7,plain,
    ( U_1865 = hAPP(nat,nat,suc,sK60(U_1866,U_1865))
    | ~ sP109(U_1866,U_1865) ),
    inference(clausify,[status(thm)],[f_481_4]) ).

fof(f_482_1,plain,
    ! [I,K] :
      ( ? [J] :
          ( K = hAPP(nat,nat,suc,J)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) )
      | K = hAPP(nat,nat,suc,I)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K)) ),
    inference(fof_nnf,[status(thm)],[fact_429_lessE]) ).

fof(f_482_2,plain,
    ! [U_1869,U_1868] :
      ( ? [U_1867] :
          ( U_1868 = hAPP(nat,nat,suc,U_1867)
          & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1869),U_1867)) )
      | U_1868 = hAPP(nat,nat,suc,U_1869)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1869),U_1868)) ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

fof(f_482_3,plain,
    ! [U_1869,U_1868] :
      ( ( U_1868 = hAPP(nat,nat,suc,sK61(U_1869,U_1868))
        & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1869),sK61(U_1869,U_1868))) )
      | U_1868 = hAPP(nat,nat,suc,U_1869)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1869),U_1868)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_1867,sK61(U_1869,U_1868))],[f_482_2]) ).

fof(f_482_4,plain,
    ( ! [U_1868,U_1869] :
        ( U_1868 = hAPP(nat,nat,suc,sK61(U_1869,U_1868))
        | ~ sP110(U_1868,U_1869) )
    & ! [U_1868,U_1869] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1869),sK61(U_1869,U_1868)))
        | ~ sP110(U_1868,U_1869) )
    & ! [U_1868,U_1869] :
        ( sP110(U_1868,U_1869)
        | U_1868 = hAPP(nat,nat,suc,U_1869)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1869),U_1868)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110])],[f_482_3]) ).

cnf(f_482_5,plain,
    ( sP110(U_1868,U_1869)
    | U_1868 = hAPP(nat,nat,suc,U_1869)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1869),U_1868)) ),
    inference(clausify,[status(thm)],[f_482_4]) ).

cnf(f_482_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1869),sK61(U_1869,U_1868)))
    | ~ sP110(U_1868,U_1869) ),
    inference(clausify,[status(thm)],[f_482_4]) ).

cnf(f_482_7,plain,
    ( U_1868 = hAPP(nat,nat,suc,sK61(U_1869,U_1868))
    | ~ sP110(U_1868,U_1869) ),
    inference(clausify,[status(thm)],[f_482_4]) ).

fof(f_483_1,plain,
    ! [X_c,X_b] :
      ( ! [C_1,F,B,A_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,C_1)),A_2))
          | ? [X_2,Y_2] :
              ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Y_2)),hAPP(X_c,X_b,F,X_2)))
              & hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Y_2),X_2)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),B))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,B)),A_2)) )
      | ~ ord(X_c)
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_430_xt6]) ).

fof(f_483_2,plain,
    ! [U_1877,U_1876] :
      ( ! [U_1875,U_1874,U_1873,U_1872] :
          ( hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less(U_1876),hAPP(U_1877,U_1876,U_1874,U_1875)),U_1872))
          | ? [U_1871,U_1870] :
              ( ~ hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less(U_1876),hAPP(U_1877,U_1876,U_1874,U_1870)),hAPP(U_1877,U_1876,U_1874,U_1871)))
              & hBOOL(hAPP(U_1877,bool,hAPP(U_1877,fun(U_1877,bool),ord_less(U_1877),U_1870),U_1871)) )
          | ~ hBOOL(hAPP(U_1877,bool,hAPP(U_1877,fun(U_1877,bool),ord_less(U_1877),U_1875),U_1873))
          | ~ hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less_eq(U_1876),hAPP(U_1877,U_1876,U_1874,U_1873)),U_1872)) )
      | ~ ord(U_1877)
      | ~ order(U_1876) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

fof(f_483_3,plain,
    ! [U_1877,U_1876] :
      ( ! [U_1875,U_1874,U_1873,U_1872] :
          ( hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less(U_1876),hAPP(U_1877,U_1876,U_1874,U_1875)),U_1872))
          | ? [U_1870] :
              ( ~ hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less(U_1876),hAPP(U_1877,U_1876,U_1874,U_1870)),hAPP(U_1877,U_1876,U_1874,sK62(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872))))
              & hBOOL(hAPP(U_1877,bool,hAPP(U_1877,fun(U_1877,bool),ord_less(U_1877),U_1870),sK62(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872))) )
          | ~ hBOOL(hAPP(U_1877,bool,hAPP(U_1877,fun(U_1877,bool),ord_less(U_1877),U_1875),U_1873))
          | ~ hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less_eq(U_1876),hAPP(U_1877,U_1876,U_1874,U_1873)),U_1872)) )
      | ~ ord(U_1877)
      | ~ order(U_1876) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_1871,sK62(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872))],[f_483_2]) ).

fof(f_483_4,plain,
    ! [U_1877,U_1876] :
      ( ! [U_1875,U_1874,U_1873,U_1872] :
          ( hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less(U_1876),hAPP(U_1877,U_1876,U_1874,U_1875)),U_1872))
          | ( ~ hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less(U_1876),hAPP(U_1877,U_1876,U_1874,sK63(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872))),hAPP(U_1877,U_1876,U_1874,sK62(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872))))
            & hBOOL(hAPP(U_1877,bool,hAPP(U_1877,fun(U_1877,bool),ord_less(U_1877),sK63(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872)),sK62(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872))) )
          | ~ hBOOL(hAPP(U_1877,bool,hAPP(U_1877,fun(U_1877,bool),ord_less(U_1877),U_1875),U_1873))
          | ~ hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less_eq(U_1876),hAPP(U_1877,U_1876,U_1874,U_1873)),U_1872)) )
      | ~ ord(U_1877)
      | ~ order(U_1876) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_1870,sK63(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872))],[f_483_3]) ).

fof(f_483_5,plain,
    ( ! [U_1876,U_1872,U_1874,U_1873,U_1875,U_1877] :
        ( ~ hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less(U_1876),hAPP(U_1877,U_1876,U_1874,sK63(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872))),hAPP(U_1877,U_1876,U_1874,sK62(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872))))
        | ~ sP111(U_1876,U_1872,U_1874,U_1873,U_1875,U_1877) )
    & ! [U_1876,U_1872,U_1874,U_1873,U_1875,U_1877] :
        ( hBOOL(hAPP(U_1877,bool,hAPP(U_1877,fun(U_1877,bool),ord_less(U_1877),sK63(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872)),sK62(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872)))
        | ~ sP111(U_1876,U_1872,U_1874,U_1873,U_1875,U_1877) )
    & ! [U_1876,U_1872,U_1874,U_1873,U_1875,U_1877] :
        ( hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less(U_1876),hAPP(U_1877,U_1876,U_1874,U_1875)),U_1872))
        | sP111(U_1876,U_1872,U_1874,U_1873,U_1875,U_1877)
        | ~ hBOOL(hAPP(U_1877,bool,hAPP(U_1877,fun(U_1877,bool),ord_less(U_1877),U_1875),U_1873))
        | ~ hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less_eq(U_1876),hAPP(U_1877,U_1876,U_1874,U_1873)),U_1872))
        | ~ ord(U_1877)
        | ~ order(U_1876) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP111])],[f_483_4]) ).

cnf(f_483_6,plain,
    ( hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less(U_1876),hAPP(U_1877,U_1876,U_1874,U_1875)),U_1872))
    | sP111(U_1876,U_1872,U_1874,U_1873,U_1875,U_1877)
    | ~ hBOOL(hAPP(U_1877,bool,hAPP(U_1877,fun(U_1877,bool),ord_less(U_1877),U_1875),U_1873))
    | ~ hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less_eq(U_1876),hAPP(U_1877,U_1876,U_1874,U_1873)),U_1872))
    | ~ ord(U_1877)
    | ~ order(U_1876) ),
    inference(clausify,[status(thm)],[f_483_5]) ).

cnf(f_483_7,plain,
    ( hBOOL(hAPP(U_1877,bool,hAPP(U_1877,fun(U_1877,bool),ord_less(U_1877),sK63(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872)),sK62(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872)))
    | ~ sP111(U_1876,U_1872,U_1874,U_1873,U_1875,U_1877) ),
    inference(clausify,[status(thm)],[f_483_5]) ).

cnf(f_483_8,plain,
    ( ~ hBOOL(hAPP(U_1876,bool,hAPP(U_1876,fun(U_1876,bool),ord_less(U_1876),hAPP(U_1877,U_1876,U_1874,sK63(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872))),hAPP(U_1877,U_1876,U_1874,sK62(U_1877,U_1876,U_1875,U_1874,U_1873,U_1872))))
    | ~ sP111(U_1876,U_1872,U_1874,U_1873,U_1875,U_1877) ),
    inference(clausify,[status(thm)],[f_483_5]) ).

fof(f_484_1,plain,
    ! [X_a] :
      ( ! [Z,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))
          | ? [X_2] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y)) ) )
      | ~ dense_linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_431_dense__le]) ).

fof(f_484_2,plain,
    ! [U_1881] :
      ( ! [U_1880,U_1879] :
          ( hBOOL(hAPP(U_1881,bool,hAPP(U_1881,fun(U_1881,bool),ord_less_eq(U_1881),U_1879),U_1880))
          | ? [U_1878] :
              ( ~ hBOOL(hAPP(U_1881,bool,hAPP(U_1881,fun(U_1881,bool),ord_less_eq(U_1881),U_1878),U_1880))
              & hBOOL(hAPP(U_1881,bool,hAPP(U_1881,fun(U_1881,bool),ord_less(U_1881),U_1878),U_1879)) ) )
      | ~ dense_linorder(U_1881) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

fof(f_484_3,plain,
    ! [U_1881] :
      ( ! [U_1880,U_1879] :
          ( hBOOL(hAPP(U_1881,bool,hAPP(U_1881,fun(U_1881,bool),ord_less_eq(U_1881),U_1879),U_1880))
          | ( ~ hBOOL(hAPP(U_1881,bool,hAPP(U_1881,fun(U_1881,bool),ord_less_eq(U_1881),sK64(U_1881,U_1880,U_1879)),U_1880))
            & hBOOL(hAPP(U_1881,bool,hAPP(U_1881,fun(U_1881,bool),ord_less(U_1881),sK64(U_1881,U_1880,U_1879)),U_1879)) ) )
      | ~ dense_linorder(U_1881) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_1878,sK64(U_1881,U_1880,U_1879))],[f_484_2]) ).

fof(f_484_4,plain,
    ( ! [U_1879,U_1880,U_1881] :
        ( ~ hBOOL(hAPP(U_1881,bool,hAPP(U_1881,fun(U_1881,bool),ord_less_eq(U_1881),sK64(U_1881,U_1880,U_1879)),U_1880))
        | ~ sP112(U_1879,U_1880,U_1881) )
    & ! [U_1879,U_1880,U_1881] :
        ( hBOOL(hAPP(U_1881,bool,hAPP(U_1881,fun(U_1881,bool),ord_less(U_1881),sK64(U_1881,U_1880,U_1879)),U_1879))
        | ~ sP112(U_1879,U_1880,U_1881) )
    & ! [U_1879,U_1880,U_1881] :
        ( hBOOL(hAPP(U_1881,bool,hAPP(U_1881,fun(U_1881,bool),ord_less_eq(U_1881),U_1879),U_1880))
        | sP112(U_1879,U_1880,U_1881)
        | ~ dense_linorder(U_1881) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112])],[f_484_3]) ).

cnf(f_484_5,plain,
    ( hBOOL(hAPP(U_1881,bool,hAPP(U_1881,fun(U_1881,bool),ord_less_eq(U_1881),U_1879),U_1880))
    | sP112(U_1879,U_1880,U_1881)
    | ~ dense_linorder(U_1881) ),
    inference(clausify,[status(thm)],[f_484_4]) ).

cnf(f_484_6,plain,
    ( hBOOL(hAPP(U_1881,bool,hAPP(U_1881,fun(U_1881,bool),ord_less(U_1881),sK64(U_1881,U_1880,U_1879)),U_1879))
    | ~ sP112(U_1879,U_1880,U_1881) ),
    inference(clausify,[status(thm)],[f_484_4]) ).

cnf(f_484_7,plain,
    ( ~ hBOOL(hAPP(U_1881,bool,hAPP(U_1881,fun(U_1881,bool),ord_less_eq(U_1881),sK64(U_1881,U_1880,U_1879)),U_1880))
    | ~ sP112(U_1879,U_1880,U_1881) ),
    inference(clausify,[status(thm)],[f_484_4]) ).

fof(f_485_1,plain,
    ! [X_a] :
      ( ! [Z,X,Y] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))
          | ? [W] :
              ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Y))
              & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W)) )
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) )
      | ~ dense_linorder(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_432_dense__le__bounded]) ).

fof(f_485_2,plain,
    ! [U_1886] :
      ( ! [U_1885,U_1884,U_1883] :
          ( hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less_eq(U_1886),U_1883),U_1885))
          | ? [U_1882] :
              ( ~ hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less_eq(U_1886),U_1882),U_1885))
              & hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less(U_1886),U_1882),U_1883))
              & hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less(U_1886),U_1884),U_1882)) )
          | ~ hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less(U_1886),U_1884),U_1883)) )
      | ~ dense_linorder(U_1886) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

fof(f_485_3,plain,
    ! [U_1886] :
      ( ! [U_1885,U_1884,U_1883] :
          ( hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less_eq(U_1886),U_1883),U_1885))
          | ( ~ hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less_eq(U_1886),sK65(U_1886,U_1885,U_1884,U_1883)),U_1885))
            & hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less(U_1886),sK65(U_1886,U_1885,U_1884,U_1883)),U_1883))
            & hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less(U_1886),U_1884),sK65(U_1886,U_1885,U_1884,U_1883))) )
          | ~ hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less(U_1886),U_1884),U_1883)) )
      | ~ dense_linorder(U_1886) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_1882,sK65(U_1886,U_1885,U_1884,U_1883))],[f_485_2]) ).

fof(f_485_4,plain,
    ( ! [U_1883,U_1886,U_1884,U_1885] :
        ( ~ hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less_eq(U_1886),sK65(U_1886,U_1885,U_1884,U_1883)),U_1885))
        | ~ sP113(U_1883,U_1886,U_1884,U_1885) )
    & ! [U_1883,U_1886,U_1884,U_1885] :
        ( hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less(U_1886),sK65(U_1886,U_1885,U_1884,U_1883)),U_1883))
        | ~ sP113(U_1883,U_1886,U_1884,U_1885) )
    & ! [U_1883,U_1886,U_1884,U_1885] :
        ( hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less(U_1886),U_1884),sK65(U_1886,U_1885,U_1884,U_1883)))
        | ~ sP113(U_1883,U_1886,U_1884,U_1885) )
    & ! [U_1883,U_1886,U_1884,U_1885] :
        ( hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less_eq(U_1886),U_1883),U_1885))
        | sP113(U_1883,U_1886,U_1884,U_1885)
        | ~ hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less(U_1886),U_1884),U_1883))
        | ~ dense_linorder(U_1886) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113])],[f_485_3]) ).

cnf(f_485_5,plain,
    ( hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less_eq(U_1886),U_1883),U_1885))
    | sP113(U_1883,U_1886,U_1884,U_1885)
    | ~ hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less(U_1886),U_1884),U_1883))
    | ~ dense_linorder(U_1886) ),
    inference(clausify,[status(thm)],[f_485_4]) ).

cnf(f_485_6,plain,
    ( hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less(U_1886),U_1884),sK65(U_1886,U_1885,U_1884,U_1883)))
    | ~ sP113(U_1883,U_1886,U_1884,U_1885) ),
    inference(clausify,[status(thm)],[f_485_4]) ).

cnf(f_485_7,plain,
    ( hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less(U_1886),sK65(U_1886,U_1885,U_1884,U_1883)),U_1883))
    | ~ sP113(U_1883,U_1886,U_1884,U_1885) ),
    inference(clausify,[status(thm)],[f_485_4]) ).

cnf(f_485_8,plain,
    ( ~ hBOOL(hAPP(U_1886,bool,hAPP(U_1886,fun(U_1886,bool),ord_less_eq(U_1886),sK65(U_1886,U_1885,U_1884,U_1883)),U_1885))
    | ~ sP113(U_1883,U_1886,U_1884,U_1885) ),
    inference(clausify,[status(thm)],[f_485_4]) ).

fof(f_486_1,plain,
    ! [X_c,X_b] :
      ( ! [C_1,F,B,A_2] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,C_1)),A_2))
          | ? [X_2,Y_2] :
              ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Y_2)),hAPP(X_c,X_b,F,X_2)))
              & hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Y_2),X_2)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),C_1),B))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,B)),A_2)) )
      | ~ order(X_c)
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_433_xt4]) ).

fof(f_486_2,plain,
    ! [U_1894,U_1893] :
      ( ! [U_1892,U_1891,U_1890,U_1889] :
          ( hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less(U_1893),hAPP(U_1894,U_1893,U_1891,U_1892)),U_1889))
          | ? [U_1888,U_1887] :
              ( ~ hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less_eq(U_1893),hAPP(U_1894,U_1893,U_1891,U_1887)),hAPP(U_1894,U_1893,U_1891,U_1888)))
              & hBOOL(hAPP(U_1894,bool,hAPP(U_1894,fun(U_1894,bool),ord_less_eq(U_1894),U_1887),U_1888)) )
          | ~ hBOOL(hAPP(U_1894,bool,hAPP(U_1894,fun(U_1894,bool),ord_less_eq(U_1894),U_1892),U_1890))
          | ~ hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less(U_1893),hAPP(U_1894,U_1893,U_1891,U_1890)),U_1889)) )
      | ~ order(U_1894)
      | ~ order(U_1893) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

fof(f_486_3,plain,
    ! [U_1894,U_1893] :
      ( ! [U_1892,U_1891,U_1890,U_1889] :
          ( hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less(U_1893),hAPP(U_1894,U_1893,U_1891,U_1892)),U_1889))
          | ? [U_1887] :
              ( ~ hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less_eq(U_1893),hAPP(U_1894,U_1893,U_1891,U_1887)),hAPP(U_1894,U_1893,U_1891,sK66(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889))))
              & hBOOL(hAPP(U_1894,bool,hAPP(U_1894,fun(U_1894,bool),ord_less_eq(U_1894),U_1887),sK66(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889))) )
          | ~ hBOOL(hAPP(U_1894,bool,hAPP(U_1894,fun(U_1894,bool),ord_less_eq(U_1894),U_1892),U_1890))
          | ~ hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less(U_1893),hAPP(U_1894,U_1893,U_1891,U_1890)),U_1889)) )
      | ~ order(U_1894)
      | ~ order(U_1893) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_1888,sK66(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889))],[f_486_2]) ).

fof(f_486_4,plain,
    ! [U_1894,U_1893] :
      ( ! [U_1892,U_1891,U_1890,U_1889] :
          ( hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less(U_1893),hAPP(U_1894,U_1893,U_1891,U_1892)),U_1889))
          | ( ~ hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less_eq(U_1893),hAPP(U_1894,U_1893,U_1891,sK67(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889))),hAPP(U_1894,U_1893,U_1891,sK66(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889))))
            & hBOOL(hAPP(U_1894,bool,hAPP(U_1894,fun(U_1894,bool),ord_less_eq(U_1894),sK67(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889)),sK66(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889))) )
          | ~ hBOOL(hAPP(U_1894,bool,hAPP(U_1894,fun(U_1894,bool),ord_less_eq(U_1894),U_1892),U_1890))
          | ~ hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less(U_1893),hAPP(U_1894,U_1893,U_1891,U_1890)),U_1889)) )
      | ~ order(U_1894)
      | ~ order(U_1893) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_1887,sK67(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889))],[f_486_3]) ).

fof(f_486_5,plain,
    ( ! [U_1889,U_1892,U_1890,U_1891,U_1893,U_1894] :
        ( ~ hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less_eq(U_1893),hAPP(U_1894,U_1893,U_1891,sK67(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889))),hAPP(U_1894,U_1893,U_1891,sK66(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889))))
        | ~ sP114(U_1889,U_1892,U_1890,U_1891,U_1893,U_1894) )
    & ! [U_1889,U_1892,U_1890,U_1891,U_1893,U_1894] :
        ( hBOOL(hAPP(U_1894,bool,hAPP(U_1894,fun(U_1894,bool),ord_less_eq(U_1894),sK67(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889)),sK66(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889)))
        | ~ sP114(U_1889,U_1892,U_1890,U_1891,U_1893,U_1894) )
    & ! [U_1889,U_1892,U_1890,U_1891,U_1893,U_1894] :
        ( hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less(U_1893),hAPP(U_1894,U_1893,U_1891,U_1892)),U_1889))
        | sP114(U_1889,U_1892,U_1890,U_1891,U_1893,U_1894)
        | ~ hBOOL(hAPP(U_1894,bool,hAPP(U_1894,fun(U_1894,bool),ord_less_eq(U_1894),U_1892),U_1890))
        | ~ hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less(U_1893),hAPP(U_1894,U_1893,U_1891,U_1890)),U_1889))
        | ~ order(U_1894)
        | ~ order(U_1893) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114])],[f_486_4]) ).

cnf(f_486_6,plain,
    ( hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less(U_1893),hAPP(U_1894,U_1893,U_1891,U_1892)),U_1889))
    | sP114(U_1889,U_1892,U_1890,U_1891,U_1893,U_1894)
    | ~ hBOOL(hAPP(U_1894,bool,hAPP(U_1894,fun(U_1894,bool),ord_less_eq(U_1894),U_1892),U_1890))
    | ~ hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less(U_1893),hAPP(U_1894,U_1893,U_1891,U_1890)),U_1889))
    | ~ order(U_1894)
    | ~ order(U_1893) ),
    inference(clausify,[status(thm)],[f_486_5]) ).

cnf(f_486_7,plain,
    ( hBOOL(hAPP(U_1894,bool,hAPP(U_1894,fun(U_1894,bool),ord_less_eq(U_1894),sK67(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889)),sK66(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889)))
    | ~ sP114(U_1889,U_1892,U_1890,U_1891,U_1893,U_1894) ),
    inference(clausify,[status(thm)],[f_486_5]) ).

cnf(f_486_8,plain,
    ( ~ hBOOL(hAPP(U_1893,bool,hAPP(U_1893,fun(U_1893,bool),ord_less_eq(U_1893),hAPP(U_1894,U_1893,U_1891,sK67(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889))),hAPP(U_1894,U_1893,U_1891,sK66(U_1894,U_1893,U_1892,U_1891,U_1890,U_1889))))
    | ~ sP114(U_1889,U_1892,U_1890,U_1891,U_1893,U_1894) ),
    inference(clausify,[status(thm)],[f_486_5]) ).

fof(f_487_1,plain,
    ! [X_b,X_c] :
      ( ! [C_1,A_2,F,B] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1)))
          | ? [X_2,Y_2] :
              ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_2)))
              & hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),X_2),Y_2)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),B),C_1))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),hAPP(X_c,X_b,F,B))) )
      | ~ order(X_b)
      | ~ order(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_434_order__le__less__subst1]) ).

fof(f_487_2,plain,
    ! [U_1902,U_1901] :
      ( ! [U_1900,U_1899,U_1898,U_1897] :
          ( hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less(U_1902),U_1899),hAPP(U_1901,U_1902,U_1898,U_1900)))
          | ? [U_1896,U_1895] :
              ( ~ hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less(U_1902),hAPP(U_1901,U_1902,U_1898,U_1896)),hAPP(U_1901,U_1902,U_1898,U_1895)))
              & hBOOL(hAPP(U_1901,bool,hAPP(U_1901,fun(U_1901,bool),ord_less(U_1901),U_1896),U_1895)) )
          | ~ hBOOL(hAPP(U_1901,bool,hAPP(U_1901,fun(U_1901,bool),ord_less(U_1901),U_1897),U_1900))
          | ~ hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less_eq(U_1902),U_1899),hAPP(U_1901,U_1902,U_1898,U_1897))) )
      | ~ order(U_1902)
      | ~ order(U_1901) ),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

fof(f_487_3,plain,
    ! [U_1902,U_1901] :
      ( ! [U_1900,U_1899,U_1898,U_1897] :
          ( hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less(U_1902),U_1899),hAPP(U_1901,U_1902,U_1898,U_1900)))
          | ? [U_1895] :
              ( ~ hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less(U_1902),hAPP(U_1901,U_1902,U_1898,sK68(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897))),hAPP(U_1901,U_1902,U_1898,U_1895)))
              & hBOOL(hAPP(U_1901,bool,hAPP(U_1901,fun(U_1901,bool),ord_less(U_1901),sK68(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897)),U_1895)) )
          | ~ hBOOL(hAPP(U_1901,bool,hAPP(U_1901,fun(U_1901,bool),ord_less(U_1901),U_1897),U_1900))
          | ~ hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less_eq(U_1902),U_1899),hAPP(U_1901,U_1902,U_1898,U_1897))) )
      | ~ order(U_1902)
      | ~ order(U_1901) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_1896,sK68(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897))],[f_487_2]) ).

fof(f_487_4,plain,
    ! [U_1902,U_1901] :
      ( ! [U_1900,U_1899,U_1898,U_1897] :
          ( hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less(U_1902),U_1899),hAPP(U_1901,U_1902,U_1898,U_1900)))
          | ( ~ hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less(U_1902),hAPP(U_1901,U_1902,U_1898,sK68(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897))),hAPP(U_1901,U_1902,U_1898,sK69(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897))))
            & hBOOL(hAPP(U_1901,bool,hAPP(U_1901,fun(U_1901,bool),ord_less(U_1901),sK68(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897)),sK69(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897))) )
          | ~ hBOOL(hAPP(U_1901,bool,hAPP(U_1901,fun(U_1901,bool),ord_less(U_1901),U_1897),U_1900))
          | ~ hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less_eq(U_1902),U_1899),hAPP(U_1901,U_1902,U_1898,U_1897))) )
      | ~ order(U_1902)
      | ~ order(U_1901) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_1895,sK69(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897))],[f_487_3]) ).

fof(f_487_5,plain,
    ( ! [U_1898,U_1897,U_1899,U_1901,U_1900,U_1902] :
        ( ~ hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less(U_1902),hAPP(U_1901,U_1902,U_1898,sK68(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897))),hAPP(U_1901,U_1902,U_1898,sK69(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897))))
        | ~ sP115(U_1898,U_1897,U_1899,U_1901,U_1900,U_1902) )
    & ! [U_1898,U_1897,U_1899,U_1901,U_1900,U_1902] :
        ( hBOOL(hAPP(U_1901,bool,hAPP(U_1901,fun(U_1901,bool),ord_less(U_1901),sK68(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897)),sK69(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897)))
        | ~ sP115(U_1898,U_1897,U_1899,U_1901,U_1900,U_1902) )
    & ! [U_1898,U_1897,U_1899,U_1901,U_1900,U_1902] :
        ( hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less(U_1902),U_1899),hAPP(U_1901,U_1902,U_1898,U_1900)))
        | sP115(U_1898,U_1897,U_1899,U_1901,U_1900,U_1902)
        | ~ hBOOL(hAPP(U_1901,bool,hAPP(U_1901,fun(U_1901,bool),ord_less(U_1901),U_1897),U_1900))
        | ~ hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less_eq(U_1902),U_1899),hAPP(U_1901,U_1902,U_1898,U_1897)))
        | ~ order(U_1902)
        | ~ order(U_1901) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115])],[f_487_4]) ).

cnf(f_487_6,plain,
    ( hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less(U_1902),U_1899),hAPP(U_1901,U_1902,U_1898,U_1900)))
    | sP115(U_1898,U_1897,U_1899,U_1901,U_1900,U_1902)
    | ~ hBOOL(hAPP(U_1901,bool,hAPP(U_1901,fun(U_1901,bool),ord_less(U_1901),U_1897),U_1900))
    | ~ hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less_eq(U_1902),U_1899),hAPP(U_1901,U_1902,U_1898,U_1897)))
    | ~ order(U_1902)
    | ~ order(U_1901) ),
    inference(clausify,[status(thm)],[f_487_5]) ).

cnf(f_487_7,plain,
    ( hBOOL(hAPP(U_1901,bool,hAPP(U_1901,fun(U_1901,bool),ord_less(U_1901),sK68(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897)),sK69(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897)))
    | ~ sP115(U_1898,U_1897,U_1899,U_1901,U_1900,U_1902) ),
    inference(clausify,[status(thm)],[f_487_5]) ).

cnf(f_487_8,plain,
    ( ~ hBOOL(hAPP(U_1902,bool,hAPP(U_1902,fun(U_1902,bool),ord_less(U_1902),hAPP(U_1901,U_1902,U_1898,sK68(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897))),hAPP(U_1901,U_1902,U_1898,sK69(U_1902,U_1901,U_1900,U_1899,U_1898,U_1897))))
    | ~ sP115(U_1898,U_1897,U_1899,U_1901,U_1900,U_1902) ),
    inference(clausify,[status(thm)],[f_487_5]) ).

fof(f_488_1,plain,
    ! [X_c,X_b] :
      ( ! [C_1,F,B,A_2] :
          ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2)))
          | ? [X_2,Y_2] :
              ( ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,Y_2)),hAPP(X_b,X_c,F,X_2)))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_2)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),C_1),hAPP(X_b,X_c,F,B)))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B),A_2)) )
      | ~ order(X_c)
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_435_xt5]) ).

fof(f_488_2,plain,
    ! [U_1910,U_1909] :
      ( ! [U_1908,U_1907,U_1906,U_1905] :
          ( hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less(U_1910),U_1908),hAPP(U_1909,U_1910,U_1907,U_1905)))
          | ? [U_1904,U_1903] :
              ( ~ hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less(U_1910),hAPP(U_1909,U_1910,U_1907,U_1903)),hAPP(U_1909,U_1910,U_1907,U_1904)))
              & hBOOL(hAPP(U_1909,bool,hAPP(U_1909,fun(U_1909,bool),ord_less(U_1909),U_1903),U_1904)) )
          | ~ hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less_eq(U_1910),U_1908),hAPP(U_1909,U_1910,U_1907,U_1906)))
          | ~ hBOOL(hAPP(U_1909,bool,hAPP(U_1909,fun(U_1909,bool),ord_less(U_1909),U_1906),U_1905)) )
      | ~ order(U_1910)
      | ~ order(U_1909) ),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

fof(f_488_3,plain,
    ! [U_1910,U_1909] :
      ( ! [U_1908,U_1907,U_1906,U_1905] :
          ( hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less(U_1910),U_1908),hAPP(U_1909,U_1910,U_1907,U_1905)))
          | ? [U_1903] :
              ( ~ hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less(U_1910),hAPP(U_1909,U_1910,U_1907,U_1903)),hAPP(U_1909,U_1910,U_1907,sK70(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905))))
              & hBOOL(hAPP(U_1909,bool,hAPP(U_1909,fun(U_1909,bool),ord_less(U_1909),U_1903),sK70(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905))) )
          | ~ hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less_eq(U_1910),U_1908),hAPP(U_1909,U_1910,U_1907,U_1906)))
          | ~ hBOOL(hAPP(U_1909,bool,hAPP(U_1909,fun(U_1909,bool),ord_less(U_1909),U_1906),U_1905)) )
      | ~ order(U_1910)
      | ~ order(U_1909) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_1904,sK70(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905))],[f_488_2]) ).

fof(f_488_4,plain,
    ! [U_1910,U_1909] :
      ( ! [U_1908,U_1907,U_1906,U_1905] :
          ( hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less(U_1910),U_1908),hAPP(U_1909,U_1910,U_1907,U_1905)))
          | ( ~ hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less(U_1910),hAPP(U_1909,U_1910,U_1907,sK71(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905))),hAPP(U_1909,U_1910,U_1907,sK70(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905))))
            & hBOOL(hAPP(U_1909,bool,hAPP(U_1909,fun(U_1909,bool),ord_less(U_1909),sK71(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905)),sK70(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905))) )
          | ~ hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less_eq(U_1910),U_1908),hAPP(U_1909,U_1910,U_1907,U_1906)))
          | ~ hBOOL(hAPP(U_1909,bool,hAPP(U_1909,fun(U_1909,bool),ord_less(U_1909),U_1906),U_1905)) )
      | ~ order(U_1910)
      | ~ order(U_1909) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_1903,sK71(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905))],[f_488_3]) ).

fof(f_488_5,plain,
    ( ! [U_1907,U_1905,U_1909,U_1906,U_1908,U_1910] :
        ( ~ hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less(U_1910),hAPP(U_1909,U_1910,U_1907,sK71(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905))),hAPP(U_1909,U_1910,U_1907,sK70(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905))))
        | ~ sP116(U_1907,U_1905,U_1909,U_1906,U_1908,U_1910) )
    & ! [U_1907,U_1905,U_1909,U_1906,U_1908,U_1910] :
        ( hBOOL(hAPP(U_1909,bool,hAPP(U_1909,fun(U_1909,bool),ord_less(U_1909),sK71(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905)),sK70(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905)))
        | ~ sP116(U_1907,U_1905,U_1909,U_1906,U_1908,U_1910) )
    & ! [U_1907,U_1905,U_1909,U_1906,U_1908,U_1910] :
        ( hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less(U_1910),U_1908),hAPP(U_1909,U_1910,U_1907,U_1905)))
        | sP116(U_1907,U_1905,U_1909,U_1906,U_1908,U_1910)
        | ~ hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less_eq(U_1910),U_1908),hAPP(U_1909,U_1910,U_1907,U_1906)))
        | ~ hBOOL(hAPP(U_1909,bool,hAPP(U_1909,fun(U_1909,bool),ord_less(U_1909),U_1906),U_1905))
        | ~ order(U_1910)
        | ~ order(U_1909) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116])],[f_488_4]) ).

cnf(f_488_6,plain,
    ( hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less(U_1910),U_1908),hAPP(U_1909,U_1910,U_1907,U_1905)))
    | sP116(U_1907,U_1905,U_1909,U_1906,U_1908,U_1910)
    | ~ hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less_eq(U_1910),U_1908),hAPP(U_1909,U_1910,U_1907,U_1906)))
    | ~ hBOOL(hAPP(U_1909,bool,hAPP(U_1909,fun(U_1909,bool),ord_less(U_1909),U_1906),U_1905))
    | ~ order(U_1910)
    | ~ order(U_1909) ),
    inference(clausify,[status(thm)],[f_488_5]) ).

cnf(f_488_7,plain,
    ( hBOOL(hAPP(U_1909,bool,hAPP(U_1909,fun(U_1909,bool),ord_less(U_1909),sK71(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905)),sK70(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905)))
    | ~ sP116(U_1907,U_1905,U_1909,U_1906,U_1908,U_1910) ),
    inference(clausify,[status(thm)],[f_488_5]) ).

cnf(f_488_8,plain,
    ( ~ hBOOL(hAPP(U_1910,bool,hAPP(U_1910,fun(U_1910,bool),ord_less(U_1910),hAPP(U_1909,U_1910,U_1907,sK71(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905))),hAPP(U_1909,U_1910,U_1907,sK70(U_1910,U_1909,U_1908,U_1907,U_1906,U_1905))))
    | ~ sP116(U_1907,U_1905,U_1909,U_1906,U_1908,U_1910) ),
    inference(clausify,[status(thm)],[f_488_5]) ).

fof(f_489_1,plain,
    ! [X_c,X_b] :
      ( ! [C_1,F,B,A_2] :
          ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,A_2)))
          | ? [X_2,Y_2] :
              ( ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,Y_2)),hAPP(X_b,X_c,F,X_2)))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_2)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),C_1),hAPP(X_b,X_c,F,B)))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B),A_2)) )
      | ~ order(X_c)
      | ~ order(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_436_xt7]) ).

fof(f_489_2,plain,
    ! [U_1918,U_1917] :
      ( ! [U_1916,U_1915,U_1914,U_1913] :
          ( hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less(U_1918),U_1916),hAPP(U_1917,U_1918,U_1915,U_1913)))
          | ? [U_1912,U_1911] :
              ( ~ hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less_eq(U_1918),hAPP(U_1917,U_1918,U_1915,U_1911)),hAPP(U_1917,U_1918,U_1915,U_1912)))
              & hBOOL(hAPP(U_1917,bool,hAPP(U_1917,fun(U_1917,bool),ord_less_eq(U_1917),U_1911),U_1912)) )
          | ~ hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less(U_1918),U_1916),hAPP(U_1917,U_1918,U_1915,U_1914)))
          | ~ hBOOL(hAPP(U_1917,bool,hAPP(U_1917,fun(U_1917,bool),ord_less_eq(U_1917),U_1914),U_1913)) )
      | ~ order(U_1918)
      | ~ order(U_1917) ),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

fof(f_489_3,plain,
    ! [U_1918,U_1917] :
      ( ! [U_1916,U_1915,U_1914,U_1913] :
          ( hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less(U_1918),U_1916),hAPP(U_1917,U_1918,U_1915,U_1913)))
          | ? [U_1911] :
              ( ~ hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less_eq(U_1918),hAPP(U_1917,U_1918,U_1915,U_1911)),hAPP(U_1917,U_1918,U_1915,sK72(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913))))
              & hBOOL(hAPP(U_1917,bool,hAPP(U_1917,fun(U_1917,bool),ord_less_eq(U_1917),U_1911),sK72(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913))) )
          | ~ hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less(U_1918),U_1916),hAPP(U_1917,U_1918,U_1915,U_1914)))
          | ~ hBOOL(hAPP(U_1917,bool,hAPP(U_1917,fun(U_1917,bool),ord_less_eq(U_1917),U_1914),U_1913)) )
      | ~ order(U_1918)
      | ~ order(U_1917) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_1912,sK72(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913))],[f_489_2]) ).

fof(f_489_4,plain,
    ! [U_1918,U_1917] :
      ( ! [U_1916,U_1915,U_1914,U_1913] :
          ( hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less(U_1918),U_1916),hAPP(U_1917,U_1918,U_1915,U_1913)))
          | ( ~ hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less_eq(U_1918),hAPP(U_1917,U_1918,U_1915,sK73(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913))),hAPP(U_1917,U_1918,U_1915,sK72(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913))))
            & hBOOL(hAPP(U_1917,bool,hAPP(U_1917,fun(U_1917,bool),ord_less_eq(U_1917),sK73(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913)),sK72(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913))) )
          | ~ hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less(U_1918),U_1916),hAPP(U_1917,U_1918,U_1915,U_1914)))
          | ~ hBOOL(hAPP(U_1917,bool,hAPP(U_1917,fun(U_1917,bool),ord_less_eq(U_1917),U_1914),U_1913)) )
      | ~ order(U_1918)
      | ~ order(U_1917) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_1911,sK73(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913))],[f_489_3]) ).

fof(f_489_5,plain,
    ( ! [U_1915,U_1913,U_1914,U_1916,U_1917,U_1918] :
        ( ~ hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less_eq(U_1918),hAPP(U_1917,U_1918,U_1915,sK73(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913))),hAPP(U_1917,U_1918,U_1915,sK72(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913))))
        | ~ sP117(U_1915,U_1913,U_1914,U_1916,U_1917,U_1918) )
    & ! [U_1915,U_1913,U_1914,U_1916,U_1917,U_1918] :
        ( hBOOL(hAPP(U_1917,bool,hAPP(U_1917,fun(U_1917,bool),ord_less_eq(U_1917),sK73(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913)),sK72(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913)))
        | ~ sP117(U_1915,U_1913,U_1914,U_1916,U_1917,U_1918) )
    & ! [U_1915,U_1913,U_1914,U_1916,U_1917,U_1918] :
        ( hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less(U_1918),U_1916),hAPP(U_1917,U_1918,U_1915,U_1913)))
        | sP117(U_1915,U_1913,U_1914,U_1916,U_1917,U_1918)
        | ~ hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less(U_1918),U_1916),hAPP(U_1917,U_1918,U_1915,U_1914)))
        | ~ hBOOL(hAPP(U_1917,bool,hAPP(U_1917,fun(U_1917,bool),ord_less_eq(U_1917),U_1914),U_1913))
        | ~ order(U_1918)
        | ~ order(U_1917) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117])],[f_489_4]) ).

cnf(f_489_6,plain,
    ( hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less(U_1918),U_1916),hAPP(U_1917,U_1918,U_1915,U_1913)))
    | sP117(U_1915,U_1913,U_1914,U_1916,U_1917,U_1918)
    | ~ hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less(U_1918),U_1916),hAPP(U_1917,U_1918,U_1915,U_1914)))
    | ~ hBOOL(hAPP(U_1917,bool,hAPP(U_1917,fun(U_1917,bool),ord_less_eq(U_1917),U_1914),U_1913))
    | ~ order(U_1918)
    | ~ order(U_1917) ),
    inference(clausify,[status(thm)],[f_489_5]) ).

cnf(f_489_7,plain,
    ( hBOOL(hAPP(U_1917,bool,hAPP(U_1917,fun(U_1917,bool),ord_less_eq(U_1917),sK73(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913)),sK72(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913)))
    | ~ sP117(U_1915,U_1913,U_1914,U_1916,U_1917,U_1918) ),
    inference(clausify,[status(thm)],[f_489_5]) ).

cnf(f_489_8,plain,
    ( ~ hBOOL(hAPP(U_1918,bool,hAPP(U_1918,fun(U_1918,bool),ord_less_eq(U_1918),hAPP(U_1917,U_1918,U_1915,sK73(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913))),hAPP(U_1917,U_1918,U_1915,sK72(U_1918,U_1917,U_1916,U_1915,U_1914,U_1913))))
    | ~ sP117(U_1915,U_1913,U_1914,U_1916,U_1917,U_1918) ),
    inference(clausify,[status(thm)],[f_489_5]) ).

fof(f_490_1,plain,
    ! [X_b,X_c] :
      ( ! [C_1,A_2,F,B] :
          ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,C_1)))
          | ? [X_2,Y_2] :
              ( ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_2)))
              & hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),X_2),Y_2)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),B),C_1))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,B))) )
      | ~ order(X_b)
      | ~ order(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_437_order__less__le__subst1]) ).

fof(f_490_2,plain,
    ! [U_1926,U_1925] :
      ( ! [U_1924,U_1923,U_1922,U_1921] :
          ( hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less(U_1926),U_1923),hAPP(U_1925,U_1926,U_1922,U_1924)))
          | ? [U_1920,U_1919] :
              ( ~ hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less_eq(U_1926),hAPP(U_1925,U_1926,U_1922,U_1920)),hAPP(U_1925,U_1926,U_1922,U_1919)))
              & hBOOL(hAPP(U_1925,bool,hAPP(U_1925,fun(U_1925,bool),ord_less_eq(U_1925),U_1920),U_1919)) )
          | ~ hBOOL(hAPP(U_1925,bool,hAPP(U_1925,fun(U_1925,bool),ord_less_eq(U_1925),U_1921),U_1924))
          | ~ hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less(U_1926),U_1923),hAPP(U_1925,U_1926,U_1922,U_1921))) )
      | ~ order(U_1926)
      | ~ order(U_1925) ),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

fof(f_490_3,plain,
    ! [U_1926,U_1925] :
      ( ! [U_1924,U_1923,U_1922,U_1921] :
          ( hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less(U_1926),U_1923),hAPP(U_1925,U_1926,U_1922,U_1924)))
          | ? [U_1919] :
              ( ~ hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less_eq(U_1926),hAPP(U_1925,U_1926,U_1922,sK74(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921))),hAPP(U_1925,U_1926,U_1922,U_1919)))
              & hBOOL(hAPP(U_1925,bool,hAPP(U_1925,fun(U_1925,bool),ord_less_eq(U_1925),sK74(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921)),U_1919)) )
          | ~ hBOOL(hAPP(U_1925,bool,hAPP(U_1925,fun(U_1925,bool),ord_less_eq(U_1925),U_1921),U_1924))
          | ~ hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less(U_1926),U_1923),hAPP(U_1925,U_1926,U_1922,U_1921))) )
      | ~ order(U_1926)
      | ~ order(U_1925) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_1920,sK74(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921))],[f_490_2]) ).

fof(f_490_4,plain,
    ! [U_1926,U_1925] :
      ( ! [U_1924,U_1923,U_1922,U_1921] :
          ( hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less(U_1926),U_1923),hAPP(U_1925,U_1926,U_1922,U_1924)))
          | ( ~ hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less_eq(U_1926),hAPP(U_1925,U_1926,U_1922,sK74(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921))),hAPP(U_1925,U_1926,U_1922,sK75(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921))))
            & hBOOL(hAPP(U_1925,bool,hAPP(U_1925,fun(U_1925,bool),ord_less_eq(U_1925),sK74(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921)),sK75(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921))) )
          | ~ hBOOL(hAPP(U_1925,bool,hAPP(U_1925,fun(U_1925,bool),ord_less_eq(U_1925),U_1921),U_1924))
          | ~ hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less(U_1926),U_1923),hAPP(U_1925,U_1926,U_1922,U_1921))) )
      | ~ order(U_1926)
      | ~ order(U_1925) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_1919,sK75(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921))],[f_490_3]) ).

fof(f_490_5,plain,
    ( ! [U_1922,U_1921,U_1923,U_1924,U_1925,U_1926] :
        ( ~ hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less_eq(U_1926),hAPP(U_1925,U_1926,U_1922,sK74(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921))),hAPP(U_1925,U_1926,U_1922,sK75(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921))))
        | ~ sP118(U_1922,U_1921,U_1923,U_1924,U_1925,U_1926) )
    & ! [U_1922,U_1921,U_1923,U_1924,U_1925,U_1926] :
        ( hBOOL(hAPP(U_1925,bool,hAPP(U_1925,fun(U_1925,bool),ord_less_eq(U_1925),sK74(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921)),sK75(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921)))
        | ~ sP118(U_1922,U_1921,U_1923,U_1924,U_1925,U_1926) )
    & ! [U_1922,U_1921,U_1923,U_1924,U_1925,U_1926] :
        ( hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less(U_1926),U_1923),hAPP(U_1925,U_1926,U_1922,U_1924)))
        | sP118(U_1922,U_1921,U_1923,U_1924,U_1925,U_1926)
        | ~ hBOOL(hAPP(U_1925,bool,hAPP(U_1925,fun(U_1925,bool),ord_less_eq(U_1925),U_1921),U_1924))
        | ~ hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less(U_1926),U_1923),hAPP(U_1925,U_1926,U_1922,U_1921)))
        | ~ order(U_1926)
        | ~ order(U_1925) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP118])],[f_490_4]) ).

cnf(f_490_6,plain,
    ( hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less(U_1926),U_1923),hAPP(U_1925,U_1926,U_1922,U_1924)))
    | sP118(U_1922,U_1921,U_1923,U_1924,U_1925,U_1926)
    | ~ hBOOL(hAPP(U_1925,bool,hAPP(U_1925,fun(U_1925,bool),ord_less_eq(U_1925),U_1921),U_1924))
    | ~ hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less(U_1926),U_1923),hAPP(U_1925,U_1926,U_1922,U_1921)))
    | ~ order(U_1926)
    | ~ order(U_1925) ),
    inference(clausify,[status(thm)],[f_490_5]) ).

cnf(f_490_7,plain,
    ( hBOOL(hAPP(U_1925,bool,hAPP(U_1925,fun(U_1925,bool),ord_less_eq(U_1925),sK74(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921)),sK75(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921)))
    | ~ sP118(U_1922,U_1921,U_1923,U_1924,U_1925,U_1926) ),
    inference(clausify,[status(thm)],[f_490_5]) ).

cnf(f_490_8,plain,
    ( ~ hBOOL(hAPP(U_1926,bool,hAPP(U_1926,fun(U_1926,bool),ord_less_eq(U_1926),hAPP(U_1925,U_1926,U_1922,sK74(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921))),hAPP(U_1925,U_1926,U_1922,sK75(U_1926,U_1925,U_1924,U_1923,U_1922,U_1921))))
    | ~ sP118(U_1922,U_1921,U_1923,U_1924,U_1925,U_1926) ),
    inference(clausify,[status(thm)],[f_490_5]) ).

fof(f_491_1,plain,
    ! [X_b,X_c] :
      ( ! [F,C_1,A_2,B] :
          ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1))
          | ? [X_2,Y_2] :
              ( ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_2)))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_2)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,B)),C_1))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B)) )
      | ~ order(X_b)
      | ~ order(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_438_order__le__less__subst2]) ).

fof(f_491_2,plain,
    ! [U_1934,U_1933] :
      ( ! [U_1932,U_1931,U_1930,U_1929] :
          ( hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less(U_1933),hAPP(U_1934,U_1933,U_1932,U_1930)),U_1931))
          | ? [U_1928,U_1927] :
              ( ~ hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less_eq(U_1933),hAPP(U_1934,U_1933,U_1932,U_1928)),hAPP(U_1934,U_1933,U_1932,U_1927)))
              & hBOOL(hAPP(U_1934,bool,hAPP(U_1934,fun(U_1934,bool),ord_less_eq(U_1934),U_1928),U_1927)) )
          | ~ hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less(U_1933),hAPP(U_1934,U_1933,U_1932,U_1929)),U_1931))
          | ~ hBOOL(hAPP(U_1934,bool,hAPP(U_1934,fun(U_1934,bool),ord_less_eq(U_1934),U_1930),U_1929)) )
      | ~ order(U_1934)
      | ~ order(U_1933) ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

fof(f_491_3,plain,
    ! [U_1934,U_1933] :
      ( ! [U_1932,U_1931,U_1930,U_1929] :
          ( hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less(U_1933),hAPP(U_1934,U_1933,U_1932,U_1930)),U_1931))
          | ? [U_1927] :
              ( ~ hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less_eq(U_1933),hAPP(U_1934,U_1933,U_1932,sK76(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929))),hAPP(U_1934,U_1933,U_1932,U_1927)))
              & hBOOL(hAPP(U_1934,bool,hAPP(U_1934,fun(U_1934,bool),ord_less_eq(U_1934),sK76(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929)),U_1927)) )
          | ~ hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less(U_1933),hAPP(U_1934,U_1933,U_1932,U_1929)),U_1931))
          | ~ hBOOL(hAPP(U_1934,bool,hAPP(U_1934,fun(U_1934,bool),ord_less_eq(U_1934),U_1930),U_1929)) )
      | ~ order(U_1934)
      | ~ order(U_1933) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_1928,sK76(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929))],[f_491_2]) ).

fof(f_491_4,plain,
    ! [U_1934,U_1933] :
      ( ! [U_1932,U_1931,U_1930,U_1929] :
          ( hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less(U_1933),hAPP(U_1934,U_1933,U_1932,U_1930)),U_1931))
          | ( ~ hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less_eq(U_1933),hAPP(U_1934,U_1933,U_1932,sK76(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929))),hAPP(U_1934,U_1933,U_1932,sK77(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929))))
            & hBOOL(hAPP(U_1934,bool,hAPP(U_1934,fun(U_1934,bool),ord_less_eq(U_1934),sK76(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929)),sK77(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929))) )
          | ~ hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less(U_1933),hAPP(U_1934,U_1933,U_1932,U_1929)),U_1931))
          | ~ hBOOL(hAPP(U_1934,bool,hAPP(U_1934,fun(U_1934,bool),ord_less_eq(U_1934),U_1930),U_1929)) )
      | ~ order(U_1934)
      | ~ order(U_1933) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_1927,sK77(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929))],[f_491_3]) ).

fof(f_491_5,plain,
    ( ! [U_1930,U_1929,U_1932,U_1931,U_1933,U_1934] :
        ( ~ hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less_eq(U_1933),hAPP(U_1934,U_1933,U_1932,sK76(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929))),hAPP(U_1934,U_1933,U_1932,sK77(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929))))
        | ~ sP119(U_1930,U_1929,U_1932,U_1931,U_1933,U_1934) )
    & ! [U_1930,U_1929,U_1932,U_1931,U_1933,U_1934] :
        ( hBOOL(hAPP(U_1934,bool,hAPP(U_1934,fun(U_1934,bool),ord_less_eq(U_1934),sK76(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929)),sK77(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929)))
        | ~ sP119(U_1930,U_1929,U_1932,U_1931,U_1933,U_1934) )
    & ! [U_1930,U_1929,U_1932,U_1931,U_1933,U_1934] :
        ( hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less(U_1933),hAPP(U_1934,U_1933,U_1932,U_1930)),U_1931))
        | sP119(U_1930,U_1929,U_1932,U_1931,U_1933,U_1934)
        | ~ hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less(U_1933),hAPP(U_1934,U_1933,U_1932,U_1929)),U_1931))
        | ~ hBOOL(hAPP(U_1934,bool,hAPP(U_1934,fun(U_1934,bool),ord_less_eq(U_1934),U_1930),U_1929))
        | ~ order(U_1934)
        | ~ order(U_1933) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119])],[f_491_4]) ).

cnf(f_491_6,plain,
    ( hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less(U_1933),hAPP(U_1934,U_1933,U_1932,U_1930)),U_1931))
    | sP119(U_1930,U_1929,U_1932,U_1931,U_1933,U_1934)
    | ~ hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less(U_1933),hAPP(U_1934,U_1933,U_1932,U_1929)),U_1931))
    | ~ hBOOL(hAPP(U_1934,bool,hAPP(U_1934,fun(U_1934,bool),ord_less_eq(U_1934),U_1930),U_1929))
    | ~ order(U_1934)
    | ~ order(U_1933) ),
    inference(clausify,[status(thm)],[f_491_5]) ).

cnf(f_491_7,plain,
    ( hBOOL(hAPP(U_1934,bool,hAPP(U_1934,fun(U_1934,bool),ord_less_eq(U_1934),sK76(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929)),sK77(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929)))
    | ~ sP119(U_1930,U_1929,U_1932,U_1931,U_1933,U_1934) ),
    inference(clausify,[status(thm)],[f_491_5]) ).

cnf(f_491_8,plain,
    ( ~ hBOOL(hAPP(U_1933,bool,hAPP(U_1933,fun(U_1933,bool),ord_less_eq(U_1933),hAPP(U_1934,U_1933,U_1932,sK76(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929))),hAPP(U_1934,U_1933,U_1932,sK77(U_1934,U_1933,U_1932,U_1931,U_1930,U_1929))))
    | ~ sP119(U_1930,U_1929,U_1932,U_1931,U_1933,U_1934) ),
    inference(clausify,[status(thm)],[f_491_5]) ).

fof(f_492_1,plain,
    ! [X_b,X_c] :
      ( ! [F,C_1,A_2,B] :
          ( hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),C_1))
          | ? [X_2,Y_2] :
              ( ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_2)))
              & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_2)) )
          | ~ hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,B)),C_1))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),B)) )
      | ~ order(X_b)
      | ~ order(X_c) ),
    inference(fof_nnf,[status(thm)],[fact_439_order__less__le__subst2]) ).

fof(f_492_2,plain,
    ! [U_1942,U_1941] :
      ( ! [U_1940,U_1939,U_1938,U_1937] :
          ( hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less(U_1941),hAPP(U_1942,U_1941,U_1940,U_1938)),U_1939))
          | ? [U_1936,U_1935] :
              ( ~ hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less(U_1941),hAPP(U_1942,U_1941,U_1940,U_1936)),hAPP(U_1942,U_1941,U_1940,U_1935)))
              & hBOOL(hAPP(U_1942,bool,hAPP(U_1942,fun(U_1942,bool),ord_less(U_1942),U_1936),U_1935)) )
          | ~ hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less_eq(U_1941),hAPP(U_1942,U_1941,U_1940,U_1937)),U_1939))
          | ~ hBOOL(hAPP(U_1942,bool,hAPP(U_1942,fun(U_1942,bool),ord_less(U_1942),U_1938),U_1937)) )
      | ~ order(U_1942)
      | ~ order(U_1941) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

fof(f_492_3,plain,
    ! [U_1942,U_1941] :
      ( ! [U_1940,U_1939,U_1938,U_1937] :
          ( hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less(U_1941),hAPP(U_1942,U_1941,U_1940,U_1938)),U_1939))
          | ? [U_1935] :
              ( ~ hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less(U_1941),hAPP(U_1942,U_1941,U_1940,sK78(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937))),hAPP(U_1942,U_1941,U_1940,U_1935)))
              & hBOOL(hAPP(U_1942,bool,hAPP(U_1942,fun(U_1942,bool),ord_less(U_1942),sK78(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937)),U_1935)) )
          | ~ hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less_eq(U_1941),hAPP(U_1942,U_1941,U_1940,U_1937)),U_1939))
          | ~ hBOOL(hAPP(U_1942,bool,hAPP(U_1942,fun(U_1942,bool),ord_less(U_1942),U_1938),U_1937)) )
      | ~ order(U_1942)
      | ~ order(U_1941) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_1936,sK78(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937))],[f_492_2]) ).

fof(f_492_4,plain,
    ! [U_1942,U_1941] :
      ( ! [U_1940,U_1939,U_1938,U_1937] :
          ( hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less(U_1941),hAPP(U_1942,U_1941,U_1940,U_1938)),U_1939))
          | ( ~ hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less(U_1941),hAPP(U_1942,U_1941,U_1940,sK78(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937))),hAPP(U_1942,U_1941,U_1940,sK79(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937))))
            & hBOOL(hAPP(U_1942,bool,hAPP(U_1942,fun(U_1942,bool),ord_less(U_1942),sK78(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937)),sK79(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937))) )
          | ~ hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less_eq(U_1941),hAPP(U_1942,U_1941,U_1940,U_1937)),U_1939))
          | ~ hBOOL(hAPP(U_1942,bool,hAPP(U_1942,fun(U_1942,bool),ord_less(U_1942),U_1938),U_1937)) )
      | ~ order(U_1942)
      | ~ order(U_1941) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_1935,sK79(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937))],[f_492_3]) ).

fof(f_492_5,plain,
    ( ! [U_1937,U_1939,U_1940,U_1941,U_1938,U_1942] :
        ( ~ hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less(U_1941),hAPP(U_1942,U_1941,U_1940,sK78(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937))),hAPP(U_1942,U_1941,U_1940,sK79(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937))))
        | ~ sP120(U_1937,U_1939,U_1940,U_1941,U_1938,U_1942) )
    & ! [U_1937,U_1939,U_1940,U_1941,U_1938,U_1942] :
        ( hBOOL(hAPP(U_1942,bool,hAPP(U_1942,fun(U_1942,bool),ord_less(U_1942),sK78(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937)),sK79(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937)))
        | ~ sP120(U_1937,U_1939,U_1940,U_1941,U_1938,U_1942) )
    & ! [U_1937,U_1939,U_1940,U_1941,U_1938,U_1942] :
        ( hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less(U_1941),hAPP(U_1942,U_1941,U_1940,U_1938)),U_1939))
        | sP120(U_1937,U_1939,U_1940,U_1941,U_1938,U_1942)
        | ~ hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less_eq(U_1941),hAPP(U_1942,U_1941,U_1940,U_1937)),U_1939))
        | ~ hBOOL(hAPP(U_1942,bool,hAPP(U_1942,fun(U_1942,bool),ord_less(U_1942),U_1938),U_1937))
        | ~ order(U_1942)
        | ~ order(U_1941) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP120])],[f_492_4]) ).

cnf(f_492_6,plain,
    ( hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less(U_1941),hAPP(U_1942,U_1941,U_1940,U_1938)),U_1939))
    | sP120(U_1937,U_1939,U_1940,U_1941,U_1938,U_1942)
    | ~ hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less_eq(U_1941),hAPP(U_1942,U_1941,U_1940,U_1937)),U_1939))
    | ~ hBOOL(hAPP(U_1942,bool,hAPP(U_1942,fun(U_1942,bool),ord_less(U_1942),U_1938),U_1937))
    | ~ order(U_1942)
    | ~ order(U_1941) ),
    inference(clausify,[status(thm)],[f_492_5]) ).

cnf(f_492_7,plain,
    ( hBOOL(hAPP(U_1942,bool,hAPP(U_1942,fun(U_1942,bool),ord_less(U_1942),sK78(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937)),sK79(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937)))
    | ~ sP120(U_1937,U_1939,U_1940,U_1941,U_1938,U_1942) ),
    inference(clausify,[status(thm)],[f_492_5]) ).

cnf(f_492_8,plain,
    ( ~ hBOOL(hAPP(U_1941,bool,hAPP(U_1941,fun(U_1941,bool),ord_less(U_1941),hAPP(U_1942,U_1941,U_1940,sK78(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937))),hAPP(U_1942,U_1941,U_1940,sK79(U_1942,U_1941,U_1940,U_1939,U_1938,U_1937))))
    | ~ sP120(U_1937,U_1939,U_1940,U_1941,U_1938,U_1942) ),
    inference(clausify,[status(thm)],[f_492_5]) ).

fof(f_493_1,plain,
    ! [X_c,X_b,B_2,A_3] :
      ( hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_2))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_440_card__Plus]) ).

fof(f_493_2,plain,
    ! [U_1946,U_1945,U_1944,U_1943] :
      ( hAPP(fun(sum_sum(U_1945,U_1946),bool),nat,finite_card(sum_sum(U_1945,U_1946)),hAPP(fun(U_1946,bool),fun(sum_sum(U_1945,U_1946),bool),hAPP(fun(U_1945,bool),fun(fun(U_1946,bool),fun(sum_sum(U_1945,U_1946),bool)),sum_Plus(U_1945,U_1946),U_1943),U_1944)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1945,bool),nat,finite_card(U_1945),U_1943)),hAPP(fun(U_1946,bool),nat,finite_card(U_1946),U_1944))
      | ~ hBOOL(hAPP(fun(U_1946,bool),bool,finite_finite(U_1946),U_1944))
      | ~ hBOOL(hAPP(fun(U_1945,bool),bool,finite_finite(U_1945),U_1943)) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

fof(f_493_3,plain,
    ! [U_1945,U_1946,U_1944,U_1943] :
      ( hAPP(fun(sum_sum(U_1945,U_1946),bool),nat,finite_card(sum_sum(U_1945,U_1946)),hAPP(fun(U_1946,bool),fun(sum_sum(U_1945,U_1946),bool),hAPP(fun(U_1945,bool),fun(fun(U_1946,bool),fun(sum_sum(U_1945,U_1946),bool)),sum_Plus(U_1945,U_1946),U_1943),U_1944)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1945,bool),nat,finite_card(U_1945),U_1943)),hAPP(fun(U_1946,bool),nat,finite_card(U_1946),U_1944))
      | ~ hBOOL(hAPP(fun(U_1946,bool),bool,finite_finite(U_1946),U_1944))
      | ~ hBOOL(hAPP(fun(U_1945,bool),bool,finite_finite(U_1945),U_1943)) ),
    inference(definitional_conversion,[status(esa)],[f_493_2]) ).

cnf(f_493_4,plain,
    ( hAPP(fun(sum_sum(U_1945,U_1946),bool),nat,finite_card(sum_sum(U_1945,U_1946)),hAPP(fun(U_1946,bool),fun(sum_sum(U_1945,U_1946),bool),hAPP(fun(U_1945,bool),fun(fun(U_1946,bool),fun(sum_sum(U_1945,U_1946),bool)),sum_Plus(U_1945,U_1946),U_1943),U_1944)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1945,bool),nat,finite_card(U_1945),U_1943)),hAPP(fun(U_1946,bool),nat,finite_card(U_1946),U_1944))
    | ~ hBOOL(hAPP(fun(U_1946,bool),bool,finite_finite(U_1946),U_1944))
    | ~ hBOOL(hAPP(fun(U_1945,bool),bool,finite_finite(U_1945),U_1943)) ),
    inference(clausify,[status(thm)],[f_493_3]) ).

fof(f_494_1,plain,
    ! [X_b,X_c,A_3,B_2] :
      ( ( hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)))
        | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) )
      & ( ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
          & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) )
        | ~ hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_441_finite__Plus__iff]) ).

fof(f_494_2,plain,
    ! [U_1950,U_1949,U_1948,U_1947] :
      ( ( hBOOL(hAPP(fun(sum_sum(U_1950,U_1949),bool),bool,finite_finite(sum_sum(U_1950,U_1949)),hAPP(fun(U_1949,bool),fun(sum_sum(U_1950,U_1949),bool),hAPP(fun(U_1950,bool),fun(fun(U_1949,bool),fun(sum_sum(U_1950,U_1949),bool)),sum_Plus(U_1950,U_1949),U_1948),U_1947)))
        | ~ hBOOL(hAPP(fun(U_1949,bool),bool,finite_finite(U_1949),U_1947))
        | ~ hBOOL(hAPP(fun(U_1950,bool),bool,finite_finite(U_1950),U_1948)) )
      & ( ( hBOOL(hAPP(fun(U_1949,bool),bool,finite_finite(U_1949),U_1947))
          & hBOOL(hAPP(fun(U_1950,bool),bool,finite_finite(U_1950),U_1948)) )
        | ~ hBOOL(hAPP(fun(sum_sum(U_1950,U_1949),bool),bool,finite_finite(sum_sum(U_1950,U_1949)),hAPP(fun(U_1949,bool),fun(sum_sum(U_1950,U_1949),bool),hAPP(fun(U_1950,bool),fun(fun(U_1949,bool),fun(sum_sum(U_1950,U_1949),bool)),sum_Plus(U_1950,U_1949),U_1948),U_1947))) ) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

fof(f_494_3,plain,
    ( ! [U_1958,U_1956,U_1954,U_1952] :
        ( hBOOL(hAPP(fun(sum_sum(U_1958,U_1956),bool),bool,finite_finite(sum_sum(U_1958,U_1956)),hAPP(fun(U_1956,bool),fun(sum_sum(U_1958,U_1956),bool),hAPP(fun(U_1958,bool),fun(fun(U_1956,bool),fun(sum_sum(U_1958,U_1956),bool)),sum_Plus(U_1958,U_1956),U_1954),U_1952)))
        | ~ hBOOL(hAPP(fun(U_1956,bool),bool,finite_finite(U_1956),U_1952))
        | ~ hBOOL(hAPP(fun(U_1958,bool),bool,finite_finite(U_1958),U_1954)) )
    & ! [U_1957,U_1955,U_1953,U_1951] :
        ( ( hBOOL(hAPP(fun(U_1955,bool),bool,finite_finite(U_1955),U_1951))
          & hBOOL(hAPP(fun(U_1957,bool),bool,finite_finite(U_1957),U_1953)) )
        | ~ hBOOL(hAPP(fun(sum_sum(U_1957,U_1955),bool),bool,finite_finite(sum_sum(U_1957,U_1955)),hAPP(fun(U_1955,bool),fun(sum_sum(U_1957,U_1955),bool),hAPP(fun(U_1957,bool),fun(fun(U_1955,bool),fun(sum_sum(U_1957,U_1955),bool)),sum_Plus(U_1957,U_1955),U_1953),U_1951))) ) ),
    inference(miniscope,[status(thm)],[f_494_2]) ).

fof(f_494_4,plain,
    ( ! [U_1953,U_1951,U_1955,U_1957] :
        ( hBOOL(hAPP(fun(U_1955,bool),bool,finite_finite(U_1955),U_1951))
        | ~ sP121(U_1953,U_1951,U_1955,U_1957) )
    & ! [U_1953,U_1951,U_1955,U_1957] :
        ( hBOOL(hAPP(fun(U_1957,bool),bool,finite_finite(U_1957),U_1953))
        | ~ sP121(U_1953,U_1951,U_1955,U_1957) )
    & ! [U_1952,U_1954,U_1958,U_1956] :
        ( hBOOL(hAPP(fun(sum_sum(U_1958,U_1956),bool),bool,finite_finite(sum_sum(U_1958,U_1956)),hAPP(fun(U_1956,bool),fun(sum_sum(U_1958,U_1956),bool),hAPP(fun(U_1958,bool),fun(fun(U_1956,bool),fun(sum_sum(U_1958,U_1956),bool)),sum_Plus(U_1958,U_1956),U_1954),U_1952)))
        | ~ hBOOL(hAPP(fun(U_1956,bool),bool,finite_finite(U_1956),U_1952))
        | ~ hBOOL(hAPP(fun(U_1958,bool),bool,finite_finite(U_1958),U_1954)) )
    & ! [U_1953,U_1951,U_1955,U_1957] :
        ( sP121(U_1953,U_1951,U_1955,U_1957)
        | ~ hBOOL(hAPP(fun(sum_sum(U_1957,U_1955),bool),bool,finite_finite(sum_sum(U_1957,U_1955)),hAPP(fun(U_1955,bool),fun(sum_sum(U_1957,U_1955),bool),hAPP(fun(U_1957,bool),fun(fun(U_1955,bool),fun(sum_sum(U_1957,U_1955),bool)),sum_Plus(U_1957,U_1955),U_1953),U_1951))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP121])],[f_494_3]) ).

cnf(f_494_5,plain,
    ( sP121(U_1953,U_1951,U_1955,U_1957)
    | ~ hBOOL(hAPP(fun(sum_sum(U_1957,U_1955),bool),bool,finite_finite(sum_sum(U_1957,U_1955)),hAPP(fun(U_1955,bool),fun(sum_sum(U_1957,U_1955),bool),hAPP(fun(U_1957,bool),fun(fun(U_1955,bool),fun(sum_sum(U_1957,U_1955),bool)),sum_Plus(U_1957,U_1955),U_1953),U_1951))) ),
    inference(clausify,[status(thm)],[f_494_4]) ).

cnf(f_494_6,plain,
    ( hBOOL(hAPP(fun(sum_sum(U_1958,U_1956),bool),bool,finite_finite(sum_sum(U_1958,U_1956)),hAPP(fun(U_1956,bool),fun(sum_sum(U_1958,U_1956),bool),hAPP(fun(U_1958,bool),fun(fun(U_1956,bool),fun(sum_sum(U_1958,U_1956),bool)),sum_Plus(U_1958,U_1956),U_1954),U_1952)))
    | ~ hBOOL(hAPP(fun(U_1956,bool),bool,finite_finite(U_1956),U_1952))
    | ~ hBOOL(hAPP(fun(U_1958,bool),bool,finite_finite(U_1958),U_1954)) ),
    inference(clausify,[status(thm)],[f_494_4]) ).

cnf(f_494_7,plain,
    ( hBOOL(hAPP(fun(U_1957,bool),bool,finite_finite(U_1957),U_1953))
    | ~ sP121(U_1953,U_1951,U_1955,U_1957) ),
    inference(clausify,[status(thm)],[f_494_4]) ).

cnf(f_494_8,plain,
    ( hBOOL(hAPP(fun(U_1955,bool),bool,finite_finite(U_1955),U_1951))
    | ~ sP121(U_1953,U_1951,U_1955,U_1957) ),
    inference(clausify,[status(thm)],[f_494_4]) ).

fof(f_495_1,plain,
    ! [X_c,X_b,B_2,A_3] :
      ( hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)))
      | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
      | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_442_finite__Plus]) ).

fof(f_495_2,plain,
    ! [U_1962,U_1961,U_1960,U_1959] :
      ( hBOOL(hAPP(fun(sum_sum(U_1961,U_1962),bool),bool,finite_finite(sum_sum(U_1961,U_1962)),hAPP(fun(U_1962,bool),fun(sum_sum(U_1961,U_1962),bool),hAPP(fun(U_1961,bool),fun(fun(U_1962,bool),fun(sum_sum(U_1961,U_1962),bool)),sum_Plus(U_1961,U_1962),U_1959),U_1960)))
      | ~ hBOOL(hAPP(fun(U_1962,bool),bool,finite_finite(U_1962),U_1960))
      | ~ hBOOL(hAPP(fun(U_1961,bool),bool,finite_finite(U_1961),U_1959)) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

fof(f_495_3,plain,
    ! [U_1959,U_1961,U_1960,U_1962] :
      ( hBOOL(hAPP(fun(sum_sum(U_1961,U_1962),bool),bool,finite_finite(sum_sum(U_1961,U_1962)),hAPP(fun(U_1962,bool),fun(sum_sum(U_1961,U_1962),bool),hAPP(fun(U_1961,bool),fun(fun(U_1962,bool),fun(sum_sum(U_1961,U_1962),bool)),sum_Plus(U_1961,U_1962),U_1959),U_1960)))
      | ~ hBOOL(hAPP(fun(U_1962,bool),bool,finite_finite(U_1962),U_1960))
      | ~ hBOOL(hAPP(fun(U_1961,bool),bool,finite_finite(U_1961),U_1959)) ),
    inference(definitional_conversion,[status(esa)],[f_495_2]) ).

cnf(f_495_4,plain,
    ( hBOOL(hAPP(fun(sum_sum(U_1961,U_1962),bool),bool,finite_finite(sum_sum(U_1961,U_1962)),hAPP(fun(U_1962,bool),fun(sum_sum(U_1961,U_1962),bool),hAPP(fun(U_1961,bool),fun(fun(U_1962,bool),fun(sum_sum(U_1961,U_1962),bool)),sum_Plus(U_1961,U_1962),U_1959),U_1960)))
    | ~ hBOOL(hAPP(fun(U_1962,bool),bool,finite_finite(U_1962),U_1960))
    | ~ hBOOL(hAPP(fun(U_1961,bool),bool,finite_finite(U_1961),U_1959)) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

fof(f_496_1,plain,
    ! [X_b,X_c,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3))
      | ~ hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_443_finite__PlusD_I1_J]) ).

fof(f_496_2,plain,
    ! [U_1966,U_1965,U_1964,U_1963] :
      ( hBOOL(hAPP(fun(U_1966,bool),bool,finite_finite(U_1966),U_1964))
      | ~ hBOOL(hAPP(fun(sum_sum(U_1966,U_1965),bool),bool,finite_finite(sum_sum(U_1966,U_1965)),hAPP(fun(U_1965,bool),fun(sum_sum(U_1966,U_1965),bool),hAPP(fun(U_1966,bool),fun(fun(U_1965,bool),fun(sum_sum(U_1966,U_1965),bool)),sum_Plus(U_1966,U_1965),U_1964),U_1963))) ),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

fof(f_496_3,plain,
    ! [U_1966,U_1965,U_1964] :
      ( ! [U_1963] : ~ hBOOL(hAPP(fun(sum_sum(U_1966,U_1965),bool),bool,finite_finite(sum_sum(U_1966,U_1965)),hAPP(fun(U_1965,bool),fun(sum_sum(U_1966,U_1965),bool),hAPP(fun(U_1966,bool),fun(fun(U_1965,bool),fun(sum_sum(U_1966,U_1965),bool)),sum_Plus(U_1966,U_1965),U_1964),U_1963)))
      | hBOOL(hAPP(fun(U_1966,bool),bool,finite_finite(U_1966),U_1964)) ),
    inference(miniscope,[status(thm)],[f_496_2]) ).

fof(f_496_4,plain,
    ! [U_1964,U_1965,U_1963,U_1966] :
      ( ~ hBOOL(hAPP(fun(sum_sum(U_1966,U_1965),bool),bool,finite_finite(sum_sum(U_1966,U_1965)),hAPP(fun(U_1965,bool),fun(sum_sum(U_1966,U_1965),bool),hAPP(fun(U_1966,bool),fun(fun(U_1965,bool),fun(sum_sum(U_1966,U_1965),bool)),sum_Plus(U_1966,U_1965),U_1964),U_1963)))
      | hBOOL(hAPP(fun(U_1966,bool),bool,finite_finite(U_1966),U_1964)) ),
    inference(definitional_conversion,[status(esa)],[f_496_3]) ).

cnf(f_496_5,plain,
    ( ~ hBOOL(hAPP(fun(sum_sum(U_1966,U_1965),bool),bool,finite_finite(sum_sum(U_1966,U_1965)),hAPP(fun(U_1965,bool),fun(sum_sum(U_1966,U_1965),bool),hAPP(fun(U_1966,bool),fun(fun(U_1965,bool),fun(sum_sum(U_1966,U_1965),bool)),sum_Plus(U_1966,U_1965),U_1964),U_1963)))
    | hBOOL(hAPP(fun(U_1966,bool),bool,finite_finite(U_1966),U_1964)) ),
    inference(clausify,[status(thm)],[f_496_4]) ).

fof(f_497_1,plain,
    ! [X_b,X_c,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
      | ~ hBOOL(hAPP(fun(sum_sum(X_b,X_c),bool),bool,finite_finite(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_444_finite__PlusD_I2_J]) ).

fof(f_497_2,plain,
    ! [U_1970,U_1969,U_1968,U_1967] :
      ( hBOOL(hAPP(fun(U_1969,bool),bool,finite_finite(U_1969),U_1967))
      | ~ hBOOL(hAPP(fun(sum_sum(U_1970,U_1969),bool),bool,finite_finite(sum_sum(U_1970,U_1969)),hAPP(fun(U_1969,bool),fun(sum_sum(U_1970,U_1969),bool),hAPP(fun(U_1970,bool),fun(fun(U_1969,bool),fun(sum_sum(U_1970,U_1969),bool)),sum_Plus(U_1970,U_1969),U_1968),U_1967))) ),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

fof(f_497_3,plain,
    ! [U_1967,U_1968,U_1970,U_1969] :
      ( hBOOL(hAPP(fun(U_1969,bool),bool,finite_finite(U_1969),U_1967))
      | ~ hBOOL(hAPP(fun(sum_sum(U_1970,U_1969),bool),bool,finite_finite(sum_sum(U_1970,U_1969)),hAPP(fun(U_1969,bool),fun(sum_sum(U_1970,U_1969),bool),hAPP(fun(U_1970,bool),fun(fun(U_1969,bool),fun(sum_sum(U_1970,U_1969),bool)),sum_Plus(U_1970,U_1969),U_1968),U_1967))) ),
    inference(definitional_conversion,[status(esa)],[f_497_2]) ).

cnf(f_497_4,plain,
    ( hBOOL(hAPP(fun(U_1969,bool),bool,finite_finite(U_1969),U_1967))
    | ~ hBOOL(hAPP(fun(sum_sum(U_1970,U_1969),bool),bool,finite_finite(sum_sum(U_1970,U_1969)),hAPP(fun(U_1969,bool),fun(sum_sum(U_1970,U_1969),bool),hAPP(fun(U_1970,bool),fun(fun(U_1969,bool),fun(sum_sum(U_1970,U_1969),bool)),sum_Plus(U_1970,U_1969),U_1968),U_1967))) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

fof(f_498_1,plain,
    ! [X_c,X_b,A_3,B_2] :
      ( ( hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2) = bot_bot(fun(sum_sum(X_b,X_c),bool))
        | ti(fun(X_c,bool),B_2) != bot_bot(fun(X_c,bool))
        | ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) )
      & ( ( ti(fun(X_c,bool),B_2) = bot_bot(fun(X_c,bool))
          & ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) )
        | hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2) != bot_bot(fun(sum_sum(X_b,X_c),bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_445_Plus__eq__empty__conv]) ).

fof(f_498_2,plain,
    ! [U_1974,U_1973,U_1972,U_1971] :
      ( ( hAPP(fun(U_1974,bool),fun(sum_sum(U_1973,U_1974),bool),hAPP(fun(U_1973,bool),fun(fun(U_1974,bool),fun(sum_sum(U_1973,U_1974),bool)),sum_Plus(U_1973,U_1974),U_1972),U_1971) = bot_bot(fun(sum_sum(U_1973,U_1974),bool))
        | ti(fun(U_1974,bool),U_1971) != bot_bot(fun(U_1974,bool))
        | ti(fun(U_1973,bool),U_1972) != bot_bot(fun(U_1973,bool)) )
      & ( ( ti(fun(U_1974,bool),U_1971) = bot_bot(fun(U_1974,bool))
          & ti(fun(U_1973,bool),U_1972) = bot_bot(fun(U_1973,bool)) )
        | hAPP(fun(U_1974,bool),fun(sum_sum(U_1973,U_1974),bool),hAPP(fun(U_1973,bool),fun(fun(U_1974,bool),fun(sum_sum(U_1973,U_1974),bool)),sum_Plus(U_1973,U_1974),U_1972),U_1971) != bot_bot(fun(sum_sum(U_1973,U_1974),bool)) ) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

fof(f_498_3,plain,
    ( ! [U_1982,U_1980,U_1978,U_1976] :
        ( hAPP(fun(U_1982,bool),fun(sum_sum(U_1980,U_1982),bool),hAPP(fun(U_1980,bool),fun(fun(U_1982,bool),fun(sum_sum(U_1980,U_1982),bool)),sum_Plus(U_1980,U_1982),U_1978),U_1976) = bot_bot(fun(sum_sum(U_1980,U_1982),bool))
        | ti(fun(U_1982,bool),U_1976) != bot_bot(fun(U_1982,bool))
        | ti(fun(U_1980,bool),U_1978) != bot_bot(fun(U_1980,bool)) )
    & ! [U_1981,U_1979,U_1977,U_1975] :
        ( ( ti(fun(U_1981,bool),U_1975) = bot_bot(fun(U_1981,bool))
          & ti(fun(U_1979,bool),U_1977) = bot_bot(fun(U_1979,bool)) )
        | hAPP(fun(U_1981,bool),fun(sum_sum(U_1979,U_1981),bool),hAPP(fun(U_1979,bool),fun(fun(U_1981,bool),fun(sum_sum(U_1979,U_1981),bool)),sum_Plus(U_1979,U_1981),U_1977),U_1975) != bot_bot(fun(sum_sum(U_1979,U_1981),bool)) ) ),
    inference(miniscope,[status(thm)],[f_498_2]) ).

fof(f_498_4,plain,
    ( ! [U_1979,U_1975,U_1977,U_1981] :
        ( ti(fun(U_1981,bool),U_1975) = bot_bot(fun(U_1981,bool))
        | ~ sP122(U_1979,U_1975,U_1977,U_1981) )
    & ! [U_1979,U_1975,U_1977,U_1981] :
        ( ti(fun(U_1979,bool),U_1977) = bot_bot(fun(U_1979,bool))
        | ~ sP122(U_1979,U_1975,U_1977,U_1981) )
    & ! [U_1978,U_1976,U_1980,U_1982] :
        ( hAPP(fun(U_1982,bool),fun(sum_sum(U_1980,U_1982),bool),hAPP(fun(U_1980,bool),fun(fun(U_1982,bool),fun(sum_sum(U_1980,U_1982),bool)),sum_Plus(U_1980,U_1982),U_1978),U_1976) = bot_bot(fun(sum_sum(U_1980,U_1982),bool))
        | ti(fun(U_1982,bool),U_1976) != bot_bot(fun(U_1982,bool))
        | ti(fun(U_1980,bool),U_1978) != bot_bot(fun(U_1980,bool)) )
    & ! [U_1979,U_1975,U_1977,U_1981] :
        ( sP122(U_1979,U_1975,U_1977,U_1981)
        | hAPP(fun(U_1981,bool),fun(sum_sum(U_1979,U_1981),bool),hAPP(fun(U_1979,bool),fun(fun(U_1981,bool),fun(sum_sum(U_1979,U_1981),bool)),sum_Plus(U_1979,U_1981),U_1977),U_1975) != bot_bot(fun(sum_sum(U_1979,U_1981),bool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122])],[f_498_3]) ).

cnf(f_498_5,plain,
    ( sP122(U_1979,U_1975,U_1977,U_1981)
    | hAPP(fun(U_1981,bool),fun(sum_sum(U_1979,U_1981),bool),hAPP(fun(U_1979,bool),fun(fun(U_1981,bool),fun(sum_sum(U_1979,U_1981),bool)),sum_Plus(U_1979,U_1981),U_1977),U_1975) != bot_bot(fun(sum_sum(U_1979,U_1981),bool)) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_6,plain,
    ( hAPP(fun(U_1982,bool),fun(sum_sum(U_1980,U_1982),bool),hAPP(fun(U_1980,bool),fun(fun(U_1982,bool),fun(sum_sum(U_1980,U_1982),bool)),sum_Plus(U_1980,U_1982),U_1978),U_1976) = bot_bot(fun(sum_sum(U_1980,U_1982),bool))
    | ti(fun(U_1982,bool),U_1976) != bot_bot(fun(U_1982,bool))
    | ti(fun(U_1980,bool),U_1978) != bot_bot(fun(U_1980,bool)) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_7,plain,
    ( ti(fun(U_1979,bool),U_1977) = bot_bot(fun(U_1979,bool))
    | ~ sP122(U_1979,U_1975,U_1977,U_1981) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_8,plain,
    ( ti(fun(U_1981,bool),U_1975) = bot_bot(fun(U_1981,bool))
    | ~ sP122(U_1979,U_1975,U_1977,U_1981) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

fof(f_499_1,plain,
    ! [X_c,X_b,B_2,A_3] :
      ( ( hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)) = zero_zero(nat)
        | ( hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
          & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ) )
      & ( hAPP(fun(sum_sum(X_b,X_c),bool),nat,finite_card(sum_sum(X_b,X_c)),hAPP(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool),hAPP(fun(X_b,bool),fun(fun(X_c,bool),fun(sum_sum(X_b,X_c),bool)),sum_Plus(X_b,X_c),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_c,bool),nat,finite_card(X_c),B_2))
        | ~ hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B_2))
        | ~ hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ) ),
    inference(fof_nnf,[status(thm)],[fact_446_card__Plus__conv__if]) ).

fof(f_499_2,plain,
    ! [U_1986,U_1985,U_1984,U_1983] :
      ( ( hAPP(fun(sum_sum(U_1985,U_1986),bool),nat,finite_card(sum_sum(U_1985,U_1986)),hAPP(fun(U_1986,bool),fun(sum_sum(U_1985,U_1986),bool),hAPP(fun(U_1985,bool),fun(fun(U_1986,bool),fun(sum_sum(U_1985,U_1986),bool)),sum_Plus(U_1985,U_1986),U_1983),U_1984)) = zero_zero(nat)
        | ( hBOOL(hAPP(fun(U_1986,bool),bool,finite_finite(U_1986),U_1984))
          & hBOOL(hAPP(fun(U_1985,bool),bool,finite_finite(U_1985),U_1983)) ) )
      & ( hAPP(fun(sum_sum(U_1985,U_1986),bool),nat,finite_card(sum_sum(U_1985,U_1986)),hAPP(fun(U_1986,bool),fun(sum_sum(U_1985,U_1986),bool),hAPP(fun(U_1985,bool),fun(fun(U_1986,bool),fun(sum_sum(U_1985,U_1986),bool)),sum_Plus(U_1985,U_1986),U_1983),U_1984)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1985,bool),nat,finite_card(U_1985),U_1983)),hAPP(fun(U_1986,bool),nat,finite_card(U_1986),U_1984))
        | ~ hBOOL(hAPP(fun(U_1986,bool),bool,finite_finite(U_1986),U_1984))
        | ~ hBOOL(hAPP(fun(U_1985,bool),bool,finite_finite(U_1985),U_1983)) ) ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

fof(f_499_3,plain,
    ( ! [U_1994,U_1992,U_1990,U_1988] :
        ( hAPP(fun(sum_sum(U_1992,U_1994),bool),nat,finite_card(sum_sum(U_1992,U_1994)),hAPP(fun(U_1994,bool),fun(sum_sum(U_1992,U_1994),bool),hAPP(fun(U_1992,bool),fun(fun(U_1994,bool),fun(sum_sum(U_1992,U_1994),bool)),sum_Plus(U_1992,U_1994),U_1988),U_1990)) = zero_zero(nat)
        | ( hBOOL(hAPP(fun(U_1994,bool),bool,finite_finite(U_1994),U_1990))
          & hBOOL(hAPP(fun(U_1992,bool),bool,finite_finite(U_1992),U_1988)) ) )
    & ! [U_1993,U_1991,U_1989,U_1987] :
        ( hAPP(fun(sum_sum(U_1991,U_1993),bool),nat,finite_card(sum_sum(U_1991,U_1993)),hAPP(fun(U_1993,bool),fun(sum_sum(U_1991,U_1993),bool),hAPP(fun(U_1991,bool),fun(fun(U_1993,bool),fun(sum_sum(U_1991,U_1993),bool)),sum_Plus(U_1991,U_1993),U_1987),U_1989)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1991,bool),nat,finite_card(U_1991),U_1987)),hAPP(fun(U_1993,bool),nat,finite_card(U_1993),U_1989))
        | ~ hBOOL(hAPP(fun(U_1993,bool),bool,finite_finite(U_1993),U_1989))
        | ~ hBOOL(hAPP(fun(U_1991,bool),bool,finite_finite(U_1991),U_1987)) ) ),
    inference(miniscope,[status(thm)],[f_499_2]) ).

fof(f_499_4,plain,
    ( ! [U_1992,U_1990,U_1988,U_1994] :
        ( hBOOL(hAPP(fun(U_1994,bool),bool,finite_finite(U_1994),U_1990))
        | ~ sP123(U_1992,U_1990,U_1988,U_1994) )
    & ! [U_1992,U_1990,U_1988,U_1994] :
        ( hBOOL(hAPP(fun(U_1992,bool),bool,finite_finite(U_1992),U_1988))
        | ~ sP123(U_1992,U_1990,U_1988,U_1994) )
    & ! [U_1992,U_1990,U_1988,U_1994] :
        ( hAPP(fun(sum_sum(U_1992,U_1994),bool),nat,finite_card(sum_sum(U_1992,U_1994)),hAPP(fun(U_1994,bool),fun(sum_sum(U_1992,U_1994),bool),hAPP(fun(U_1992,bool),fun(fun(U_1994,bool),fun(sum_sum(U_1992,U_1994),bool)),sum_Plus(U_1992,U_1994),U_1988),U_1990)) = zero_zero(nat)
        | sP123(U_1992,U_1990,U_1988,U_1994) )
    & ! [U_1987,U_1991,U_1989,U_1993] :
        ( hAPP(fun(sum_sum(U_1991,U_1993),bool),nat,finite_card(sum_sum(U_1991,U_1993)),hAPP(fun(U_1993,bool),fun(sum_sum(U_1991,U_1993),bool),hAPP(fun(U_1991,bool),fun(fun(U_1993,bool),fun(sum_sum(U_1991,U_1993),bool)),sum_Plus(U_1991,U_1993),U_1987),U_1989)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1991,bool),nat,finite_card(U_1991),U_1987)),hAPP(fun(U_1993,bool),nat,finite_card(U_1993),U_1989))
        | ~ hBOOL(hAPP(fun(U_1993,bool),bool,finite_finite(U_1993),U_1989))
        | ~ hBOOL(hAPP(fun(U_1991,bool),bool,finite_finite(U_1991),U_1987)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP123])],[f_499_3]) ).

cnf(f_499_5,plain,
    ( hAPP(fun(sum_sum(U_1991,U_1993),bool),nat,finite_card(sum_sum(U_1991,U_1993)),hAPP(fun(U_1993,bool),fun(sum_sum(U_1991,U_1993),bool),hAPP(fun(U_1991,bool),fun(fun(U_1993,bool),fun(sum_sum(U_1991,U_1993),bool)),sum_Plus(U_1991,U_1993),U_1987),U_1989)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(U_1991,bool),nat,finite_card(U_1991),U_1987)),hAPP(fun(U_1993,bool),nat,finite_card(U_1993),U_1989))
    | ~ hBOOL(hAPP(fun(U_1993,bool),bool,finite_finite(U_1993),U_1989))
    | ~ hBOOL(hAPP(fun(U_1991,bool),bool,finite_finite(U_1991),U_1987)) ),
    inference(clausify,[status(thm)],[f_499_4]) ).

cnf(f_499_6,plain,
    ( hAPP(fun(sum_sum(U_1992,U_1994),bool),nat,finite_card(sum_sum(U_1992,U_1994)),hAPP(fun(U_1994,bool),fun(sum_sum(U_1992,U_1994),bool),hAPP(fun(U_1992,bool),fun(fun(U_1994,bool),fun(sum_sum(U_1992,U_1994),bool)),sum_Plus(U_1992,U_1994),U_1988),U_1990)) = zero_zero(nat)
    | sP123(U_1992,U_1990,U_1988,U_1994) ),
    inference(clausify,[status(thm)],[f_499_4]) ).

cnf(f_499_7,plain,
    ( hBOOL(hAPP(fun(U_1992,bool),bool,finite_finite(U_1992),U_1988))
    | ~ sP123(U_1992,U_1990,U_1988,U_1994) ),
    inference(clausify,[status(thm)],[f_499_4]) ).

cnf(f_499_8,plain,
    ( hBOOL(hAPP(fun(U_1994,bool),bool,finite_finite(U_1994),U_1990))
    | ~ sP123(U_1992,U_1990,U_1988,U_1994) ),
    inference(clausify,[status(thm)],[f_499_4]) ).

fof(f_500_1,plain,
    ! [N] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat))),
    inference(fof_nnf,[status(thm)],[fact_447_less__zeroE]) ).

fof(f_500_2,plain,
    ! [U_1995] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1995),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

fof(f_500_3,plain,
    ! [U_1995] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1995),zero_zero(nat))),
    inference(definitional_conversion,[status(esa)],[f_500_2]) ).

cnf(f_500_4,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),U_1995),zero_zero(nat))),
    inference(clausify,[status(thm)],[f_500_3]) ).

fof(f_501_1,plain,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N)),
    inference(fof_nnf,[status(thm)],[fact_448_le0]) ).

fof(f_501_2,plain,
    ! [U_1996] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_1996)),
    inference(variable_rename,[status(thm)],[f_501_1]) ).

fof(f_501_3,plain,
    ! [U_1996] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_1996)),
    inference(definitional_conversion,[status(esa)],[f_501_2]) ).

cnf(f_501_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_1996)),
    inference(clausify,[status(thm)],[f_501_3]) ).

fof(f_502_1,plain,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N))),
    inference(fof_nnf,[status(thm)],[fact_449_zero__less__Suc]) ).

fof(f_502_2,plain,
    ! [U_1997] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,U_1997))),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

fof(f_502_3,plain,
    ! [U_1997] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,U_1997))),
    inference(definitional_conversion,[status(esa)],[f_502_2]) ).

cnf(f_502_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,U_1997))),
    inference(clausify,[status(thm)],[f_502_3]) ).

fof(f_503_1,plain,
    ! [X_b,A_3] :
      ( hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = zero_zero(nat)
      | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_3)) ),
    inference(fof_nnf,[status(thm)],[fact_450_card__infinite]) ).

fof(f_503_2,plain,
    ! [U_1999,U_1998] :
      ( hAPP(fun(U_1999,bool),nat,finite_card(U_1999),U_1998) = zero_zero(nat)
      | hBOOL(hAPP(fun(U_1999,bool),bool,finite_finite(U_1999),U_1998)) ),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

fof(f_503_3,plain,
    ! [U_1998,U_1999] :
      ( hAPP(fun(U_1999,bool),nat,finite_card(U_1999),U_1998) = zero_zero(nat)
      | hBOOL(hAPP(fun(U_1999,bool),bool,finite_finite(U_1999),U_1998)) ),
    inference(definitional_conversion,[status(esa)],[f_503_2]) ).

cnf(f_503_4,plain,
    ( hAPP(fun(U_1999,bool),nat,finite_card(U_1999),U_1998) = zero_zero(nat)
    | hBOOL(hAPP(fun(U_1999,bool),bool,finite_finite(U_1999),U_1998)) ),
    inference(clausify,[status(thm)],[f_503_3]) ).

fof(f_504_1,plain,
    ! [X_b] : hAPP(fun(X_b,bool),nat,finite_card(X_b),bot_bot(fun(X_b,bool))) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_451_card_Oempty]) ).

fof(f_504_2,plain,
    ! [U_2000] : hAPP(fun(U_2000,bool),nat,finite_card(U_2000),bot_bot(fun(U_2000,bool))) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

fof(f_504_3,plain,
    ! [U_2000] : hAPP(fun(U_2000,bool),nat,finite_card(U_2000),bot_bot(fun(U_2000,bool))) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_504_2]) ).

cnf(f_504_4,plain,
    hAPP(fun(U_2000,bool),nat,finite_card(U_2000),bot_bot(fun(U_2000,bool))) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_504_3]) ).

fof(f_505_1,plain,
    ! [X_a] :
      ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a)))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_452_zero__less__one]) ).

fof(f_505_2,plain,
    ! [U_2001] :
      ( hBOOL(hAPP(U_2001,bool,hAPP(U_2001,fun(U_2001,bool),ord_less(U_2001),zero_zero(U_2001)),one_one(U_2001)))
      | ~ linordered_semidom(U_2001) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

fof(f_505_3,plain,
    ! [U_2001] :
      ( hBOOL(hAPP(U_2001,bool,hAPP(U_2001,fun(U_2001,bool),ord_less(U_2001),zero_zero(U_2001)),one_one(U_2001)))
      | ~ linordered_semidom(U_2001) ),
    inference(definitional_conversion,[status(esa)],[f_505_2]) ).

cnf(f_505_4,plain,
    ( hBOOL(hAPP(U_2001,bool,hAPP(U_2001,fun(U_2001,bool),ord_less(U_2001),zero_zero(U_2001)),one_one(U_2001)))
    | ~ linordered_semidom(U_2001) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

fof(f_506_1,plain,
    ! [X_a] :
      ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a)))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_453_not__one__less__zero]) ).

fof(f_506_2,plain,
    ! [U_2002] :
      ( ~ hBOOL(hAPP(U_2002,bool,hAPP(U_2002,fun(U_2002,bool),ord_less(U_2002),one_one(U_2002)),zero_zero(U_2002)))
      | ~ linordered_semidom(U_2002) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

fof(f_506_3,plain,
    ! [U_2002] :
      ( ~ hBOOL(hAPP(U_2002,bool,hAPP(U_2002,fun(U_2002,bool),ord_less(U_2002),one_one(U_2002)),zero_zero(U_2002)))
      | ~ linordered_semidom(U_2002) ),
    inference(definitional_conversion,[status(esa)],[f_506_2]) ).

cnf(f_506_4,plain,
    ( ~ hBOOL(hAPP(U_2002,bool,hAPP(U_2002,fun(U_2002,bool),ord_less(U_2002),one_one(U_2002)),zero_zero(U_2002)))
    | ~ linordered_semidom(U_2002) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

fof(f_507_1,plain,
    ! [X_a] :
      ( ! [B_1,C,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) )
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_454_pos__add__strict]) ).

fof(f_507_2,plain,
    ! [U_2006] :
      ( ! [U_2005,U_2004,U_2003] :
          ( hBOOL(hAPP(U_2006,bool,hAPP(U_2006,fun(U_2006,bool),ord_less(U_2006),U_2005),hAPP(U_2006,U_2006,hAPP(U_2006,fun(U_2006,U_2006),plus_plus(U_2006),U_2003),U_2004)))
          | ~ hBOOL(hAPP(U_2006,bool,hAPP(U_2006,fun(U_2006,bool),ord_less(U_2006),U_2005),U_2004))
          | ~ hBOOL(hAPP(U_2006,bool,hAPP(U_2006,fun(U_2006,bool),ord_less(U_2006),zero_zero(U_2006)),U_2003)) )
      | ~ linordered_semidom(U_2006) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

fof(f_507_3,plain,
    ! [U_2004,U_2006,U_2003,U_2005] :
      ( hBOOL(hAPP(U_2006,bool,hAPP(U_2006,fun(U_2006,bool),ord_less(U_2006),U_2005),hAPP(U_2006,U_2006,hAPP(U_2006,fun(U_2006,U_2006),plus_plus(U_2006),U_2003),U_2004)))
      | ~ hBOOL(hAPP(U_2006,bool,hAPP(U_2006,fun(U_2006,bool),ord_less(U_2006),U_2005),U_2004))
      | ~ hBOOL(hAPP(U_2006,bool,hAPP(U_2006,fun(U_2006,bool),ord_less(U_2006),zero_zero(U_2006)),U_2003))
      | ~ linordered_semidom(U_2006) ),
    inference(definitional_conversion,[status(esa)],[f_507_2]) ).

cnf(f_507_4,plain,
    ( hBOOL(hAPP(U_2006,bool,hAPP(U_2006,fun(U_2006,bool),ord_less(U_2006),U_2005),hAPP(U_2006,U_2006,hAPP(U_2006,fun(U_2006,U_2006),plus_plus(U_2006),U_2003),U_2004)))
    | ~ hBOOL(hAPP(U_2006,bool,hAPP(U_2006,fun(U_2006,bool),ord_less(U_2006),U_2005),U_2004))
    | ~ hBOOL(hAPP(U_2006,bool,hAPP(U_2006,fun(U_2006,bool),ord_less(U_2006),zero_zero(U_2006)),U_2003))
    | ~ linordered_semidom(U_2006) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

fof(f_508_1,plain,
    ! [X_a] :
      ( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),zero_zero(X_a)))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_455_not__one__le__zero]) ).

fof(f_508_2,plain,
    ! [U_2007] :
      ( ~ hBOOL(hAPP(U_2007,bool,hAPP(U_2007,fun(U_2007,bool),ord_less_eq(U_2007),one_one(U_2007)),zero_zero(U_2007)))
      | ~ linordered_semidom(U_2007) ),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

fof(f_508_3,plain,
    ! [U_2007] :
      ( ~ hBOOL(hAPP(U_2007,bool,hAPP(U_2007,fun(U_2007,bool),ord_less_eq(U_2007),one_one(U_2007)),zero_zero(U_2007)))
      | ~ linordered_semidom(U_2007) ),
    inference(definitional_conversion,[status(esa)],[f_508_2]) ).

cnf(f_508_4,plain,
    ( ~ hBOOL(hAPP(U_2007,bool,hAPP(U_2007,fun(U_2007,bool),ord_less_eq(U_2007),one_one(U_2007)),zero_zero(U_2007)))
    | ~ linordered_semidom(U_2007) ),
    inference(clausify,[status(thm)],[f_508_3]) ).

fof(f_509_1,plain,
    ! [X_a] :
      ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),one_one(X_a)))
      | ~ linordered_semidom(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_456_zero__le__one]) ).

fof(f_509_2,plain,
    ! [U_2008] :
      ( hBOOL(hAPP(U_2008,bool,hAPP(U_2008,fun(U_2008,bool),ord_less_eq(U_2008),zero_zero(U_2008)),one_one(U_2008)))
      | ~ linordered_semidom(U_2008) ),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

fof(f_509_3,plain,
    ! [U_2008] :
      ( hBOOL(hAPP(U_2008,bool,hAPP(U_2008,fun(U_2008,bool),ord_less_eq(U_2008),zero_zero(U_2008)),one_one(U_2008)))
      | ~ linordered_semidom(U_2008) ),
    inference(definitional_conversion,[status(esa)],[f_509_2]) ).

cnf(f_509_4,plain,
    ( hBOOL(hAPP(U_2008,bool,hAPP(U_2008,fun(U_2008,bool),ord_less_eq(U_2008),zero_zero(U_2008)),one_one(U_2008)))
    | ~ linordered_semidom(U_2008) ),
    inference(clausify,[status(thm)],[f_509_3]) ).

fof(f_510_1,plain,
    ! [X_a] :
      ( one_one(X_a) != zero_zero(X_a)
      | ~ zero_neq_one(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_457_one__neq__zero]) ).

fof(f_510_2,plain,
    ! [U_2009] :
      ( one_one(U_2009) != zero_zero(U_2009)
      | ~ zero_neq_one(U_2009) ),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

fof(f_510_3,plain,
    ! [U_2009] :
      ( one_one(U_2009) != zero_zero(U_2009)
      | ~ zero_neq_one(U_2009) ),
    inference(definitional_conversion,[status(esa)],[f_510_2]) ).

cnf(f_510_4,plain,
    ( one_one(U_2009) != zero_zero(U_2009)
    | ~ zero_neq_one(U_2009) ),
    inference(clausify,[status(thm)],[f_510_3]) ).

fof(f_511_1,plain,
    ! [X_a] :
      ( zero_zero(X_a) != one_one(X_a)
      | ~ zero_neq_one(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_458_zero__neq__one]) ).

fof(f_511_2,plain,
    ! [U_2010] :
      ( zero_zero(U_2010) != one_one(U_2010)
      | ~ zero_neq_one(U_2010) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

fof(f_511_3,plain,
    ! [U_2010] :
      ( zero_zero(U_2010) != one_one(U_2010)
      | ~ zero_neq_one(U_2010) ),
    inference(definitional_conversion,[status(esa)],[f_511_2]) ).

cnf(f_511_4,plain,
    ( zero_zero(U_2010) != one_one(U_2010)
    | ~ zero_neq_one(U_2010) ),
    inference(clausify,[status(thm)],[f_511_3]) ).

fof(f_512_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),A_2)) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),A_2))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2))) ) )
      | ~ linord219039673up_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_459_zero__le__double__add__iff__zero__le__single__add]) ).

fof(f_512_2,plain,
    ! [U_2012] :
      ( ! [U_2011] :
          ( ( hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),hAPP(U_2012,U_2012,hAPP(U_2012,fun(U_2012,U_2012),plus_plus(U_2012),U_2011),U_2011)))
            | ~ hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),U_2011)) )
          & ( hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),U_2011))
            | ~ hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),hAPP(U_2012,U_2012,hAPP(U_2012,fun(U_2012,U_2012),plus_plus(U_2012),U_2011),U_2011))) ) )
      | ~ linord219039673up_add(U_2012) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

fof(f_512_3,plain,
    ! [U_2012] :
      ( ( ! [U_2014] :
            ( hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),hAPP(U_2012,U_2012,hAPP(U_2012,fun(U_2012,U_2012),plus_plus(U_2012),U_2014),U_2014)))
            | ~ hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),U_2014)) )
        & ! [U_2013] :
            ( hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),U_2013))
            | ~ hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),hAPP(U_2012,U_2012,hAPP(U_2012,fun(U_2012,U_2012),plus_plus(U_2012),U_2013),U_2013))) ) )
      | ~ linord219039673up_add(U_2012) ),
    inference(miniscope,[status(thm)],[f_512_2]) ).

fof(f_512_4,plain,
    ( ! [U_2012,U_2013,U_2014] :
        ( hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),hAPP(U_2012,U_2012,hAPP(U_2012,fun(U_2012,U_2012),plus_plus(U_2012),U_2014),U_2014)))
        | ~ hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),U_2014))
        | ~ sP124(U_2012,U_2013,U_2014) )
    & ! [U_2012,U_2013,U_2014] :
        ( hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),U_2013))
        | ~ hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),hAPP(U_2012,U_2012,hAPP(U_2012,fun(U_2012,U_2012),plus_plus(U_2012),U_2013),U_2013)))
        | ~ sP124(U_2012,U_2013,U_2014) )
    & ! [U_2012,U_2013,U_2014] :
        ( sP124(U_2012,U_2013,U_2014)
        | ~ linord219039673up_add(U_2012) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124])],[f_512_3]) ).

cnf(f_512_5,plain,
    ( sP124(U_2012,U_2013,U_2014)
    | ~ linord219039673up_add(U_2012) ),
    inference(clausify,[status(thm)],[f_512_4]) ).

cnf(f_512_6,plain,
    ( hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),U_2013))
    | ~ hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),hAPP(U_2012,U_2012,hAPP(U_2012,fun(U_2012,U_2012),plus_plus(U_2012),U_2013),U_2013)))
    | ~ sP124(U_2012,U_2013,U_2014) ),
    inference(clausify,[status(thm)],[f_512_4]) ).

cnf(f_512_7,plain,
    ( hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),hAPP(U_2012,U_2012,hAPP(U_2012,fun(U_2012,U_2012),plus_plus(U_2012),U_2014),U_2014)))
    | ~ hBOOL(hAPP(U_2012,bool,hAPP(U_2012,fun(U_2012,bool),ord_less_eq(U_2012),zero_zero(U_2012)),U_2014))
    | ~ sP124(U_2012,U_2013,U_2014) ),
    inference(clausify,[status(thm)],[f_512_4]) ).

fof(f_513_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),zero_zero(X_b))) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),zero_zero(X_b)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))) ) )
      | ~ linord219039673up_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_460_double__add__le__zero__iff__single__add__le__zero]) ).

fof(f_513_2,plain,
    ! [U_2016] :
      ( ! [U_2015] :
          ( ( hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),hAPP(U_2016,U_2016,hAPP(U_2016,fun(U_2016,U_2016),plus_plus(U_2016),U_2015),U_2015)),zero_zero(U_2016)))
            | ~ hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),U_2015),zero_zero(U_2016))) )
          & ( hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),U_2015),zero_zero(U_2016)))
            | ~ hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),hAPP(U_2016,U_2016,hAPP(U_2016,fun(U_2016,U_2016),plus_plus(U_2016),U_2015),U_2015)),zero_zero(U_2016))) ) )
      | ~ linord219039673up_add(U_2016) ),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

fof(f_513_3,plain,
    ! [U_2016] :
      ( ( ! [U_2018] :
            ( hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),hAPP(U_2016,U_2016,hAPP(U_2016,fun(U_2016,U_2016),plus_plus(U_2016),U_2018),U_2018)),zero_zero(U_2016)))
            | ~ hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),U_2018),zero_zero(U_2016))) )
        & ! [U_2017] :
            ( hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),U_2017),zero_zero(U_2016)))
            | ~ hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),hAPP(U_2016,U_2016,hAPP(U_2016,fun(U_2016,U_2016),plus_plus(U_2016),U_2017),U_2017)),zero_zero(U_2016))) ) )
      | ~ linord219039673up_add(U_2016) ),
    inference(miniscope,[status(thm)],[f_513_2]) ).

fof(f_513_4,plain,
    ( ! [U_2016,U_2018,U_2017] :
        ( hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),hAPP(U_2016,U_2016,hAPP(U_2016,fun(U_2016,U_2016),plus_plus(U_2016),U_2018),U_2018)),zero_zero(U_2016)))
        | ~ hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),U_2018),zero_zero(U_2016)))
        | ~ sP125(U_2016,U_2018,U_2017) )
    & ! [U_2016,U_2018,U_2017] :
        ( hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),U_2017),zero_zero(U_2016)))
        | ~ hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),hAPP(U_2016,U_2016,hAPP(U_2016,fun(U_2016,U_2016),plus_plus(U_2016),U_2017),U_2017)),zero_zero(U_2016)))
        | ~ sP125(U_2016,U_2018,U_2017) )
    & ! [U_2016,U_2018,U_2017] :
        ( sP125(U_2016,U_2018,U_2017)
        | ~ linord219039673up_add(U_2016) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125])],[f_513_3]) ).

cnf(f_513_5,plain,
    ( sP125(U_2016,U_2018,U_2017)
    | ~ linord219039673up_add(U_2016) ),
    inference(clausify,[status(thm)],[f_513_4]) ).

cnf(f_513_6,plain,
    ( hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),U_2017),zero_zero(U_2016)))
    | ~ hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),hAPP(U_2016,U_2016,hAPP(U_2016,fun(U_2016,U_2016),plus_plus(U_2016),U_2017),U_2017)),zero_zero(U_2016)))
    | ~ sP125(U_2016,U_2018,U_2017) ),
    inference(clausify,[status(thm)],[f_513_4]) ).

cnf(f_513_7,plain,
    ( hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),hAPP(U_2016,U_2016,hAPP(U_2016,fun(U_2016,U_2016),plus_plus(U_2016),U_2018),U_2018)),zero_zero(U_2016)))
    | ~ hBOOL(hAPP(U_2016,bool,hAPP(U_2016,fun(U_2016,bool),ord_less_eq(U_2016),U_2018),zero_zero(U_2016)))
    | ~ sP125(U_2016,U_2018,U_2017) ),
    inference(clausify,[status(thm)],[f_513_4]) ).

fof(f_514_1,plain,
    ! [X_a] :
      ( ! [B_1,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_461_add__nonneg__nonneg]) ).

fof(f_514_2,plain,
    ! [U_2021] :
      ( ! [U_2020,U_2019] :
          ( hBOOL(hAPP(U_2021,bool,hAPP(U_2021,fun(U_2021,bool),ord_less_eq(U_2021),zero_zero(U_2021)),hAPP(U_2021,U_2021,hAPP(U_2021,fun(U_2021,U_2021),plus_plus(U_2021),U_2019),U_2020)))
          | ~ hBOOL(hAPP(U_2021,bool,hAPP(U_2021,fun(U_2021,bool),ord_less_eq(U_2021),zero_zero(U_2021)),U_2020))
          | ~ hBOOL(hAPP(U_2021,bool,hAPP(U_2021,fun(U_2021,bool),ord_less_eq(U_2021),zero_zero(U_2021)),U_2019)) )
      | ~ ordere216010020id_add(U_2021) ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

fof(f_514_3,plain,
    ! [U_2019,U_2020,U_2021] :
      ( hBOOL(hAPP(U_2021,bool,hAPP(U_2021,fun(U_2021,bool),ord_less_eq(U_2021),zero_zero(U_2021)),hAPP(U_2021,U_2021,hAPP(U_2021,fun(U_2021,U_2021),plus_plus(U_2021),U_2019),U_2020)))
      | ~ hBOOL(hAPP(U_2021,bool,hAPP(U_2021,fun(U_2021,bool),ord_less_eq(U_2021),zero_zero(U_2021)),U_2020))
      | ~ hBOOL(hAPP(U_2021,bool,hAPP(U_2021,fun(U_2021,bool),ord_less_eq(U_2021),zero_zero(U_2021)),U_2019))
      | ~ ordere216010020id_add(U_2021) ),
    inference(definitional_conversion,[status(esa)],[f_514_2]) ).

cnf(f_514_4,plain,
    ( hBOOL(hAPP(U_2021,bool,hAPP(U_2021,fun(U_2021,bool),ord_less_eq(U_2021),zero_zero(U_2021)),hAPP(U_2021,U_2021,hAPP(U_2021,fun(U_2021,U_2021),plus_plus(U_2021),U_2019),U_2020)))
    | ~ hBOOL(hAPP(U_2021,bool,hAPP(U_2021,fun(U_2021,bool),ord_less_eq(U_2021),zero_zero(U_2021)),U_2020))
    | ~ hBOOL(hAPP(U_2021,bool,hAPP(U_2021,fun(U_2021,bool),ord_less_eq(U_2021),zero_zero(U_2021)),U_2019))
    | ~ ordere216010020id_add(U_2021) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

fof(f_515_1,plain,
    ! [X_b] :
      ( ! [Y_1,X_1] :
          ( ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_1),Y_1) = zero_zero(X_b)
              | ti(X_b,Y_1) != zero_zero(X_b)
              | ti(X_b,X_1) != zero_zero(X_b) )
            & ( ( ti(X_b,Y_1) = zero_zero(X_b)
                & ti(X_b,X_1) = zero_zero(X_b) )
              | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),X_1),Y_1) != zero_zero(X_b) ) )
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),Y_1))
          | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),X_1)) )
      | ~ ordere216010020id_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_462_add__nonneg__eq__0__iff]) ).

fof(f_515_2,plain,
    ! [U_2024] :
      ( ! [U_2023,U_2022] :
          ( ( ( hAPP(U_2024,U_2024,hAPP(U_2024,fun(U_2024,U_2024),plus_plus(U_2024),U_2022),U_2023) = zero_zero(U_2024)
              | ti(U_2024,U_2023) != zero_zero(U_2024)
              | ti(U_2024,U_2022) != zero_zero(U_2024) )
            & ( ( ti(U_2024,U_2023) = zero_zero(U_2024)
                & ti(U_2024,U_2022) = zero_zero(U_2024) )
              | hAPP(U_2024,U_2024,hAPP(U_2024,fun(U_2024,U_2024),plus_plus(U_2024),U_2022),U_2023) != zero_zero(U_2024) ) )
          | ~ hBOOL(hAPP(U_2024,bool,hAPP(U_2024,fun(U_2024,bool),ord_less_eq(U_2024),zero_zero(U_2024)),U_2023))
          | ~ hBOOL(hAPP(U_2024,bool,hAPP(U_2024,fun(U_2024,bool),ord_less_eq(U_2024),zero_zero(U_2024)),U_2022)) )
      | ~ ordere216010020id_add(U_2024) ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

fof(f_515_3,plain,
    ( ! [U_2022,U_2023,U_2024] :
        ( ti(U_2024,U_2023) = zero_zero(U_2024)
        | ~ sP126(U_2022,U_2023,U_2024) )
    & ! [U_2022,U_2023,U_2024] :
        ( ti(U_2024,U_2022) = zero_zero(U_2024)
        | ~ sP126(U_2022,U_2023,U_2024) )
    & ! [U_2022,U_2023,U_2024] :
        ( hAPP(U_2024,U_2024,hAPP(U_2024,fun(U_2024,U_2024),plus_plus(U_2024),U_2022),U_2023) = zero_zero(U_2024)
        | ti(U_2024,U_2023) != zero_zero(U_2024)
        | ti(U_2024,U_2022) != zero_zero(U_2024)
        | ~ sP127(U_2022,U_2023,U_2024) )
    & ! [U_2022,U_2023,U_2024] :
        ( sP126(U_2022,U_2023,U_2024)
        | hAPP(U_2024,U_2024,hAPP(U_2024,fun(U_2024,U_2024),plus_plus(U_2024),U_2022),U_2023) != zero_zero(U_2024)
        | ~ sP127(U_2022,U_2023,U_2024) )
    & ! [U_2022,U_2023,U_2024] :
        ( sP127(U_2022,U_2023,U_2024)
        | ~ hBOOL(hAPP(U_2024,bool,hAPP(U_2024,fun(U_2024,bool),ord_less_eq(U_2024),zero_zero(U_2024)),U_2023))
        | ~ hBOOL(hAPP(U_2024,bool,hAPP(U_2024,fun(U_2024,bool),ord_less_eq(U_2024),zero_zero(U_2024)),U_2022))
        | ~ ordere216010020id_add(U_2024) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126,sP127])],[f_515_2]) ).

cnf(f_515_4,plain,
    ( sP127(U_2022,U_2023,U_2024)
    | ~ hBOOL(hAPP(U_2024,bool,hAPP(U_2024,fun(U_2024,bool),ord_less_eq(U_2024),zero_zero(U_2024)),U_2023))
    | ~ hBOOL(hAPP(U_2024,bool,hAPP(U_2024,fun(U_2024,bool),ord_less_eq(U_2024),zero_zero(U_2024)),U_2022))
    | ~ ordere216010020id_add(U_2024) ),
    inference(clausify,[status(thm)],[f_515_3]) ).

cnf(f_515_5,plain,
    ( sP126(U_2022,U_2023,U_2024)
    | hAPP(U_2024,U_2024,hAPP(U_2024,fun(U_2024,U_2024),plus_plus(U_2024),U_2022),U_2023) != zero_zero(U_2024)
    | ~ sP127(U_2022,U_2023,U_2024) ),
    inference(clausify,[status(thm)],[f_515_3]) ).

cnf(f_515_6,plain,
    ( hAPP(U_2024,U_2024,hAPP(U_2024,fun(U_2024,U_2024),plus_plus(U_2024),U_2022),U_2023) = zero_zero(U_2024)
    | ti(U_2024,U_2023) != zero_zero(U_2024)
    | ti(U_2024,U_2022) != zero_zero(U_2024)
    | ~ sP127(U_2022,U_2023,U_2024) ),
    inference(clausify,[status(thm)],[f_515_3]) ).

cnf(f_515_7,plain,
    ( ti(U_2024,U_2022) = zero_zero(U_2024)
    | ~ sP126(U_2022,U_2023,U_2024) ),
    inference(clausify,[status(thm)],[f_515_3]) ).

cnf(f_515_8,plain,
    ( ti(U_2024,U_2023) = zero_zero(U_2024)
    | ~ sP126(U_2022,U_2023,U_2024) ),
    inference(clausify,[status(thm)],[f_515_3]) ).

fof(f_516_1,plain,
    ! [X_a] :
      ( ! [B_1,C,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_463_add__increasing]) ).

fof(f_516_2,plain,
    ! [U_2028] :
      ( ! [U_2027,U_2026,U_2025] :
          ( hBOOL(hAPP(U_2028,bool,hAPP(U_2028,fun(U_2028,bool),ord_less_eq(U_2028),U_2027),hAPP(U_2028,U_2028,hAPP(U_2028,fun(U_2028,U_2028),plus_plus(U_2028),U_2025),U_2026)))
          | ~ hBOOL(hAPP(U_2028,bool,hAPP(U_2028,fun(U_2028,bool),ord_less_eq(U_2028),U_2027),U_2026))
          | ~ hBOOL(hAPP(U_2028,bool,hAPP(U_2028,fun(U_2028,bool),ord_less_eq(U_2028),zero_zero(U_2028)),U_2025)) )
      | ~ ordere216010020id_add(U_2028) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

fof(f_516_3,plain,
    ! [U_2027,U_2026,U_2025,U_2028] :
      ( hBOOL(hAPP(U_2028,bool,hAPP(U_2028,fun(U_2028,bool),ord_less_eq(U_2028),U_2027),hAPP(U_2028,U_2028,hAPP(U_2028,fun(U_2028,U_2028),plus_plus(U_2028),U_2025),U_2026)))
      | ~ hBOOL(hAPP(U_2028,bool,hAPP(U_2028,fun(U_2028,bool),ord_less_eq(U_2028),U_2027),U_2026))
      | ~ hBOOL(hAPP(U_2028,bool,hAPP(U_2028,fun(U_2028,bool),ord_less_eq(U_2028),zero_zero(U_2028)),U_2025))
      | ~ ordere216010020id_add(U_2028) ),
    inference(definitional_conversion,[status(esa)],[f_516_2]) ).

cnf(f_516_4,plain,
    ( hBOOL(hAPP(U_2028,bool,hAPP(U_2028,fun(U_2028,bool),ord_less_eq(U_2028),U_2027),hAPP(U_2028,U_2028,hAPP(U_2028,fun(U_2028,U_2028),plus_plus(U_2028),U_2025),U_2026)))
    | ~ hBOOL(hAPP(U_2028,bool,hAPP(U_2028,fun(U_2028,bool),ord_less_eq(U_2028),U_2027),U_2026))
    | ~ hBOOL(hAPP(U_2028,bool,hAPP(U_2028,fun(U_2028,bool),ord_less_eq(U_2028),zero_zero(U_2028)),U_2025))
    | ~ ordere216010020id_add(U_2028) ),
    inference(clausify,[status(thm)],[f_516_3]) ).

fof(f_517_1,plain,
    ! [X_a] :
      ( ! [B_1,A_1,C] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_1))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_464_add__increasing2]) ).

fof(f_517_2,plain,
    ! [U_2032] :
      ( ! [U_2031,U_2030,U_2029] :
          ( hBOOL(hAPP(U_2032,bool,hAPP(U_2032,fun(U_2032,bool),ord_less_eq(U_2032),U_2031),hAPP(U_2032,U_2032,hAPP(U_2032,fun(U_2032,U_2032),plus_plus(U_2032),U_2030),U_2029)))
          | ~ hBOOL(hAPP(U_2032,bool,hAPP(U_2032,fun(U_2032,bool),ord_less_eq(U_2032),U_2031),U_2030))
          | ~ hBOOL(hAPP(U_2032,bool,hAPP(U_2032,fun(U_2032,bool),ord_less_eq(U_2032),zero_zero(U_2032)),U_2029)) )
      | ~ ordere216010020id_add(U_2032) ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

fof(f_517_3,plain,
    ! [U_2032,U_2029,U_2030,U_2031] :
      ( hBOOL(hAPP(U_2032,bool,hAPP(U_2032,fun(U_2032,bool),ord_less_eq(U_2032),U_2031),hAPP(U_2032,U_2032,hAPP(U_2032,fun(U_2032,U_2032),plus_plus(U_2032),U_2030),U_2029)))
      | ~ hBOOL(hAPP(U_2032,bool,hAPP(U_2032,fun(U_2032,bool),ord_less_eq(U_2032),U_2031),U_2030))
      | ~ hBOOL(hAPP(U_2032,bool,hAPP(U_2032,fun(U_2032,bool),ord_less_eq(U_2032),zero_zero(U_2032)),U_2029))
      | ~ ordere216010020id_add(U_2032) ),
    inference(definitional_conversion,[status(esa)],[f_517_2]) ).

cnf(f_517_4,plain,
    ( hBOOL(hAPP(U_2032,bool,hAPP(U_2032,fun(U_2032,bool),ord_less_eq(U_2032),U_2031),hAPP(U_2032,U_2032,hAPP(U_2032,fun(U_2032,U_2032),plus_plus(U_2032),U_2030),U_2029)))
    | ~ hBOOL(hAPP(U_2032,bool,hAPP(U_2032,fun(U_2032,bool),ord_less_eq(U_2032),U_2031),U_2030))
    | ~ hBOOL(hAPP(U_2032,bool,hAPP(U_2032,fun(U_2032,bool),ord_less_eq(U_2032),zero_zero(U_2032)),U_2029))
    | ~ ordere216010020id_add(U_2032) ),
    inference(clausify,[status(thm)],[f_517_3]) ).

fof(f_518_1,plain,
    ! [X_a] :
      ( ! [B_1,A_1] :
          ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B_1)),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a)))
          | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) )
      | ~ ordere216010020id_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_465_add__nonpos__nonpos]) ).

fof(f_518_2,plain,
    ! [U_2035] :
      ( ! [U_2034,U_2033] :
          ( hBOOL(hAPP(U_2035,bool,hAPP(U_2035,fun(U_2035,bool),ord_less_eq(U_2035),hAPP(U_2035,U_2035,hAPP(U_2035,fun(U_2035,U_2035),plus_plus(U_2035),U_2033),U_2034)),zero_zero(U_2035)))
          | ~ hBOOL(hAPP(U_2035,bool,hAPP(U_2035,fun(U_2035,bool),ord_less_eq(U_2035),U_2034),zero_zero(U_2035)))
          | ~ hBOOL(hAPP(U_2035,bool,hAPP(U_2035,fun(U_2035,bool),ord_less_eq(U_2035),U_2033),zero_zero(U_2035))) )
      | ~ ordere216010020id_add(U_2035) ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

fof(f_518_3,plain,
    ! [U_2034,U_2035,U_2033] :
      ( hBOOL(hAPP(U_2035,bool,hAPP(U_2035,fun(U_2035,bool),ord_less_eq(U_2035),hAPP(U_2035,U_2035,hAPP(U_2035,fun(U_2035,U_2035),plus_plus(U_2035),U_2033),U_2034)),zero_zero(U_2035)))
      | ~ hBOOL(hAPP(U_2035,bool,hAPP(U_2035,fun(U_2035,bool),ord_less_eq(U_2035),U_2034),zero_zero(U_2035)))
      | ~ hBOOL(hAPP(U_2035,bool,hAPP(U_2035,fun(U_2035,bool),ord_less_eq(U_2035),U_2033),zero_zero(U_2035)))
      | ~ ordere216010020id_add(U_2035) ),
    inference(definitional_conversion,[status(esa)],[f_518_2]) ).

cnf(f_518_4,plain,
    ( hBOOL(hAPP(U_2035,bool,hAPP(U_2035,fun(U_2035,bool),ord_less_eq(U_2035),hAPP(U_2035,U_2035,hAPP(U_2035,fun(U_2035,U_2035),plus_plus(U_2035),U_2033),U_2034)),zero_zero(U_2035)))
    | ~ hBOOL(hAPP(U_2035,bool,hAPP(U_2035,fun(U_2035,bool),ord_less_eq(U_2035),U_2034),zero_zero(U_2035)))
    | ~ hBOOL(hAPP(U_2035,bool,hAPP(U_2035,fun(U_2035,bool),ord_less_eq(U_2035),U_2033),zero_zero(U_2035)))
    | ~ ordere216010020id_add(U_2035) ),
    inference(clausify,[status(thm)],[f_518_3]) ).

fof(f_519_1,plain,
    ! [X_b] :
      ( ! [A_2,B] :
          ( ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B)),zero_zero(X_b))) )
          & ( hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B)),zero_zero(X_b)))
            | ~ hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),B)) ) )
      | ~ ordered_ab_group_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_466_le__iff__diff__le__0]) ).

fof(f_519_2,plain,
    ! [U_2038] :
      ( ! [U_2037,U_2036] :
          ( ( hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),U_2037),U_2036))
            | ~ hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),hAPP(U_2038,U_2038,hAPP(U_2038,fun(U_2038,U_2038),minus_minus(U_2038),U_2037),U_2036)),zero_zero(U_2038))) )
          & ( hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),hAPP(U_2038,U_2038,hAPP(U_2038,fun(U_2038,U_2038),minus_minus(U_2038),U_2037),U_2036)),zero_zero(U_2038)))
            | ~ hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),U_2037),U_2036)) ) )
      | ~ ordered_ab_group_add(U_2038) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

fof(f_519_3,plain,
    ! [U_2038] :
      ( ( ! [U_2042,U_2040] :
            ( hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),U_2042),U_2040))
            | ~ hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),hAPP(U_2038,U_2038,hAPP(U_2038,fun(U_2038,U_2038),minus_minus(U_2038),U_2042),U_2040)),zero_zero(U_2038))) )
        & ! [U_2041,U_2039] :
            ( hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),hAPP(U_2038,U_2038,hAPP(U_2038,fun(U_2038,U_2038),minus_minus(U_2038),U_2041),U_2039)),zero_zero(U_2038)))
            | ~ hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),U_2041),U_2039)) ) )
      | ~ ordered_ab_group_add(U_2038) ),
    inference(miniscope,[status(thm)],[f_519_2]) ).

fof(f_519_4,plain,
    ( ! [U_2038,U_2041,U_2039,U_2040,U_2042] :
        ( hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),U_2042),U_2040))
        | ~ hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),hAPP(U_2038,U_2038,hAPP(U_2038,fun(U_2038,U_2038),minus_minus(U_2038),U_2042),U_2040)),zero_zero(U_2038)))
        | ~ sP128(U_2038,U_2041,U_2039,U_2040,U_2042) )
    & ! [U_2038,U_2041,U_2039,U_2040,U_2042] :
        ( hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),hAPP(U_2038,U_2038,hAPP(U_2038,fun(U_2038,U_2038),minus_minus(U_2038),U_2041),U_2039)),zero_zero(U_2038)))
        | ~ hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),U_2041),U_2039))
        | ~ sP128(U_2038,U_2041,U_2039,U_2040,U_2042) )
    & ! [U_2038,U_2041,U_2039,U_2040,U_2042] :
        ( sP128(U_2038,U_2041,U_2039,U_2040,U_2042)
        | ~ ordered_ab_group_add(U_2038) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128])],[f_519_3]) ).

cnf(f_519_5,plain,
    ( sP128(U_2038,U_2041,U_2039,U_2040,U_2042)
    | ~ ordered_ab_group_add(U_2038) ),
    inference(clausify,[status(thm)],[f_519_4]) ).

cnf(f_519_6,plain,
    ( hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),hAPP(U_2038,U_2038,hAPP(U_2038,fun(U_2038,U_2038),minus_minus(U_2038),U_2041),U_2039)),zero_zero(U_2038)))
    | ~ hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),U_2041),U_2039))
    | ~ sP128(U_2038,U_2041,U_2039,U_2040,U_2042) ),
    inference(clausify,[status(thm)],[f_519_4]) ).

cnf(f_519_7,plain,
    ( hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),U_2042),U_2040))
    | ~ hBOOL(hAPP(U_2038,bool,hAPP(U_2038,fun(U_2038,bool),ord_less_eq(U_2038),hAPP(U_2038,U_2038,hAPP(U_2038,fun(U_2038,U_2038),minus_minus(U_2038),U_2042),U_2040)),zero_zero(U_2038)))
    | ~ sP128(U_2038,U_2041,U_2039,U_2040,U_2042) ),
    inference(clausify,[status(thm)],[f_519_4]) ).

fof(f_520_1,plain,
    ! [M_1,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),Na) = hAPP(nat,nat,suc,zero_zero(nat))
        | ( ( Na != hAPP(nat,nat,suc,zero_zero(nat))
            | M_1 != zero_zero(nat) )
          & ( Na != zero_zero(nat)
            | M_1 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
      & ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M_1 = zero_zero(nat) )
        | ( Na = zero_zero(nat)
          & M_1 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),Na) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_467_add__is__1]) ).

fof(f_520_2,plain,
    ! [U_2044,U_2043] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2044),U_2043) = hAPP(nat,nat,suc,zero_zero(nat))
        | ( ( U_2043 != hAPP(nat,nat,suc,zero_zero(nat))
            | U_2044 != zero_zero(nat) )
          & ( U_2043 != zero_zero(nat)
            | U_2044 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
      & ( ( U_2043 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_2044 = zero_zero(nat) )
        | ( U_2043 = zero_zero(nat)
          & U_2044 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2044),U_2043) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

fof(f_520_3,plain,
    ( ! [U_2048,U_2046] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2048),U_2046) = hAPP(nat,nat,suc,zero_zero(nat))
        | ( ( U_2046 != hAPP(nat,nat,suc,zero_zero(nat))
            | U_2048 != zero_zero(nat) )
          & ( U_2046 != zero_zero(nat)
            | U_2048 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
    & ! [U_2047,U_2045] :
        ( ( U_2045 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_2047 = zero_zero(nat) )
        | ( U_2045 = zero_zero(nat)
          & U_2047 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2047),U_2045) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(miniscope,[status(thm)],[f_520_2]) ).

fof(f_520_4,plain,
    ( ! [U_2046,U_2048] :
        ( U_2046 != hAPP(nat,nat,suc,zero_zero(nat))
        | U_2048 != zero_zero(nat)
        | ~ sP131(U_2046,U_2048) )
    & ! [U_2046,U_2048] :
        ( U_2046 != zero_zero(nat)
        | U_2048 != hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP131(U_2046,U_2048) )
    & ! [U_2045,U_2047] :
        ( U_2045 = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP130(U_2045,U_2047) )
    & ! [U_2045,U_2047] :
        ( U_2047 = zero_zero(nat)
        | ~ sP130(U_2045,U_2047) )
    & ! [U_2045,U_2047] :
        ( U_2045 = zero_zero(nat)
        | ~ sP129(U_2045,U_2047) )
    & ! [U_2045,U_2047] :
        ( U_2047 = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP129(U_2045,U_2047) )
    & ! [U_2046,U_2048] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2048),U_2046) = hAPP(nat,nat,suc,zero_zero(nat))
        | sP131(U_2046,U_2048) )
    & ! [U_2045,U_2047] :
        ( sP130(U_2045,U_2047)
        | sP129(U_2045,U_2047)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2047),U_2045) != hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129,sP130,sP131])],[f_520_3]) ).

cnf(f_520_5,plain,
    ( sP130(U_2045,U_2047)
    | sP129(U_2045,U_2047)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2047),U_2045) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

cnf(f_520_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2048),U_2046) = hAPP(nat,nat,suc,zero_zero(nat))
    | sP131(U_2046,U_2048) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

cnf(f_520_7,plain,
    ( U_2047 = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP129(U_2045,U_2047) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

cnf(f_520_8,plain,
    ( U_2045 = zero_zero(nat)
    | ~ sP129(U_2045,U_2047) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

cnf(f_520_9,plain,
    ( U_2047 = zero_zero(nat)
    | ~ sP130(U_2045,U_2047) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

cnf(f_520_10,plain,
    ( U_2045 = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP130(U_2045,U_2047) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

cnf(f_520_11,plain,
    ( U_2046 != zero_zero(nat)
    | U_2048 != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP131(U_2046,U_2048) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

cnf(f_520_12,plain,
    ( U_2046 != hAPP(nat,nat,suc,zero_zero(nat))
    | U_2048 != zero_zero(nat)
    | ~ sP131(U_2046,U_2048) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

fof(f_521_1,plain,
    ! [M_1,Na] :
      ( ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),Na)
        | ( ( Na != hAPP(nat,nat,suc,zero_zero(nat))
            | M_1 != zero_zero(nat) )
          & ( Na != zero_zero(nat)
            | M_1 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
      & ( ( Na = hAPP(nat,nat,suc,zero_zero(nat))
          & M_1 = zero_zero(nat) )
        | ( Na = zero_zero(nat)
          & M_1 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_468_one__is__add]) ).

fof(f_521_2,plain,
    ! [U_2050,U_2049] :
      ( ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2050),U_2049)
        | ( ( U_2049 != hAPP(nat,nat,suc,zero_zero(nat))
            | U_2050 != zero_zero(nat) )
          & ( U_2049 != zero_zero(nat)
            | U_2050 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
      & ( ( U_2049 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_2050 = zero_zero(nat) )
        | ( U_2049 = zero_zero(nat)
          & U_2050 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2050),U_2049) ) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

fof(f_521_3,plain,
    ( ! [U_2054,U_2052] :
        ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2054),U_2052)
        | ( ( U_2052 != hAPP(nat,nat,suc,zero_zero(nat))
            | U_2054 != zero_zero(nat) )
          & ( U_2052 != zero_zero(nat)
            | U_2054 != hAPP(nat,nat,suc,zero_zero(nat)) ) ) )
    & ! [U_2053,U_2051] :
        ( ( U_2051 = hAPP(nat,nat,suc,zero_zero(nat))
          & U_2053 = zero_zero(nat) )
        | ( U_2051 = zero_zero(nat)
          & U_2053 = hAPP(nat,nat,suc,zero_zero(nat)) )
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2053),U_2051) ) ),
    inference(miniscope,[status(thm)],[f_521_2]) ).

fof(f_521_4,plain,
    ( ! [U_2054,U_2052] :
        ( U_2052 != hAPP(nat,nat,suc,zero_zero(nat))
        | U_2054 != zero_zero(nat)
        | ~ sP134(U_2054,U_2052) )
    & ! [U_2054,U_2052] :
        ( U_2052 != zero_zero(nat)
        | U_2054 != hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP134(U_2054,U_2052) )
    & ! [U_2051,U_2053] :
        ( U_2051 = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP133(U_2051,U_2053) )
    & ! [U_2051,U_2053] :
        ( U_2053 = zero_zero(nat)
        | ~ sP133(U_2051,U_2053) )
    & ! [U_2051,U_2053] :
        ( U_2051 = zero_zero(nat)
        | ~ sP132(U_2051,U_2053) )
    & ! [U_2051,U_2053] :
        ( U_2053 = hAPP(nat,nat,suc,zero_zero(nat))
        | ~ sP132(U_2051,U_2053) )
    & ! [U_2054,U_2052] :
        ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2054),U_2052)
        | sP134(U_2054,U_2052) )
    & ! [U_2051,U_2053] :
        ( sP133(U_2051,U_2053)
        | sP132(U_2051,U_2053)
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2053),U_2051) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP132,sP133,sP134])],[f_521_3]) ).

cnf(f_521_5,plain,
    ( sP133(U_2051,U_2053)
    | sP132(U_2051,U_2053)
    | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2053),U_2051) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_6,plain,
    ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2054),U_2052)
    | sP134(U_2054,U_2052) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_7,plain,
    ( U_2053 = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP132(U_2051,U_2053) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_8,plain,
    ( U_2051 = zero_zero(nat)
    | ~ sP132(U_2051,U_2053) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_9,plain,
    ( U_2053 = zero_zero(nat)
    | ~ sP133(U_2051,U_2053) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_10,plain,
    ( U_2051 = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP133(U_2051,U_2053) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_11,plain,
    ( U_2052 != zero_zero(nat)
    | U_2054 != hAPP(nat,nat,suc,zero_zero(nat))
    | ~ sP134(U_2054,U_2052) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

cnf(f_521_12,plain,
    ( U_2052 != hAPP(nat,nat,suc,zero_zero(nat))
    | U_2054 != zero_zero(nat)
    | ~ sP134(U_2054,U_2052) ),
    inference(clausify,[status(thm)],[f_521_4]) ).

fof(f_522_1,plain,
    ! [N,M] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_469_diff__add__0]) ).

fof(f_522_2,plain,
    ! [U_2056,U_2055] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2056),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2056),U_2055)) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

fof(f_522_3,plain,
    ! [U_2055,U_2056] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2056),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2056),U_2055)) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_522_2]) ).

cnf(f_522_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2056),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),U_2056),U_2055)) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_522_3]) ).

fof(f_523_1,plain,
    ! [M,N] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = zero_zero(nat)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) ),
    inference(fof_nnf,[status(thm)],[fact_470_diff__is__0__eq_H]) ).

fof(f_523_2,plain,
    ! [U_2058,U_2057] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2058),U_2057) = zero_zero(nat)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2058),U_2057)) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

fof(f_523_3,plain,
    ! [U_2058,U_2057] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2058),U_2057) = zero_zero(nat)
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2058),U_2057)) ),
    inference(definitional_conversion,[status(esa)],[f_523_2]) ).

cnf(f_523_4,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2058),U_2057) = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2058),U_2057)) ),
    inference(clausify,[status(thm)],[f_523_3]) ).

fof(f_524_1,plain,
    ! [M_1,Na] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),Na) = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),Na))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),Na) != zero_zero(nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_471_diff__is__0__eq]) ).

fof(f_524_2,plain,
    ! [U_2060,U_2059] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2060),U_2059) = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2060),U_2059)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2060),U_2059))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2060),U_2059) != zero_zero(nat) ) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

fof(f_524_3,plain,
    ( ! [U_2064,U_2062] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2064),U_2062) = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2064),U_2062)) )
    & ! [U_2063,U_2061] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2063),U_2061))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2063),U_2061) != zero_zero(nat) ) ),
    inference(miniscope,[status(thm)],[f_524_2]) ).

fof(f_524_4,plain,
    ( ! [U_2062,U_2064] :
        ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2064),U_2062) = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2064),U_2062)) )
    & ! [U_2061,U_2063] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2063),U_2061))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2063),U_2061) != zero_zero(nat) ) ),
    inference(definitional_conversion,[status(esa)],[f_524_3]) ).

cnf(f_524_5,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2063),U_2061))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2063),U_2061) != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_524_4]) ).

cnf(f_524_6,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2064),U_2062) = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2064),U_2062)) ),
    inference(clausify,[status(thm)],[f_524_4]) ).

fof(f_525_1,plain,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(fof_nnf,[status(thm)],[fact_472_One__nat__def]) ).

fof(f_525_2,plain,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(definitional_conversion,[status(esa)],[f_525_1]) ).

cnf(f_525_3,plain,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(clausify,[status(thm)],[f_525_2]) ).

fof(f_526_1,plain,
    ! [M,N] :
      ( M = N
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M) != zero_zero(nat)
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) != zero_zero(nat) ),
    inference(fof_nnf,[status(thm)],[fact_473_diffs0__imp__equal]) ).

fof(f_526_2,plain,
    ! [U_2066,U_2065] :
      ( U_2066 = U_2065
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2065),U_2066) != zero_zero(nat)
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2066),U_2065) != zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

fof(f_526_3,plain,
    ! [U_2066,U_2065] :
      ( U_2066 = U_2065
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2065),U_2066) != zero_zero(nat)
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2066),U_2065) != zero_zero(nat) ),
    inference(definitional_conversion,[status(esa)],[f_526_2]) ).

cnf(f_526_4,plain,
    ( U_2066 = U_2065
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2065),U_2066) != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2066),U_2065) != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_526_3]) ).

fof(f_527_1,plain,
    ! [M] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_474_diff__self__eq__0]) ).

fof(f_527_2,plain,
    ! [U_2067] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2067),U_2067) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

fof(f_527_3,plain,
    ! [U_2067] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2067),U_2067) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_527_2]) ).

cnf(f_527_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2067),U_2067) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_527_3]) ).

fof(f_528_1,plain,
    ! [M] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat)) = M,
    inference(fof_nnf,[status(thm)],[fact_475_minus__nat_Odiff__0]) ).

fof(f_528_2,plain,
    ! [U_2068] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2068),zero_zero(nat)) = U_2068,
    inference(variable_rename,[status(thm)],[f_528_1]) ).

fof(f_528_3,plain,
    ! [U_2068] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2068),zero_zero(nat)) = U_2068,
    inference(definitional_conversion,[status(esa)],[f_528_2]) ).

cnf(f_528_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_2068),zero_zero(nat)) = U_2068,
    inference(clausify,[status(thm)],[f_528_3]) ).

fof(f_529_1,plain,
    ! [N] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_476_diff__0__eq__0]) ).

fof(f_529_2,plain,
    ! [U_2069] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),U_2069) = zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

fof(f_529_3,plain,
    ! [U_2069] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),U_2069) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_529_2]) ).

cnf(f_529_4,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),U_2069) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_529_3]) ).

fof(f_530_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)
      | ~ group_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_477_diff__0__right]) ).

fof(f_530_2,plain,
    ! [U_2071] :
      ( ! [U_2070] : hAPP(U_2071,U_2071,hAPP(U_2071,fun(U_2071,U_2071),minus_minus(U_2071),U_2070),zero_zero(U_2071)) = ti(U_2071,U_2070)
      | ~ group_add(U_2071) ),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

fof(f_530_3,plain,
    ! [U_2070,U_2071] :
      ( hAPP(U_2071,U_2071,hAPP(U_2071,fun(U_2071,U_2071),minus_minus(U_2071),U_2070),zero_zero(U_2071)) = ti(U_2071,U_2070)
      | ~ group_add(U_2071) ),
    inference(definitional_conversion,[status(esa)],[f_530_2]) ).

cnf(f_530_4,plain,
    ( hAPP(U_2071,U_2071,hAPP(U_2071,fun(U_2071,U_2071),minus_minus(U_2071),U_2070),zero_zero(U_2071)) = ti(U_2071,U_2070)
    | ~ group_add(U_2071) ),
    inference(clausify,[status(thm)],[f_530_3]) ).

fof(f_531_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1) = zero_zero(X_a)
      | ~ group_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_478_diff__self]) ).

fof(f_531_2,plain,
    ! [U_2073] :
      ( ! [U_2072] : hAPP(U_2073,U_2073,hAPP(U_2073,fun(U_2073,U_2073),minus_minus(U_2073),U_2072),U_2072) = zero_zero(U_2073)
      | ~ group_add(U_2073) ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

fof(f_531_3,plain,
    ! [U_2072,U_2073] :
      ( hAPP(U_2073,U_2073,hAPP(U_2073,fun(U_2073,U_2073),minus_minus(U_2073),U_2072),U_2072) = zero_zero(U_2073)
      | ~ group_add(U_2073) ),
    inference(definitional_conversion,[status(esa)],[f_531_2]) ).

cnf(f_531_4,plain,
    ( hAPP(U_2073,U_2073,hAPP(U_2073,fun(U_2073,U_2073),minus_minus(U_2073),U_2072),U_2072) = zero_zero(U_2073)
    | ~ group_add(U_2073) ),
    inference(clausify,[status(thm)],[f_531_3]) ).

fof(f_532_1,plain,
    ! [X_b] :
      ( ! [A_2,B] :
          ( ( ti(X_b,A_2) = ti(X_b,B)
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) != zero_zero(X_b) )
          & ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) = zero_zero(X_b)
            | ti(X_b,A_2) != ti(X_b,B) ) )
      | ~ ab_group_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_479_eq__iff__diff__eq__0]) ).

fof(f_532_2,plain,
    ! [U_2076] :
      ( ! [U_2075,U_2074] :
          ( ( ti(U_2076,U_2075) = ti(U_2076,U_2074)
            | hAPP(U_2076,U_2076,hAPP(U_2076,fun(U_2076,U_2076),minus_minus(U_2076),U_2075),U_2074) != zero_zero(U_2076) )
          & ( hAPP(U_2076,U_2076,hAPP(U_2076,fun(U_2076,U_2076),minus_minus(U_2076),U_2075),U_2074) = zero_zero(U_2076)
            | ti(U_2076,U_2075) != ti(U_2076,U_2074) ) )
      | ~ ab_group_add(U_2076) ),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

fof(f_532_3,plain,
    ! [U_2076] :
      ( ( ! [U_2080,U_2078] :
            ( ti(U_2076,U_2080) = ti(U_2076,U_2078)
            | hAPP(U_2076,U_2076,hAPP(U_2076,fun(U_2076,U_2076),minus_minus(U_2076),U_2080),U_2078) != zero_zero(U_2076) )
        & ! [U_2079,U_2077] :
            ( hAPP(U_2076,U_2076,hAPP(U_2076,fun(U_2076,U_2076),minus_minus(U_2076),U_2079),U_2077) = zero_zero(U_2076)
            | ti(U_2076,U_2079) != ti(U_2076,U_2077) ) )
      | ~ ab_group_add(U_2076) ),
    inference(miniscope,[status(thm)],[f_532_2]) ).

fof(f_532_4,plain,
    ( ! [U_2076,U_2077,U_2080,U_2078,U_2079] :
        ( ti(U_2076,U_2080) = ti(U_2076,U_2078)
        | hAPP(U_2076,U_2076,hAPP(U_2076,fun(U_2076,U_2076),minus_minus(U_2076),U_2080),U_2078) != zero_zero(U_2076)
        | ~ sP135(U_2076,U_2077,U_2080,U_2078,U_2079) )
    & ! [U_2076,U_2077,U_2080,U_2078,U_2079] :
        ( hAPP(U_2076,U_2076,hAPP(U_2076,fun(U_2076,U_2076),minus_minus(U_2076),U_2079),U_2077) = zero_zero(U_2076)
        | ti(U_2076,U_2079) != ti(U_2076,U_2077)
        | ~ sP135(U_2076,U_2077,U_2080,U_2078,U_2079) )
    & ! [U_2076,U_2077,U_2080,U_2078,U_2079] :
        ( sP135(U_2076,U_2077,U_2080,U_2078,U_2079)
        | ~ ab_group_add(U_2076) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP135])],[f_532_3]) ).

cnf(f_532_5,plain,
    ( sP135(U_2076,U_2077,U_2080,U_2078,U_2079)
    | ~ ab_group_add(U_2076) ),
    inference(clausify,[status(thm)],[f_532_4]) ).

cnf(f_532_6,plain,
    ( hAPP(U_2076,U_2076,hAPP(U_2076,fun(U_2076,U_2076),minus_minus(U_2076),U_2079),U_2077) = zero_zero(U_2076)
    | ti(U_2076,U_2079) != ti(U_2076,U_2077)
    | ~ sP135(U_2076,U_2077,U_2080,U_2078,U_2079) ),
    inference(clausify,[status(thm)],[f_532_4]) ).

cnf(f_532_7,plain,
    ( ti(U_2076,U_2080) = ti(U_2076,U_2078)
    | hAPP(U_2076,U_2076,hAPP(U_2076,fun(U_2076,U_2076),minus_minus(U_2076),U_2080),U_2078) != zero_zero(U_2076)
    | ~ sP135(U_2076,U_2077,U_2080,U_2078,U_2079) ),
    inference(clausify,[status(thm)],[f_532_4]) ).

fof(f_533_1,plain,
    ! [X_b] :
      ( ! [A_2,B] :
          ( ( hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) = zero_zero(X_b)
            | ti(X_b,A_2) != ti(X_b,B) )
          & ( ti(X_b,A_2) = ti(X_b,B)
            | hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B) != zero_zero(X_b) ) )
      | ~ group_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_480_right__minus__eq]) ).

fof(f_533_2,plain,
    ! [U_2083] :
      ( ! [U_2082,U_2081] :
          ( ( hAPP(U_2083,U_2083,hAPP(U_2083,fun(U_2083,U_2083),minus_minus(U_2083),U_2082),U_2081) = zero_zero(U_2083)
            | ti(U_2083,U_2082) != ti(U_2083,U_2081) )
          & ( ti(U_2083,U_2082) = ti(U_2083,U_2081)
            | hAPP(U_2083,U_2083,hAPP(U_2083,fun(U_2083,U_2083),minus_minus(U_2083),U_2082),U_2081) != zero_zero(U_2083) ) )
      | ~ group_add(U_2083) ),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

fof(f_533_3,plain,
    ! [U_2083] :
      ( ( ! [U_2087,U_2085] :
            ( hAPP(U_2083,U_2083,hAPP(U_2083,fun(U_2083,U_2083),minus_minus(U_2083),U_2087),U_2085) = zero_zero(U_2083)
            | ti(U_2083,U_2087) != ti(U_2083,U_2085) )
        & ! [U_2086,U_2084] :
            ( ti(U_2083,U_2086) = ti(U_2083,U_2084)
            | hAPP(U_2083,U_2083,hAPP(U_2083,fun(U_2083,U_2083),minus_minus(U_2083),U_2086),U_2084) != zero_zero(U_2083) ) )
      | ~ group_add(U_2083) ),
    inference(miniscope,[status(thm)],[f_533_2]) ).

fof(f_533_4,plain,
    ( ! [U_2083,U_2087,U_2085,U_2084,U_2086] :
        ( hAPP(U_2083,U_2083,hAPP(U_2083,fun(U_2083,U_2083),minus_minus(U_2083),U_2087),U_2085) = zero_zero(U_2083)
        | ti(U_2083,U_2087) != ti(U_2083,U_2085)
        | ~ sP136(U_2083,U_2087,U_2085,U_2084,U_2086) )
    & ! [U_2083,U_2087,U_2085,U_2084,U_2086] :
        ( ti(U_2083,U_2086) = ti(U_2083,U_2084)
        | hAPP(U_2083,U_2083,hAPP(U_2083,fun(U_2083,U_2083),minus_minus(U_2083),U_2086),U_2084) != zero_zero(U_2083)
        | ~ sP136(U_2083,U_2087,U_2085,U_2084,U_2086) )
    & ! [U_2083,U_2087,U_2085,U_2084,U_2086] :
        ( sP136(U_2083,U_2087,U_2085,U_2084,U_2086)
        | ~ group_add(U_2083) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136])],[f_533_3]) ).

cnf(f_533_5,plain,
    ( sP136(U_2083,U_2087,U_2085,U_2084,U_2086)
    | ~ group_add(U_2083) ),
    inference(clausify,[status(thm)],[f_533_4]) ).

cnf(f_533_6,plain,
    ( ti(U_2083,U_2086) = ti(U_2083,U_2084)
    | hAPP(U_2083,U_2083,hAPP(U_2083,fun(U_2083,U_2083),minus_minus(U_2083),U_2086),U_2084) != zero_zero(U_2083)
    | ~ sP136(U_2083,U_2087,U_2085,U_2084,U_2086) ),
    inference(clausify,[status(thm)],[f_533_4]) ).

cnf(f_533_7,plain,
    ( hAPP(U_2083,U_2083,hAPP(U_2083,fun(U_2083,U_2083),minus_minus(U_2083),U_2087),U_2085) = zero_zero(U_2083)
    | ti(U_2083,U_2087) != ti(U_2083,U_2085)
    | ~ sP136(U_2083,U_2087,U_2085,U_2084,U_2086) ),
    inference(clausify,[status(thm)],[f_533_4]) ).

fof(f_534_1,plain,
    ! [M] : hAPP(nat,nat,suc,M) != zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_481_Suc__neq__Zero]) ).

fof(f_534_2,plain,
    ! [U_2088] : hAPP(nat,nat,suc,U_2088) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

fof(f_534_3,plain,
    ! [U_2088] : hAPP(nat,nat,suc,U_2088) != zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_534_2]) ).

cnf(f_534_4,plain,
    hAPP(nat,nat,suc,U_2088) != zero_zero(nat),
    inference(clausify,[status(thm)],[f_534_3]) ).

fof(f_535_1,plain,
    ! [M] : zero_zero(nat) != hAPP(nat,nat,suc,M),
    inference(fof_nnf,[status(thm)],[fact_482_Zero__neq__Suc]) ).

fof(f_535_2,plain,
    ! [U_2089] : zero_zero(nat) != hAPP(nat,nat,suc,U_2089),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

fof(f_535_3,plain,
    ! [U_2089] : zero_zero(nat) != hAPP(nat,nat,suc,U_2089),
    inference(definitional_conversion,[status(esa)],[f_535_2]) ).

cnf(f_535_4,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,U_2089),
    inference(clausify,[status(thm)],[f_535_3]) ).

fof(f_536_1,plain,
    ! [Nat_1] : hAPP(nat,nat,suc,Nat_1) != zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_483_nat_Osimps_I3_J]) ).

fof(f_536_2,plain,
    ! [U_2090] : hAPP(nat,nat,suc,U_2090) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

fof(f_536_3,plain,
    ! [U_2090] : hAPP(nat,nat,suc,U_2090) != zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_536_2]) ).

cnf(f_536_4,plain,
    hAPP(nat,nat,suc,U_2090) != zero_zero(nat),
    inference(clausify,[status(thm)],[f_536_3]) ).

fof(f_537_1,plain,
    ! [M] : hAPP(nat,nat,suc,M) != zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_484_Suc__not__Zero]) ).

fof(f_537_2,plain,
    ! [U_2091] : hAPP(nat,nat,suc,U_2091) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

fof(f_537_3,plain,
    ! [U_2091] : hAPP(nat,nat,suc,U_2091) != zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_537_2]) ).

cnf(f_537_4,plain,
    hAPP(nat,nat,suc,U_2091) != zero_zero(nat),
    inference(clausify,[status(thm)],[f_537_3]) ).

fof(f_538_1,plain,
    ! [Nat] : zero_zero(nat) != hAPP(nat,nat,suc,Nat),
    inference(fof_nnf,[status(thm)],[fact_485_nat_Osimps_I2_J]) ).

fof(f_538_2,plain,
    ! [U_2092] : zero_zero(nat) != hAPP(nat,nat,suc,U_2092),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

fof(f_538_3,plain,
    ! [U_2092] : zero_zero(nat) != hAPP(nat,nat,suc,U_2092),
    inference(definitional_conversion,[status(esa)],[f_538_2]) ).

cnf(f_538_4,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,U_2092),
    inference(clausify,[status(thm)],[f_538_3]) ).

fof(f_539_1,plain,
    ! [M] : zero_zero(nat) != hAPP(nat,nat,suc,M),
    inference(fof_nnf,[status(thm)],[fact_486_Zero__not__Suc]) ).

fof(f_539_2,plain,
    ! [U_2093] : zero_zero(nat) != hAPP(nat,nat,suc,U_2093),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

fof(f_539_3,plain,
    ! [U_2093] : zero_zero(nat) != hAPP(nat,nat,suc,U_2093),
    inference(definitional_conversion,[status(esa)],[f_539_2]) ).

cnf(f_539_4,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,U_2093),
    inference(clausify,[status(thm)],[f_539_3]) ).

fof(f_540_1,plain,
    ! [X_b] :
      ( ! [X_1] :
          ( ( zero_zero(X_b) = ti(X_b,X_1)
            | ti(X_b,X_1) != zero_zero(X_b) )
          & ( ti(X_b,X_1) = zero_zero(X_b)
            | zero_zero(X_b) != ti(X_b,X_1) ) )
      | ~ zero(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_487_zero__reorient]) ).

fof(f_540_2,plain,
    ! [U_2095] :
      ( ! [U_2094] :
          ( ( zero_zero(U_2095) = ti(U_2095,U_2094)
            | ti(U_2095,U_2094) != zero_zero(U_2095) )
          & ( ti(U_2095,U_2094) = zero_zero(U_2095)
            | zero_zero(U_2095) != ti(U_2095,U_2094) ) )
      | ~ zero(U_2095) ),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

fof(f_540_3,plain,
    ! [U_2095] :
      ( ( ! [U_2097] :
            ( zero_zero(U_2095) = ti(U_2095,U_2097)
            | ti(U_2095,U_2097) != zero_zero(U_2095) )
        & ! [U_2096] :
            ( ti(U_2095,U_2096) = zero_zero(U_2095)
            | zero_zero(U_2095) != ti(U_2095,U_2096) ) )
      | ~ zero(U_2095) ),
    inference(miniscope,[status(thm)],[f_540_2]) ).

fof(f_540_4,plain,
    ( ! [U_2095,U_2097,U_2096] :
        ( zero_zero(U_2095) = ti(U_2095,U_2097)
        | ti(U_2095,U_2097) != zero_zero(U_2095)
        | ~ sP137(U_2095,U_2097,U_2096) )
    & ! [U_2095,U_2097,U_2096] :
        ( ti(U_2095,U_2096) = zero_zero(U_2095)
        | zero_zero(U_2095) != ti(U_2095,U_2096)
        | ~ sP137(U_2095,U_2097,U_2096) )
    & ! [U_2095,U_2097,U_2096] :
        ( sP137(U_2095,U_2097,U_2096)
        | ~ zero(U_2095) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137])],[f_540_3]) ).

cnf(f_540_5,plain,
    ( sP137(U_2095,U_2097,U_2096)
    | ~ zero(U_2095) ),
    inference(clausify,[status(thm)],[f_540_4]) ).

cnf(f_540_6,plain,
    ( ti(U_2095,U_2096) = zero_zero(U_2095)
    | zero_zero(U_2095) != ti(U_2095,U_2096)
    | ~ sP137(U_2095,U_2097,U_2096) ),
    inference(clausify,[status(thm)],[f_540_4]) ).

cnf(f_540_7,plain,
    ( zero_zero(U_2095) = ti(U_2095,U_2097)
    | ti(U_2095,U_2097) != zero_zero(U_2095)
    | ~ sP137(U_2095,U_2097,U_2096) ),
    inference(clausify,[status(thm)],[f_540_4]) ).

fof(f_541_1,plain,
    bot_bot(nat) = zero_zero(nat),
    inference(fof_nnf,[status(thm)],[fact_488_bot__nat__def]) ).

fof(f_541_2,plain,
    bot_bot(nat) = zero_zero(nat),
    inference(definitional_conversion,[status(esa)],[f_541_1]) ).

cnf(f_541_3,plain,
    bot_bot(nat) = zero_zero(nat),
    inference(clausify,[status(thm)],[f_541_2]) ).

fof(f_542_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),zero_zero(nat)))
        | Na != zero_zero(nat) )
      & ( Na = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),zero_zero(nat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_489_le__0__eq]) ).

fof(f_542_2,plain,
    ! [U_2098] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2098),zero_zero(nat)))
        | U_2098 != zero_zero(nat) )
      & ( U_2098 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2098),zero_zero(nat))) ) ),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

fof(f_542_3,plain,
    ( ! [U_2100] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2100),zero_zero(nat)))
        | U_2100 != zero_zero(nat) )
    & ! [U_2099] :
        ( U_2099 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2099),zero_zero(nat))) ) ),
    inference(miniscope,[status(thm)],[f_542_2]) ).

fof(f_542_4,plain,
    ( ! [U_2100] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2100),zero_zero(nat)))
        | U_2100 != zero_zero(nat) )
    & ! [U_2099] :
        ( U_2099 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2099),zero_zero(nat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_542_3]) ).

cnf(f_542_5,plain,
    ( U_2099 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2099),zero_zero(nat))) ),
    inference(clausify,[status(thm)],[f_542_4]) ).

cnf(f_542_6,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),U_2100),zero_zero(nat)))
    | U_2100 != zero_zero(nat) ),
    inference(clausify,[status(thm)],[f_542_4]) ).

fof(f_543_1,plain,
    ! [N] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N)),
    inference(fof_nnf,[status(thm)],[fact_490_less__eq__nat_Osimps_I1_J]) ).

fof(f_543_2,plain,
    ! [U_2101] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_2101)),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

fof(f_543_3,plain,
    ! [U_2101] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_2101)),
    inference(definitional_conversion,[status(esa)],[f_543_2]) ).

cnf(f_543_4,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),U_2101)),
    inference(clausify,[status(thm)],[f_543_3]) ).

fof(f_544_1,plain,
    ! [X_b,F1,F2] : hAPP(nat,X_b,hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(X_b,fun(fun(nat,X_b),fun(nat,X_b)),nat_case(X_b),F1),F2),zero_zero(nat)) = ti(X_b,F1),
    inference(fof_nnf,[status(thm)],[fact_491_nat__case__0]) ).

fof(f_544_2,plain,
    ! [U_2104,U_2103,U_2102] : hAPP(nat,U_2104,hAPP(fun(nat,U_2104),fun(nat,U_2104),hAPP(U_2104,fun(fun(nat,U_2104),fun(nat,U_2104)),nat_case(U_2104),U_2103),U_2102),zero_zero(nat)) = ti(U_2104,U_2103),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

fof(f_544_3,plain,
    ! [U_2102,U_2103,U_2104] : hAPP(nat,U_2104,hAPP(fun(nat,U_2104),fun(nat,U_2104),hAPP(U_2104,fun(fun(nat,U_2104),fun(nat,U_2104)),nat_case(U_2104),U_2103),U_2102),zero_zero(nat)) = ti(U_2104,U_2103),
    inference(definitional_conversion,[status(esa)],[f_544_2]) ).

cnf(f_544_4,plain,
    hAPP(nat,U_2104,hAPP(fun(nat,U_2104),fun(nat,U_2104),hAPP(U_2104,fun(fun(nat,U_2104),fun(nat,U_2104)),nat_case(U_2104),U_2103),U_2102),zero_zero(nat)) = ti(U_2104,U_2103),
    inference(clausify,[status(thm)],[f_544_3]) ).

fof(f_545_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)
      | ~ monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_492_add__0__left]) ).

fof(f_545_2,plain,
    ! [U_2106] :
      ( ! [U_2105] : hAPP(U_2106,U_2106,hAPP(U_2106,fun(U_2106,U_2106),plus_plus(U_2106),zero_zero(U_2106)),U_2105) = ti(U_2106,U_2105)
      | ~ monoid_add(U_2106) ),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

fof(f_545_3,plain,
    ! [U_2105,U_2106] :
      ( hAPP(U_2106,U_2106,hAPP(U_2106,fun(U_2106,U_2106),plus_plus(U_2106),zero_zero(U_2106)),U_2105) = ti(U_2106,U_2105)
      | ~ monoid_add(U_2106) ),
    inference(definitional_conversion,[status(esa)],[f_545_2]) ).

cnf(f_545_4,plain,
    ( hAPP(U_2106,U_2106,hAPP(U_2106,fun(U_2106,U_2106),plus_plus(U_2106),zero_zero(U_2106)),U_2105) = ti(U_2106,U_2105)
    | ~ monoid_add(U_2106) ),
    inference(clausify,[status(thm)],[f_545_3]) ).

fof(f_546_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_493_add__0]) ).

fof(f_546_2,plain,
    ! [U_2108] :
      ( ! [U_2107] : hAPP(U_2108,U_2108,hAPP(U_2108,fun(U_2108,U_2108),plus_plus(U_2108),zero_zero(U_2108)),U_2107) = ti(U_2108,U_2107)
      | ~ comm_monoid_add(U_2108) ),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

fof(f_546_3,plain,
    ! [U_2107,U_2108] :
      ( hAPP(U_2108,U_2108,hAPP(U_2108,fun(U_2108,U_2108),plus_plus(U_2108),zero_zero(U_2108)),U_2107) = ti(U_2108,U_2107)
      | ~ comm_monoid_add(U_2108) ),
    inference(definitional_conversion,[status(esa)],[f_546_2]) ).

cnf(f_546_4,plain,
    ( hAPP(U_2108,U_2108,hAPP(U_2108,fun(U_2108,U_2108),plus_plus(U_2108),zero_zero(U_2108)),U_2107) = ti(U_2108,U_2107)
    | ~ comm_monoid_add(U_2108) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

fof(f_547_1,plain,
    ! [X_b] :
      ( ! [A_2] :
          ( ( zero_zero(X_b) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)
            | ti(X_b,A_2) != zero_zero(X_b) )
          & ( ti(X_b,A_2) = zero_zero(X_b)
            | zero_zero(X_b) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2) ) )
      | ~ linord219039673up_add(X_b) ),
    inference(fof_nnf,[status(thm)],[fact_494_double__zero__sym]) ).

fof(f_547_2,plain,
    ! [U_2110] :
      ( ! [U_2109] :
          ( ( zero_zero(U_2110) = hAPP(U_2110,U_2110,hAPP(U_2110,fun(U_2110,U_2110),plus_plus(U_2110),U_2109),U_2109)
            | ti(U_2110,U_2109) != zero_zero(U_2110) )
          & ( ti(U_2110,U_2109) = zero_zero(U_2110)
            | zero_zero(U_2110) != hAPP(U_2110,U_2110,hAPP(U_2110,fun(U_2110,U_2110),plus_plus(U_2110),U_2109),U_2109) ) )
      | ~ linord219039673up_add(U_2110) ),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

fof(f_547_3,plain,
    ! [U_2110] :
      ( ( ! [U_2112] :
            ( zero_zero(U_2110) = hAPP(U_2110,U_2110,hAPP(U_2110,fun(U_2110,U_2110),plus_plus(U_2110),U_2112),U_2112)
            | ti(U_2110,U_2112) != zero_zero(U_2110) )
        & ! [U_2111] :
            ( ti(U_2110,U_2111) = zero_zero(U_2110)
            | zero_zero(U_2110) != hAPP(U_2110,U_2110,hAPP(U_2110,fun(U_2110,U_2110),plus_plus(U_2110),U_2111),U_2111) ) )
      | ~ linord219039673up_add(U_2110) ),
    inference(miniscope,[status(thm)],[f_547_2]) ).

fof(f_547_4,plain,
    ( ! [U_2110,U_2112,U_2111] :
        ( zero_zero(U_2110) = hAPP(U_2110,U_2110,hAPP(U_2110,fun(U_2110,U_2110),plus_plus(U_2110),U_2112),U_2112)
        | ti(U_2110,U_2112) != zero_zero(U_2110)
        | ~ sP138(U_2110,U_2112,U_2111) )
    & ! [U_2110,U_2112,U_2111] :
        ( ti(U_2110,U_2111) = zero_zero(U_2110)
        | zero_zero(U_2110) != hAPP(U_2110,U_2110,hAPP(U_2110,fun(U_2110,U_2110),plus_plus(U_2110),U_2111),U_2111)
        | ~ sP138(U_2110,U_2112,U_2111) )
    & ! [U_2110,U_2112,U_2111] :
        ( sP138(U_2110,U_2112,U_2111)
        | ~ linord219039673up_add(U_2110) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138])],[f_547_3]) ).

cnf(f_547_5,plain,
    ( sP138(U_2110,U_2112,U_2111)
    | ~ linord219039673up_add(U_2110) ),
    inference(clausify,[status(thm)],[f_547_4]) ).

cnf(f_547_6,plain,
    ( ti(U_2110,U_2111) = zero_zero(U_2110)
    | zero_zero(U_2110) != hAPP(U_2110,U_2110,hAPP(U_2110,fun(U_2110,U_2110),plus_plus(U_2110),U_2111),U_2111)
    | ~ sP138(U_2110,U_2112,U_2111) ),
    inference(clausify,[status(thm)],[f_547_4]) ).

cnf(f_547_7,plain,
    ( zero_zero(U_2110) = hAPP(U_2110,U_2110,hAPP(U_2110,fun(U_2110,U_2110),plus_plus(U_2110),U_2112),U_2112)
    | ti(U_2110,U_2112) != zero_zero(U_2110)
    | ~ sP138(U_2110,U_2112,U_2111) ),
    inference(clausify,[status(thm)],[f_547_4]) ).

fof(f_548_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)
      | ~ monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_495_add__0__right]) ).

fof(f_548_2,plain,
    ! [U_2114] :
      ( ! [U_2113] : hAPP(U_2114,U_2114,hAPP(U_2114,fun(U_2114,U_2114),plus_plus(U_2114),U_2113),zero_zero(U_2114)) = ti(U_2114,U_2113)
      | ~ monoid_add(U_2114) ),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

fof(f_548_3,plain,
    ! [U_2114,U_2113] :
      ( hAPP(U_2114,U_2114,hAPP(U_2114,fun(U_2114,U_2114),plus_plus(U_2114),U_2113),zero_zero(U_2114)) = ti(U_2114,U_2113)
      | ~ monoid_add(U_2114) ),
    inference(definitional_conversion,[status(esa)],[f_548_2]) ).

cnf(f_548_4,plain,
    ( hAPP(U_2114,U_2114,hAPP(U_2114,fun(U_2114,U_2114),plus_plus(U_2114),U_2113),zero_zero(U_2114)) = ti(U_2114,U_2113)
    | ~ monoid_add(U_2114) ),
    inference(clausify,[status(thm)],[f_548_3]) ).

fof(f_549_1,plain,
    ! [X_a] :
      ( ! [A_1] : hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)
      | ~ comm_monoid_add(X_a) ),
    inference(fof_nnf,[status(thm)],[fact_496_add_Ocomm__neutral]) ).

fof(f_549_2,plain,
    ! [U_2116] :
      ( ! [U_2115] : hAPP(U_2116,U_2116,hAPP(U_2116,fun(U_2116,U_2116),plus_plus(U_2116),U_2115),zero_zero(U_2116)) = ti(U_2116,U_2115)
      | ~ comm_monoid_add(U_2116) ),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

fof(f_549_3,plain,
    ! [U_2116,U_2115] :
      ( hAPP(U_2116,U_2116,hAPP(U_2116,fun(U_2116,U_2116),plus_plus(U_2116),U_2115),zero_zero(U_2116)) = ti(U_2116,U_2115)
      | ~ comm_monoid_add(U_2116) ),
    inference(definitional_conversion,[status(esa)],[f_549_2]) ).

cnf(f_549_4,plain,
    ( hAPP(U_2116,U_2116,hAPP(U_2116,fun(U_2116,U_2116),plus_plus(U_2116),U_2115),zero_zero(U_2116)) = ti(U_2116,U_2115)
    | ~ comm_monoid_add(U_2116) ),
    inference(clausify,[status(thm)],[f_549_3]) ).

fof(f_550_1,plain,
    ! [T_2,T_1] :
      ( preorder(fun(T_2,T_1))
      | ~ preorder(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Opreorder]) ).

fof(f_550_2,plain,
    ! [U_2118,U_2117] :
      ( preorder(fun(U_2118,U_2117))
      | ~ preorder(U_2117) ),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

fof(f_550_3,plain,
    ! [U_2118,U_2117] :
      ( preorder(fun(U_2118,U_2117))
      | ~ preorder(U_2117) ),
    inference(definitional_conversion,[status(esa)],[f_550_2]) ).

cnf(f_550_4,plain,
    ( preorder(fun(U_2118,U_2117))
    | ~ preorder(U_2117) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

fof(f_551_1,plain,
    ! [T_2,T_1] :
      ( finite_finite_1(fun(T_2,T_1))
      | ~ finite_finite_1(T_2)
      | ~ finite_finite_1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Finite__Set_Ofinite]) ).

fof(f_551_2,plain,
    ! [U_2120,U_2119] :
      ( finite_finite_1(fun(U_2120,U_2119))
      | ~ finite_finite_1(U_2120)
      | ~ finite_finite_1(U_2119) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

fof(f_551_3,plain,
    ! [U_2119,U_2120] :
      ( finite_finite_1(fun(U_2120,U_2119))
      | ~ finite_finite_1(U_2120)
      | ~ finite_finite_1(U_2119) ),
    inference(definitional_conversion,[status(esa)],[f_551_2]) ).

cnf(f_551_4,plain,
    ( finite_finite_1(fun(U_2120,U_2119))
    | ~ finite_finite_1(U_2120)
    | ~ finite_finite_1(U_2119) ),
    inference(clausify,[status(thm)],[f_551_3]) ).

fof(f_552_1,plain,
    ! [T_2,T_1] :
      ( order(fun(T_2,T_1))
      | ~ order(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oorder]) ).

fof(f_552_2,plain,
    ! [U_2122,U_2121] :
      ( order(fun(U_2122,U_2121))
      | ~ order(U_2121) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

fof(f_552_3,plain,
    ! [U_2122,U_2121] :
      ( order(fun(U_2122,U_2121))
      | ~ order(U_2121) ),
    inference(definitional_conversion,[status(esa)],[f_552_2]) ).

cnf(f_552_4,plain,
    ( order(fun(U_2122,U_2121))
    | ~ order(U_2121) ),
    inference(clausify,[status(thm)],[f_552_3]) ).

fof(f_553_1,plain,
    ! [T_2,T_1] :
      ( ord(fun(T_2,T_1))
      | ~ ord(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Oord]) ).

fof(f_553_2,plain,
    ! [U_2124,U_2123] :
      ( ord(fun(U_2124,U_2123))
      | ~ ord(U_2123) ),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

fof(f_553_3,plain,
    ! [U_2123,U_2124] :
      ( ord(fun(U_2124,U_2123))
      | ~ ord(U_2123) ),
    inference(definitional_conversion,[status(esa)],[f_553_2]) ).

cnf(f_553_4,plain,
    ( ord(fun(U_2124,U_2123))
    | ~ ord(U_2123) ),
    inference(clausify,[status(thm)],[f_553_3]) ).

fof(f_554_1,plain,
    ! [T_2,T_1] :
      ( bot(fun(T_2,T_1))
      | ~ bot(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Orderings_Obot]) ).

fof(f_554_2,plain,
    ! [U_2126,U_2125] :
      ( bot(fun(U_2126,U_2125))
      | ~ bot(U_2125) ),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

fof(f_554_3,plain,
    ! [U_2125,U_2126] :
      ( bot(fun(U_2126,U_2125))
      | ~ bot(U_2125) ),
    inference(definitional_conversion,[status(esa)],[f_554_2]) ).

cnf(f_554_4,plain,
    ( bot(fun(U_2126,U_2125))
    | ~ bot(U_2125) ),
    inference(clausify,[status(thm)],[f_554_3]) ).

fof(f_555_1,plain,
    ! [T_2,T_1] :
      ( minus(fun(T_2,T_1))
      | ~ minus(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun___Groups_Ominus]) ).

fof(f_555_2,plain,
    ! [U_2128,U_2127] :
      ( minus(fun(U_2128,U_2127))
      | ~ minus(U_2127) ),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

fof(f_555_3,plain,
    ! [U_2127,U_2128] :
      ( minus(fun(U_2128,U_2127))
      | ~ minus(U_2127) ),
    inference(definitional_conversion,[status(esa)],[f_555_2]) ).

cnf(f_555_4,plain,
    ( minus(fun(U_2128,U_2127))
    | ~ minus(U_2127) ),
    inference(clausify,[status(thm)],[f_555_3]) ).

fof(f_556_1,plain,
    ordere223160158up_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add]) ).

fof(f_556_2,plain,
    ordere223160158up_add(nat),
    inference(definitional_conversion,[status(esa)],[f_556_1]) ).

cnf(f_556_3,plain,
    ordere223160158up_add(nat),
    inference(clausify,[status(thm)],[f_556_2]) ).

fof(f_557_1,plain,
    ordere236663937imp_le(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le]) ).

fof(f_557_2,plain,
    ordere236663937imp_le(nat),
    inference(definitional_conversion,[status(esa)],[f_557_1]) ).

cnf(f_557_3,plain,
    ordere236663937imp_le(nat),
    inference(clausify,[status(thm)],[f_557_2]) ).

fof(f_558_1,plain,
    ordere779506340up_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__ab__semigroup__add]) ).

fof(f_558_2,plain,
    ordere779506340up_add(nat),
    inference(definitional_conversion,[status(esa)],[f_558_1]) ).

cnf(f_558_3,plain,
    ordere779506340up_add(nat),
    inference(clausify,[status(thm)],[f_558_2]) ).

fof(f_559_1,plain,
    ordere216010020id_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oordered__comm__monoid__add]) ).

fof(f_559_2,plain,
    ordere216010020id_add(nat),
    inference(definitional_conversion,[status(esa)],[f_559_1]) ).

cnf(f_559_3,plain,
    ordere216010020id_add(nat),
    inference(clausify,[status(thm)],[f_559_2]) ).

fof(f_560_1,plain,
    cancel146912293up_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add]) ).

fof(f_560_2,plain,
    cancel146912293up_add(nat),
    inference(definitional_conversion,[status(esa)],[f_560_1]) ).

cnf(f_560_3,plain,
    cancel146912293up_add(nat),
    inference(clausify,[status(thm)],[f_560_2]) ).

fof(f_561_1,plain,
    cancel_semigroup_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocancel__semigroup__add]) ).

fof(f_561_2,plain,
    cancel_semigroup_add(nat),
    inference(definitional_conversion,[status(esa)],[f_561_1]) ).

cnf(f_561_3,plain,
    cancel_semigroup_add(nat),
    inference(clausify,[status(thm)],[f_561_2]) ).

fof(f_562_1,plain,
    linordered_semidom(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Olinordered__semidom]) ).

fof(f_562_2,plain,
    linordered_semidom(nat),
    inference(definitional_conversion,[status(esa)],[f_562_1]) ).

cnf(f_562_3,plain,
    linordered_semidom(nat),
    inference(clausify,[status(thm)],[f_562_2]) ).

fof(f_563_1,plain,
    ab_semigroup_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oab__semigroup__add]) ).

fof(f_563_2,plain,
    ab_semigroup_add(nat),
    inference(definitional_conversion,[status(esa)],[f_563_1]) ).

cnf(f_563_3,plain,
    ab_semigroup_add(nat),
    inference(clausify,[status(thm)],[f_563_2]) ).

fof(f_564_1,plain,
    comm_monoid_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ocomm__monoid__add]) ).

fof(f_564_2,plain,
    comm_monoid_add(nat),
    inference(definitional_conversion,[status(esa)],[f_564_1]) ).

cnf(f_564_3,plain,
    comm_monoid_add(nat),
    inference(clausify,[status(thm)],[f_564_2]) ).

fof(f_565_1,plain,
    zero_neq_one(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Rings_Ozero__neq__one]) ).

fof(f_565_2,plain,
    zero_neq_one(nat),
    inference(definitional_conversion,[status(esa)],[f_565_1]) ).

cnf(f_565_3,plain,
    zero_neq_one(nat),
    inference(clausify,[status(thm)],[f_565_2]) ).

fof(f_566_1,plain,
    preorder(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Opreorder]) ).

fof(f_566_2,plain,
    preorder(nat),
    inference(definitional_conversion,[status(esa)],[f_566_1]) ).

cnf(f_566_3,plain,
    preorder(nat),
    inference(clausify,[status(thm)],[f_566_2]) ).

fof(f_567_1,plain,
    linorder(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Olinorder]) ).

fof(f_567_2,plain,
    linorder(nat),
    inference(definitional_conversion,[status(esa)],[f_567_1]) ).

cnf(f_567_3,plain,
    linorder(nat),
    inference(clausify,[status(thm)],[f_567_2]) ).

fof(f_568_1,plain,
    monoid_add(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Omonoid__add]) ).

fof(f_568_2,plain,
    monoid_add(nat),
    inference(definitional_conversion,[status(esa)],[f_568_1]) ).

cnf(f_568_3,plain,
    monoid_add(nat),
    inference(clausify,[status(thm)],[f_568_2]) ).

fof(f_569_1,plain,
    order(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Oorder]) ).

fof(f_569_2,plain,
    order(nat),
    inference(definitional_conversion,[status(esa)],[f_569_1]) ).

cnf(f_569_3,plain,
    order(nat),
    inference(clausify,[status(thm)],[f_569_2]) ).

fof(f_570_1,plain,
    ord(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Oord]) ).

fof(f_570_2,plain,
    ord(nat),
    inference(definitional_conversion,[status(esa)],[f_570_1]) ).

cnf(f_570_3,plain,
    ord(nat),
    inference(clausify,[status(thm)],[f_570_2]) ).

fof(f_571_1,plain,
    bot(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Orderings_Obot]) ).

fof(f_571_2,plain,
    bot(nat),
    inference(definitional_conversion,[status(esa)],[f_571_1]) ).

cnf(f_571_3,plain,
    bot(nat),
    inference(clausify,[status(thm)],[f_571_2]) ).

fof(f_572_1,plain,
    minus(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ominus]) ).

fof(f_572_2,plain,
    minus(nat),
    inference(definitional_conversion,[status(esa)],[f_572_1]) ).

cnf(f_572_3,plain,
    minus(nat),
    inference(clausify,[status(thm)],[f_572_2]) ).

fof(f_573_1,plain,
    zero(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Ozero]) ).

fof(f_573_2,plain,
    zero(nat),
    inference(definitional_conversion,[status(esa)],[f_573_1]) ).

cnf(f_573_3,plain,
    zero(nat),
    inference(clausify,[status(thm)],[f_573_2]) ).

fof(f_574_1,plain,
    one(nat),
    inference(fof_nnf,[status(thm)],[arity_Nat_Onat___Groups_Oone]) ).

fof(f_574_2,plain,
    one(nat),
    inference(definitional_conversion,[status(esa)],[f_574_1]) ).

cnf(f_574_3,plain,
    one(nat),
    inference(clausify,[status(thm)],[f_574_2]) ).

fof(f_575_1,plain,
    preorder(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Opreorder]) ).

fof(f_575_2,plain,
    preorder(bool),
    inference(definitional_conversion,[status(esa)],[f_575_1]) ).

cnf(f_575_3,plain,
    preorder(bool),
    inference(clausify,[status(thm)],[f_575_2]) ).

fof(f_576_1,plain,
    finite_finite_1(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Finite__Set_Ofinite]) ).

fof(f_576_2,plain,
    finite_finite_1(bool),
    inference(definitional_conversion,[status(esa)],[f_576_1]) ).

cnf(f_576_3,plain,
    finite_finite_1(bool),
    inference(clausify,[status(thm)],[f_576_2]) ).

fof(f_577_1,plain,
    order(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Oorder]) ).

fof(f_577_2,plain,
    order(bool),
    inference(definitional_conversion,[status(esa)],[f_577_1]) ).

cnf(f_577_3,plain,
    order(bool),
    inference(clausify,[status(thm)],[f_577_2]) ).

fof(f_578_1,plain,
    ord(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Oord]) ).

fof(f_578_2,plain,
    ord(bool),
    inference(definitional_conversion,[status(esa)],[f_578_1]) ).

cnf(f_578_3,plain,
    ord(bool),
    inference(clausify,[status(thm)],[f_578_2]) ).

fof(f_579_1,plain,
    bot(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Orderings_Obot]) ).

fof(f_579_2,plain,
    bot(bool),
    inference(definitional_conversion,[status(esa)],[f_579_1]) ).

cnf(f_579_3,plain,
    bot(bool),
    inference(clausify,[status(thm)],[f_579_2]) ).

fof(f_580_1,plain,
    minus(bool),
    inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Groups_Ominus]) ).

fof(f_580_2,plain,
    minus(bool),
    inference(definitional_conversion,[status(esa)],[f_580_1]) ).

cnf(f_580_3,plain,
    minus(bool),
    inference(clausify,[status(thm)],[f_580_2]) ).

fof(f_581_1,plain,
    ! [T_2,T_1] :
      ( finite_finite_1(sum_sum(T_2,T_1))
      | ~ finite_finite_1(T_2)
      | ~ finite_finite_1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_sum___Finite__Set_Ofinite]) ).

fof(f_581_2,plain,
    ! [U_2130,U_2129] :
      ( finite_finite_1(sum_sum(U_2130,U_2129))
      | ~ finite_finite_1(U_2130)
      | ~ finite_finite_1(U_2129) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

fof(f_581_3,plain,
    ! [U_2130,U_2129] :
      ( finite_finite_1(sum_sum(U_2130,U_2129))
      | ~ finite_finite_1(U_2130)
      | ~ finite_finite_1(U_2129) ),
    inference(definitional_conversion,[status(esa)],[f_581_2]) ).

cnf(f_581_4,plain,
    ( finite_finite_1(sum_sum(U_2130,U_2129))
    | ~ finite_finite_1(U_2130)
    | ~ finite_finite_1(U_2129) ),
    inference(clausify,[status(thm)],[f_581_3]) ).

fof(f_582_1,plain,
    ! [T,A] : ti(T,ti(T,A)) = ti(T,A),
    inference(fof_nnf,[status(thm)],[help_ti_idem]) ).

fof(f_582_2,plain,
    ! [U_2132,U_2131] : ti(U_2132,ti(U_2132,U_2131)) = ti(U_2132,U_2131),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

fof(f_582_3,plain,
    ! [U_2131,U_2132] : ti(U_2132,ti(U_2132,U_2131)) = ti(U_2132,U_2131),
    inference(definitional_conversion,[status(esa)],[f_582_2]) ).

cnf(f_582_4,plain,
    ti(U_2132,ti(U_2132,U_2131)) = ti(U_2132,U_2131),
    inference(clausify,[status(thm)],[f_582_3]) ).

fof(f_583_1,plain,
    ! [P] :
      ( ~ hBOOL(P)
      | ~ hBOOL(hAPP(bool,bool,fNot,P)) ),
    inference(fof_nnf,[status(thm)],[help_fNot_1_1_U]) ).

fof(f_583_2,plain,
    ! [U_2133] :
      ( ~ hBOOL(U_2133)
      | ~ hBOOL(hAPP(bool,bool,fNot,U_2133)) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

fof(f_583_3,plain,
    ! [U_2133] :
      ( ~ hBOOL(U_2133)
      | ~ hBOOL(hAPP(bool,bool,fNot,U_2133)) ),
    inference(definitional_conversion,[status(esa)],[f_583_2]) ).

cnf(f_583_4,plain,
    ( ~ hBOOL(U_2133)
    | ~ hBOOL(hAPP(bool,bool,fNot,U_2133)) ),
    inference(clausify,[status(thm)],[f_583_3]) ).

fof(f_584_1,plain,
    ! [P] :
      ( hBOOL(hAPP(bool,bool,fNot,P))
      | hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fNot_2_1_U]) ).

fof(f_584_2,plain,
    ! [U_2134] :
      ( hBOOL(hAPP(bool,bool,fNot,U_2134))
      | hBOOL(U_2134) ),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

fof(f_584_3,plain,
    ! [U_2134] :
      ( hBOOL(hAPP(bool,bool,fNot,U_2134))
      | hBOOL(U_2134) ),
    inference(definitional_conversion,[status(esa)],[f_584_2]) ).

cnf(f_584_4,plain,
    ( hBOOL(hAPP(bool,bool,fNot,U_2134))
    | hBOOL(U_2134) ),
    inference(clausify,[status(thm)],[f_584_3]) ).

fof(f_585_1,plain,
    ! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_U]) ).

fof(f_585_2,plain,
    ! [U_2140,U_2139,U_2138,U_2137,U_2136,U_2135] : hAPP(U_2140,U_2139,hAPP(fun(U_2140,U_2138),fun(U_2140,U_2139),hAPP(fun(U_2138,U_2139),fun(fun(U_2140,U_2138),fun(U_2140,U_2139)),combb(U_2138,U_2139,U_2140),U_2137),U_2136),U_2135) = hAPP(U_2138,U_2139,U_2137,hAPP(U_2140,U_2138,U_2136,U_2135)),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

fof(f_585_3,plain,
    ! [U_2138,U_2135,U_2136,U_2137,U_2139,U_2140] : hAPP(U_2140,U_2139,hAPP(fun(U_2140,U_2138),fun(U_2140,U_2139),hAPP(fun(U_2138,U_2139),fun(fun(U_2140,U_2138),fun(U_2140,U_2139)),combb(U_2138,U_2139,U_2140),U_2137),U_2136),U_2135) = hAPP(U_2138,U_2139,U_2137,hAPP(U_2140,U_2138,U_2136,U_2135)),
    inference(definitional_conversion,[status(esa)],[f_585_2]) ).

cnf(f_585_4,plain,
    hAPP(U_2140,U_2139,hAPP(fun(U_2140,U_2138),fun(U_2140,U_2139),hAPP(fun(U_2138,U_2139),fun(fun(U_2140,U_2138),fun(U_2140,U_2139)),combb(U_2138,U_2139,U_2140),U_2137),U_2136),U_2135) = hAPP(U_2138,U_2139,U_2137,hAPP(U_2140,U_2138,U_2136,U_2135)),
    inference(clausify,[status(thm)],[f_585_3]) ).

fof(f_586_1,plain,
    ! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_U]) ).

fof(f_586_2,plain,
    ! [U_2146,U_2145,U_2144,U_2143,U_2142,U_2141] : hAPP(U_2146,U_2145,hAPP(U_2144,fun(U_2146,U_2145),hAPP(fun(U_2146,fun(U_2144,U_2145)),fun(U_2144,fun(U_2146,U_2145)),combc(U_2146,U_2144,U_2145),U_2143),U_2142),U_2141) = hAPP(U_2144,U_2145,hAPP(U_2146,fun(U_2144,U_2145),U_2143,U_2141),U_2142),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

fof(f_586_3,plain,
    ! [U_2141,U_2142,U_2144,U_2143,U_2145,U_2146] : hAPP(U_2146,U_2145,hAPP(U_2144,fun(U_2146,U_2145),hAPP(fun(U_2146,fun(U_2144,U_2145)),fun(U_2144,fun(U_2146,U_2145)),combc(U_2146,U_2144,U_2145),U_2143),U_2142),U_2141) = hAPP(U_2144,U_2145,hAPP(U_2146,fun(U_2144,U_2145),U_2143,U_2141),U_2142),
    inference(definitional_conversion,[status(esa)],[f_586_2]) ).

cnf(f_586_4,plain,
    hAPP(U_2146,U_2145,hAPP(U_2144,fun(U_2146,U_2145),hAPP(fun(U_2146,fun(U_2144,U_2145)),fun(U_2144,fun(U_2146,U_2145)),combc(U_2146,U_2144,U_2145),U_2143),U_2142),U_2141) = hAPP(U_2144,U_2145,hAPP(U_2146,fun(U_2144,U_2145),U_2143,U_2141),U_2142),
    inference(clausify,[status(thm)],[f_586_3]) ).

fof(f_587_1,plain,
    ! [X_a,P] : hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P),
    inference(fof_nnf,[status(thm)],[help_COMBI_1_1_U]) ).

fof(f_587_2,plain,
    ! [U_2148,U_2147] : hAPP(U_2148,U_2148,combi(U_2148),U_2147) = ti(U_2148,U_2147),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

fof(f_587_3,plain,
    ! [U_2148,U_2147] : hAPP(U_2148,U_2148,combi(U_2148),U_2147) = ti(U_2148,U_2147),
    inference(definitional_conversion,[status(esa)],[f_587_2]) ).

cnf(f_587_4,plain,
    hAPP(U_2148,U_2148,combi(U_2148),U_2147) = ti(U_2148,U_2147),
    inference(clausify,[status(thm)],[f_587_3]) ).

fof(f_588_1,plain,
    ! [X_b,X_a,P,Q] : hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_U]) ).

fof(f_588_2,plain,
    ! [U_2152,U_2151,U_2150,U_2149] : hAPP(U_2152,U_2151,hAPP(U_2151,fun(U_2152,U_2151),combk(U_2151,U_2152),U_2150),U_2149) = ti(U_2151,U_2150),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

fof(f_588_3,plain,
    ! [U_2149,U_2150,U_2151,U_2152] : hAPP(U_2152,U_2151,hAPP(U_2151,fun(U_2152,U_2151),combk(U_2151,U_2152),U_2150),U_2149) = ti(U_2151,U_2150),
    inference(definitional_conversion,[status(esa)],[f_588_2]) ).

cnf(f_588_4,plain,
    hAPP(U_2152,U_2151,hAPP(U_2151,fun(U_2152,U_2151),combk(U_2151,U_2152),U_2150),U_2149) = ti(U_2151,U_2150),
    inference(clausify,[status(thm)],[f_588_3]) ).

fof(f_589_1,plain,
    ! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_U]) ).

fof(f_589_2,plain,
    ! [U_2158,U_2157,U_2156,U_2155,U_2154,U_2153] : hAPP(U_2158,U_2157,hAPP(fun(U_2158,U_2156),fun(U_2158,U_2157),hAPP(fun(U_2158,fun(U_2156,U_2157)),fun(fun(U_2158,U_2156),fun(U_2158,U_2157)),combs(U_2158,U_2156,U_2157),U_2155),U_2154),U_2153) = hAPP(U_2156,U_2157,hAPP(U_2158,fun(U_2156,U_2157),U_2155,U_2153),hAPP(U_2158,U_2156,U_2154,U_2153)),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

fof(f_589_3,plain,
    ! [U_2156,U_2153,U_2154,U_2155,U_2157,U_2158] : hAPP(U_2158,U_2157,hAPP(fun(U_2158,U_2156),fun(U_2158,U_2157),hAPP(fun(U_2158,fun(U_2156,U_2157)),fun(fun(U_2158,U_2156),fun(U_2158,U_2157)),combs(U_2158,U_2156,U_2157),U_2155),U_2154),U_2153) = hAPP(U_2156,U_2157,hAPP(U_2158,fun(U_2156,U_2157),U_2155,U_2153),hAPP(U_2158,U_2156,U_2154,U_2153)),
    inference(definitional_conversion,[status(esa)],[f_589_2]) ).

cnf(f_589_4,plain,
    hAPP(U_2158,U_2157,hAPP(fun(U_2158,U_2156),fun(U_2158,U_2157),hAPP(fun(U_2158,fun(U_2156,U_2157)),fun(fun(U_2158,U_2156),fun(U_2158,U_2157)),combs(U_2158,U_2156,U_2157),U_2155),U_2154),U_2153) = hAPP(U_2156,U_2157,hAPP(U_2158,fun(U_2156,U_2157),U_2155,U_2153),hAPP(U_2158,U_2156,U_2154,U_2153)),
    inference(clausify,[status(thm)],[f_589_3]) ).

fof(f_590_1,plain,
    ! [Q,P] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))
      | ~ hBOOL(Q)
      | ~ hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fconj_1_1_U]) ).

fof(f_590_2,plain,
    ! [U_2160,U_2159] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2159),U_2160))
      | ~ hBOOL(U_2160)
      | ~ hBOOL(U_2159) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

fof(f_590_3,plain,
    ! [U_2160] :
      ( ! [U_2159] :
          ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2159),U_2160))
          | ~ hBOOL(U_2159) )
      | ~ hBOOL(U_2160) ),
    inference(miniscope,[status(thm)],[f_590_2]) ).

fof(f_590_4,plain,
    ! [U_2160,U_2159] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2159),U_2160))
      | ~ hBOOL(U_2159)
      | ~ hBOOL(U_2160) ),
    inference(definitional_conversion,[status(esa)],[f_590_3]) ).

cnf(f_590_5,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2159),U_2160))
    | ~ hBOOL(U_2159)
    | ~ hBOOL(U_2160) ),
    inference(clausify,[status(thm)],[f_590_4]) ).

fof(f_591_1,plain,
    ! [P,Q] :
      ( hBOOL(P)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fconj_2_1_U]) ).

fof(f_591_2,plain,
    ! [U_2162,U_2161] :
      ( hBOOL(U_2162)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2162),U_2161)) ),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

fof(f_591_3,plain,
    ! [U_2162] :
      ( ! [U_2161] : ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2162),U_2161))
      | hBOOL(U_2162) ),
    inference(miniscope,[status(thm)],[f_591_2]) ).

fof(f_591_4,plain,
    ! [U_2162,U_2161] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2162),U_2161))
      | hBOOL(U_2162) ),
    inference(definitional_conversion,[status(esa)],[f_591_3]) ).

cnf(f_591_5,plain,
    ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2162),U_2161))
    | hBOOL(U_2162) ),
    inference(clausify,[status(thm)],[f_591_4]) ).

fof(f_592_1,plain,
    ! [P,Q] :
      ( hBOOL(Q)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fconj_3_1_U]) ).

fof(f_592_2,plain,
    ! [U_2164,U_2163] :
      ( hBOOL(U_2163)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2164),U_2163)) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

fof(f_592_3,plain,
    ! [U_2163,U_2164] :
      ( hBOOL(U_2163)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2164),U_2163)) ),
    inference(definitional_conversion,[status(esa)],[f_592_2]) ).

cnf(f_592_4,plain,
    ( hBOOL(U_2163)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_2164),U_2163)) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

fof(f_593_1,plain,
    ! [Q,P] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))
      | ~ hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fdisj_1_1_U]) ).

fof(f_593_2,plain,
    ! [U_2166,U_2165] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2165),U_2166))
      | ~ hBOOL(U_2165) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

fof(f_593_3,plain,
    ! [U_2165,U_2166] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2165),U_2166))
      | ~ hBOOL(U_2165) ),
    inference(definitional_conversion,[status(esa)],[f_593_2]) ).

cnf(f_593_4,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2165),U_2166))
    | ~ hBOOL(U_2165) ),
    inference(clausify,[status(thm)],[f_593_3]) ).

fof(f_594_1,plain,
    ! [P,Q] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))
      | ~ hBOOL(Q) ),
    inference(fof_nnf,[status(thm)],[help_fdisj_2_1_U]) ).

fof(f_594_2,plain,
    ! [U_2168,U_2167] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2168),U_2167))
      | ~ hBOOL(U_2167) ),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

fof(f_594_3,plain,
    ! [U_2167,U_2168] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2168),U_2167))
      | ~ hBOOL(U_2167) ),
    inference(definitional_conversion,[status(esa)],[f_594_2]) ).

cnf(f_594_4,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2168),U_2167))
    | ~ hBOOL(U_2167) ),
    inference(clausify,[status(thm)],[f_594_3]) ).

fof(f_595_1,plain,
    ! [P,Q] :
      ( hBOOL(Q)
      | hBOOL(P)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fdisj_3_1_U]) ).

fof(f_595_2,plain,
    ! [U_2170,U_2169] :
      ( hBOOL(U_2169)
      | hBOOL(U_2170)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2170),U_2169)) ),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

fof(f_595_3,plain,
    ! [U_2170] :
      ( ! [U_2169] :
          ( hBOOL(U_2169)
          | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2170),U_2169)) )
      | hBOOL(U_2170) ),
    inference(miniscope,[status(thm)],[f_595_2]) ).

fof(f_595_4,plain,
    ! [U_2169,U_2170] :
      ( hBOOL(U_2169)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2170),U_2169))
      | hBOOL(U_2170) ),
    inference(definitional_conversion,[status(esa)],[f_595_3]) ).

cnf(f_595_5,plain,
    ( hBOOL(U_2169)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_2170),U_2169))
    | hBOOL(U_2170) ),
    inference(clausify,[status(thm)],[f_595_4]) ).

fof(f_596_1,plain,
    ~ hBOOL(fFalse),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_U]) ).

fof(f_596_2,plain,
    ~ hBOOL(fFalse),
    inference(definitional_conversion,[status(esa)],[f_596_1]) ).

cnf(f_596_3,plain,
    ~ hBOOL(fFalse),
    inference(clausify,[status(thm)],[f_596_2]) ).

fof(f_597_1,plain,
    ! [P] :
      ( ti(bool,P) = fFalse
      | ti(bool,P) = fTrue ),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T]) ).

fof(f_597_2,plain,
    ! [U_2171] :
      ( ti(bool,U_2171) = fFalse
      | ti(bool,U_2171) = fTrue ),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

fof(f_597_3,plain,
    ! [U_2171] :
      ( ti(bool,U_2171) = fFalse
      | ti(bool,U_2171) = fTrue ),
    inference(definitional_conversion,[status(esa)],[f_597_2]) ).

cnf(f_597_4,plain,
    ( ti(bool,U_2171) = fFalse
    | ti(bool,U_2171) = fTrue ),
    inference(clausify,[status(thm)],[f_597_3]) ).

fof(f_598_1,plain,
    ! [X_a,X,Y] :
      ( ti(X_a,X) = ti(X_a,Y)
      | ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_T]) ).

fof(f_598_2,plain,
    ! [U_2174,U_2173,U_2172] :
      ( ti(U_2174,U_2173) = ti(U_2174,U_2172)
      | ~ hBOOL(hAPP(U_2174,bool,hAPP(U_2174,fun(U_2174,bool),fequal(U_2174),U_2173),U_2172)) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

fof(f_598_3,plain,
    ! [U_2172,U_2173,U_2174] :
      ( ti(U_2174,U_2173) = ti(U_2174,U_2172)
      | ~ hBOOL(hAPP(U_2174,bool,hAPP(U_2174,fun(U_2174,bool),fequal(U_2174),U_2173),U_2172)) ),
    inference(definitional_conversion,[status(esa)],[f_598_2]) ).

cnf(f_598_4,plain,
    ( ti(U_2174,U_2173) = ti(U_2174,U_2172)
    | ~ hBOOL(hAPP(U_2174,bool,hAPP(U_2174,fun(U_2174,bool),fequal(U_2174),U_2173),U_2172)) ),
    inference(clausify,[status(thm)],[f_598_3]) ).

fof(f_599_1,plain,
    ! [X_a,X,Y] :
      ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y))
      | ti(X_a,X) != ti(X_a,Y) ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_T]) ).

fof(f_599_2,plain,
    ! [U_2177,U_2176,U_2175] :
      ( hBOOL(hAPP(U_2177,bool,hAPP(U_2177,fun(U_2177,bool),fequal(U_2177),U_2176),U_2175))
      | ti(U_2177,U_2176) != ti(U_2177,U_2175) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

fof(f_599_3,plain,
    ! [U_2175,U_2176,U_2177] :
      ( hBOOL(hAPP(U_2177,bool,hAPP(U_2177,fun(U_2177,bool),fequal(U_2177),U_2176),U_2175))
      | ti(U_2177,U_2176) != ti(U_2177,U_2175) ),
    inference(definitional_conversion,[status(esa)],[f_599_2]) ).

cnf(f_599_4,plain,
    ( hBOOL(hAPP(U_2177,bool,hAPP(U_2177,fun(U_2177,bool),fequal(U_2177),U_2176),U_2175))
    | ti(U_2177,U_2176) != ti(U_2177,U_2175) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

fof(f_600_1,plain,
    ! [Q,P] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))
      | hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fimplies_1_1_U]) ).

fof(f_600_2,plain,
    ! [U_2179,U_2178] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_2178),U_2179))
      | hBOOL(U_2178) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

fof(f_600_3,plain,
    ! [U_2178,U_2179] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_2178),U_2179))
      | hBOOL(U_2178) ),
    inference(definitional_conversion,[status(esa)],[f_600_2]) ).

cnf(f_600_4,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_2178),U_2179))
    | hBOOL(U_2178) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

fof(f_601_1,plain,
    ! [P,Q] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))
      | ~ hBOOL(Q) ),
    inference(fof_nnf,[status(thm)],[help_fimplies_2_1_U]) ).

fof(f_601_2,plain,
    ! [U_2181,U_2180] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_2181),U_2180))
      | ~ hBOOL(U_2180) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

fof(f_601_3,plain,
    ! [U_2180,U_2181] :
      ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_2181),U_2180))
      | ~ hBOOL(U_2180) ),
    inference(definitional_conversion,[status(esa)],[f_601_2]) ).

cnf(f_601_4,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_2181),U_2180))
    | ~ hBOOL(U_2180) ),
    inference(clausify,[status(thm)],[f_601_3]) ).

fof(f_602_1,plain,
    ! [P,Q] :
      ( hBOOL(Q)
      | ~ hBOOL(P)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fimplies_3_1_U]) ).

fof(f_602_2,plain,
    ! [U_2183,U_2182] :
      ( hBOOL(U_2182)
      | ~ hBOOL(U_2183)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_2183),U_2182)) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

fof(f_602_3,plain,
    ! [U_2183] :
      ( ! [U_2182] :
          ( hBOOL(U_2182)
          | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_2183),U_2182)) )
      | ~ hBOOL(U_2183) ),
    inference(miniscope,[status(thm)],[f_602_2]) ).

fof(f_602_4,plain,
    ! [U_2182,U_2183] :
      ( hBOOL(U_2182)
      | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_2183),U_2182))
      | ~ hBOOL(U_2183) ),
    inference(definitional_conversion,[status(esa)],[f_602_3]) ).

cnf(f_602_5,plain,
    ( hBOOL(U_2182)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_2183),U_2182))
    | ~ hBOOL(U_2183) ),
    inference(clausify,[status(thm)],[f_602_4]) ).

fof(f_603_1,plain,
    hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

fof(f_603_2,plain,
    hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
    inference(definitional_conversion,[status(esa)],[f_603_1]) ).

cnf(f_603_3,plain,
    hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
    inference(clausify,[status(thm)],[f_603_2]) ).

fof(f_604_1,plain,
    hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    inference(fof_nnf,[status(thm)],[conj_1]) ).

fof(f_604_2,plain,
    hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    inference(definitional_conversion,[status(esa)],[f_604_1]) ).

cnf(f_604_3,plain,
    hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    inference(clausify,[status(thm)],[f_604_2]) ).

fof(f_605_1,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))),
    inference(fof_nnf,[status(thm)],[conj_2]) ).

fof(f_605_2,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))),
    inference(definitional_conversion,[status(esa)],[f_605_1]) ).

cnf(f_605_3,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))),
    inference(clausify,[status(thm)],[f_605_2]) ).

fof(f_606_1,plain,
    hAPP(fun(x_a,bool),nat,finite_card(x_a),g) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)),
    inference(fof_nnf,[status(thm)],[conj_3]) ).

fof(f_606_2,plain,
    hAPP(fun(x_a,bool),nat,finite_card(x_a),g) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)),
    inference(definitional_conversion,[status(esa)],[f_606_1]) ).

cnf(f_606_3,plain,
    hAPP(fun(x_a,bool),nat,finite_card(x_a),g) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)),
    inference(clausify,[status(thm)],[f_606_2]) ).

fof(f_607_1,plain,
    hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
    inference(fof_nnf,[status(thm)],[conj_4]) ).

fof(f_607_2,plain,
    hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
    inference(definitional_conversion,[status(esa)],[f_607_1]) ).

cnf(f_607_3,plain,
    hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
    inference(clausify,[status(thm)],[f_607_2]) ).

fof(f_608_1,plain,
    ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),
    inference(fof_nnf,[status(thm)],[conj_5]) ).

fof(f_608_2,plain,
    ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),
    inference(definitional_conversion,[status(esa)],[f_608_1]) ).

cnf(f_608_3,plain,
    ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),
    inference(clausify,[status(thm)],[f_608_2]) ).

fof(f_609_1,negated_conjecture,
    ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    inference(negate,[status(cth)],[conj_6]) ).

fof(f_609_2,negated_conjecture,
    ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    inference(definitional_conversion,[status(esa)],[f_609_1]) ).

cnf(f_609_3,negated_conjecture,
    ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    inference(clausify,[status(thm)],[f_609_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,
    ( 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_5,axiom,
    ( combb(Eq_x_0,Eq_x_1,Eq_x_2) = combb(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_6,axiom,
    ( ti(Eq_x_0,Eq_x_1) = ti(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_7,axiom,
    ( combc(Eq_x_0,Eq_x_1,Eq_x_2) = combc(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_8,axiom,
    ( combi(Eq_x_0) = combi(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_9,axiom,
    ( combk(Eq_x_0,Eq_x_1) = combk(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_10,axiom,
    ( combs(Eq_x_0,Eq_x_1,Eq_x_2) = combs(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_11,axiom,
    ( option(Eq_x_0) = option(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_12,axiom,
    ( finite_card(Eq_x_0) = finite_card(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_13,axiom,
    ( finite_comp_fun_idem(Eq_x_0,Eq_x_1) = finite_comp_fun_idem(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,axiom,
    ( finite_finite(Eq_x_0) = finite_finite(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_15,axiom,
    ( finite1357897459simple(Eq_x_0,Eq_x_1) = finite1357897459simple(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_16,axiom,
    ( finite_folding_one(Eq_x_0) = finite_folding_one(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_17,axiom,
    ( finite2073411215e_idem(Eq_x_0) = finite2073411215e_idem(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,axiom,
    ( minus_minus(Eq_x_0) = minus_minus(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,axiom,
    ( one_one(Eq_x_0) = one_one(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_20,axiom,
    ( plus_plus(Eq_x_0) = plus_plus(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( zero_zero(Eq_x_0) = zero_zero(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_22,axiom,
    ( the(Eq_x_0) = the(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_23,axiom,
    ( undefined(Eq_x_0) = undefined(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_24,axiom,
    ( nat_case(Eq_x_0) = nat_case(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,axiom,
    ( the_1(Eq_x_0) = the_1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_26,axiom,
    ( bot_bot(Eq_x_0) = bot_bot(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,axiom,
    ( ord_less(Eq_x_0) = ord_less(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_28,axiom,
    ( ord_less_eq(Eq_x_0) = ord_less_eq(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,axiom,
    ( partial_flat_lub(Eq_x_0) = partial_flat_lub(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_30,axiom,
    ( collect(Eq_x_0) = collect(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_31,axiom,
    ( image(Eq_x_0,Eq_x_1) = image(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,
    ( insert(Eq_x_0) = insert(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_33,axiom,
    ( the_elem(Eq_x_0) = the_elem(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_34,axiom,
    ( sum_sum(Eq_x_0,Eq_x_1) = sum_sum(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,
    ( sum_Plus(Eq_x_0,Eq_x_1) = sum_Plus(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,
    ( fequal(Eq_x_0) = fequal(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_37,axiom,
    ( hAPP(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = hAPP(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_38,axiom,
    ( member(Eq_x_0) = member(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_39,axiom,
    ( sK1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_40,axiom,
    ( sK2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_41,axiom,
    ( sK3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_42,axiom,
    ( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_43,axiom,
    ( sK5(Eq_x_0,Eq_x_1) = sK5(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,
    ( sK6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_45,axiom,
    ( sK7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_46,axiom,
    ( sK8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_47,axiom,
    ( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_48,axiom,
    ( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_49,axiom,
    ( sK11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_50,axiom,
    ( sK12(Eq_x_0) = sK12(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_51,axiom,
    ( sK13(Eq_x_0,Eq_x_1) = sK13(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,
    ( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_53,axiom,
    ( sK15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_54,axiom,
    ( sK16(Eq_x_0,Eq_x_1) = sK16(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,
    ( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_56,axiom,
    ( sK18(Eq_x_0,Eq_x_1) = sK18(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,
    ( sK19(Eq_x_0,Eq_x_1) = sK19(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_58,axiom,
    ( sK20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_59,axiom,
    ( sK21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_60,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_61,axiom,
    ( sK23(Eq_x_0,Eq_x_1,Eq_x_2) = sK23(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_62,axiom,
    ( sK24(Eq_x_0,Eq_x_1) = sK24(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_63,axiom,
    ( sK25(Eq_x_0,Eq_x_1) = sK25(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_64,axiom,
    ( sK26(Eq_x_0,Eq_x_1) = sK26(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,
    ( sK27(Eq_x_0,Eq_x_1) = sK27(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_66,axiom,
    ( sK28(Eq_x_0,Eq_x_1) = sK28(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_67,axiom,
    ( sK29(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_68,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_69,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_70,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_71,axiom,
    ( sK33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_72,axiom,
    ( sK34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_73,axiom,
    ( sK35(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_74,axiom,
    ( sK36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_75,axiom,
    ( sK37(Eq_x_0,Eq_x_1,Eq_x_2) = sK37(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_76,axiom,
    ( sK38(Eq_x_0,Eq_x_1,Eq_x_2) = sK38(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_77,axiom,
    ( sK39(Eq_x_0,Eq_x_1,Eq_x_2) = sK39(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_78,axiom,
    ( sK40(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK40(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_79,axiom,
    ( sK41(Eq_x_0,Eq_x_1,Eq_x_2) = sK41(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_80,axiom,
    ( sK42(Eq_x_0,Eq_x_1,Eq_x_2) = sK42(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_81,axiom,
    ( sK43(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK43(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_82,axiom,
    ( sK44(Eq_x_0,Eq_x_1) = sK44(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_83,axiom,
    ( sK45(Eq_x_0) = sK45(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_84,axiom,
    ( sK46(Eq_x_0,Eq_x_1) = sK46(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_85,axiom,
    ( sK47(Eq_x_0,Eq_x_1) = sK47(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_86,axiom,
    ( sK48(Eq_x_0,Eq_x_1,Eq_x_2) = sK48(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_87,axiom,
    ( sK49(Eq_x_0,Eq_x_1,Eq_x_2) = sK49(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_88,axiom,
    ( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_89,axiom,
    ( sK51(Eq_x_0,Eq_x_1) = sK51(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_90,axiom,
    ( sK52(Eq_x_0,Eq_x_1) = sK52(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_91,axiom,
    ( sK53(Eq_x_0,Eq_x_1) = sK53(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_92,axiom,
    ( sK54(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_93,axiom,
    ( sK55(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK55(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_94,axiom,
    ( sK56(Eq_x_0,Eq_x_1) = sK56(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_95,axiom,
    ( sK57(Eq_x_0,Eq_x_1,Eq_x_2) = sK57(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_96,axiom,
    ( sK58(Eq_x_0,Eq_x_1,Eq_x_2) = sK58(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_97,axiom,
    ( sK59(Eq_x_0,Eq_x_1,Eq_x_2) = sK59(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_98,axiom,
    ( sK60(Eq_x_0,Eq_x_1) = sK60(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_99,axiom,
    ( sK61(Eq_x_0,Eq_x_1) = sK61(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_100,axiom,
    ( sK62(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK62(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_101,axiom,
    ( sK63(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK63(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_102,axiom,
    ( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_103,axiom,
    ( sK65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK65(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_104,axiom,
    ( sK66(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK66(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_105,axiom,
    ( sK67(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK67(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_106,axiom,
    ( sK68(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK68(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_107,axiom,
    ( sK69(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK69(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_108,axiom,
    ( sK70(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK70(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_109,axiom,
    ( sK71(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK71(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_110,axiom,
    ( sK72(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK72(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_111,axiom,
    ( sK73(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK73(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_112,axiom,
    ( sK74(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK74(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_113,axiom,
    ( sK75(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK75(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_114,axiom,
    ( sK76(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK76(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_115,axiom,
    ( sK77(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK77(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_116,axiom,
    ( sK78(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK78(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_117,axiom,
    ( sK79(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK79(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_118,axiom,
    ( minus(Eq_y_0)
    | ~ minus(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_119,axiom,
    ( one(Eq_y_0)
    | ~ one(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_120,axiom,
    ( monoid_add(Eq_y_0)
    | ~ monoid_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_121,axiom,
    ( ab_semigroup_add(Eq_y_0)
    | ~ ab_semigroup_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_122,axiom,
    ( cancel_semigroup_add(Eq_y_0)
    | ~ cancel_semigroup_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_123,axiom,
    ( zero(Eq_y_0)
    | ~ zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_124,axiom,
    ( bot(Eq_y_0)
    | ~ bot(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_125,axiom,
    ( ord(Eq_y_0)
    | ~ ord(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_126,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_127,axiom,
    ( finite_finite_1(Eq_y_0)
    | ~ finite_finite_1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_128,axiom,
    ( order(Eq_y_0)
    | ~ order(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_129,axiom,
    ( preorder(Eq_y_0)
    | ~ preorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_130,axiom,
    ( linorder(Eq_y_0)
    | ~ linorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_131,axiom,
    ( ordered_ab_group_add(Eq_y_0)
    | ~ ordered_ab_group_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_132,axiom,
    ( ab_group_add(Eq_y_0)
    | ~ ab_group_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_133,axiom,
    ( ordere236663937imp_le(Eq_y_0)
    | ~ ordere236663937imp_le(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_134,axiom,
    ( ordere779506340up_add(Eq_y_0)
    | ~ ordere779506340up_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_135,axiom,
    ( cancel146912293up_add(Eq_y_0)
    | ~ cancel146912293up_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_136,axiom,
    ( group_add(Eq_y_0)
    | ~ group_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_137,axiom,
    ( ordere223160158up_add(Eq_y_0)
    | ~ ordere223160158up_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_138,axiom,
    ( linordered_semidom(Eq_y_0)
    | ~ linordered_semidom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_139,axiom,
    ( linordered_idom(Eq_y_0)
    | ~ linordered_idom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_140,axiom,
    ( dense_linorder(Eq_y_0)
    | ~ dense_linorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_141,axiom,
    ( zero_neq_one(Eq_y_0)
    | ~ zero_neq_one(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_142,axiom,
    ( linord219039673up_add(Eq_y_0)
    | ~ linord219039673up_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_143,axiom,
    ( ordere216010020id_add(Eq_y_0)
    | ~ ordere216010020id_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_144,axiom,
    ( comm_monoid_add(Eq_y_0)
    | ~ comm_monoid_add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_145,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_146,axiom,
    ( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_147,axiom,
    ( sP2(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_148,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_149,axiom,
    ( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_150,axiom,
    ( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_151,axiom,
    ( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_152,axiom,
    ( sP7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP7(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_153,axiom,
    ( sP8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP8(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_154,axiom,
    ( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_155,axiom,
    ( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP10(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_156,axiom,
    ( sP11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP11(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_157,axiom,
    ( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP12(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_158,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_159,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_160,axiom,
    ( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_161,axiom,
    ( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP16(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_162,axiom,
    ( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP17(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_163,axiom,
    ( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_164,axiom,
    ( sP19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_165,axiom,
    ( sP20(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_166,axiom,
    ( sP21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_167,axiom,
    ( sP22(Eq_y_0,Eq_y_1)
    | ~ sP22(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_168,axiom,
    ( sP23(Eq_y_0,Eq_y_1)
    | ~ sP23(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_169,axiom,
    ( sP24(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP24(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_170,axiom,
    ( sP25(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_171,axiom,
    ( sP26(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP26(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_172,axiom,
    ( sP27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_173,axiom,
    ( sP28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_174,axiom,
    ( sP29(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP29(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_175,axiom,
    ( sP30(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP30(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_176,axiom,
    ( sP31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP31(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_177,axiom,
    ( sP32(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP32(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_178,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_179,axiom,
    ( sP34(Eq_y_0,Eq_y_1)
    | ~ sP34(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_180,axiom,
    ( sP35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP35(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_181,axiom,
    ( sP36(Eq_y_0,Eq_y_1)
    | ~ sP36(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_182,axiom,
    ( sP37(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP37(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_183,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_184,axiom,
    ( sP39(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_185,axiom,
    ( sP40(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP40(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_186,axiom,
    ( sP41(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP41(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_187,axiom,
    ( sP42(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP42(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_188,axiom,
    ( sP43(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP43(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_189,axiom,
    ( sP44(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP44(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_190,axiom,
    ( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_191,axiom,
    ( sP46(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP46(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_192,axiom,
    ( sP47(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP47(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_193,axiom,
    ( sP48(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP48(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_194,axiom,
    ( sP49(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP49(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_195,axiom,
    ( sP50(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP50(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_196,axiom,
    ( sP51(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP51(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_197,axiom,
    ( sP52(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP52(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_198,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_199,axiom,
    ( sP54(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP54(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_200,axiom,
    ( sP55(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP55(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_201,axiom,
    ( sP56(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP56(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_202,axiom,
    ( sP57(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_203,axiom,
    ( sP58(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP58(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_204,axiom,
    ( sP59(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP59(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_205,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_206,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_207,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_208,axiom,
    ( sP63(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP63(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_209,axiom,
    ( sP64(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP64(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_210,axiom,
    ( sP65(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_211,axiom,
    ( sP66(Eq_y_0,Eq_y_1)
    | ~ sP66(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_212,axiom,
    ( sP67(Eq_y_0,Eq_y_1)
    | ~ sP67(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_213,axiom,
    ( sP68(Eq_y_0,Eq_y_1)
    | ~ sP68(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_214,axiom,
    ( sP69(Eq_y_0,Eq_y_1)
    | ~ sP69(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_215,axiom,
    ( sP70(Eq_y_0,Eq_y_1)
    | ~ sP70(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_216,axiom,
    ( sP71(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP71(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_217,axiom,
    ( sP72(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP72(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_218,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_219,axiom,
    ( sP74(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_220,axiom,
    ( sP75(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP75(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_221,axiom,
    ( sP76(Eq_y_0,Eq_y_1)
    | ~ sP76(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_222,axiom,
    ( sP77(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP77(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_223,axiom,
    ( sP78(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP78(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_224,axiom,
    ( sP79(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP79(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_225,axiom,
    ( sP80(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP80(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_226,axiom,
    ( sP81(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP81(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_227,axiom,
    ( sP82(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP82(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_228,axiom,
    ( sP83(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP83(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_229,axiom,
    ( sP84(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP84(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_230,axiom,
    ( sP85(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP85(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_231,axiom,
    ( sP86(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP86(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_232,axiom,
    ( sP87(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP87(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_233,axiom,
    ( sP88(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP88(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_234,axiom,
    ( sP89(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP89(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP90(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP90(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP91(Eq_y_0,Eq_y_1)
    | ~ sP91(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_237,axiom,
    ( sP92(Eq_y_0,Eq_y_1)
    | ~ sP92(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_238,axiom,
    ( sP93(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP93(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP94(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP94(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_240,axiom,
    ( sP95(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP95(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_241,axiom,
    ( sP96(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP96(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_242,axiom,
    ( sP97(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP97(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_243,axiom,
    ( sP98(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP98(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_244,axiom,
    ( sP99(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP99(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_245,axiom,
    ( sP100(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP100(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_246,axiom,
    ( sP101(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP101(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_247,axiom,
    ( sP102(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP102(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_248,axiom,
    ( sP103(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP103(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_249,axiom,
    ( sP104(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP104(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_250,axiom,
    ( sP105(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP105(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_251,axiom,
    ( sP106(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP106(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_252,axiom,
    ( sP107(Eq_y_0,Eq_y_1)
    | ~ sP107(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_253,axiom,
    ( sP108(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP108(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_254,axiom,
    ( sP109(Eq_y_0,Eq_y_1)
    | ~ sP109(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,
    ( sP110(Eq_y_0,Eq_y_1)
    | ~ sP110(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,
    ( sP111(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP111(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_257,axiom,
    ( sP112(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP112(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_258,axiom,
    ( sP113(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP113(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_259,axiom,
    ( sP114(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP114(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_260,axiom,
    ( sP115(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_261,axiom,
    ( sP116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_262,axiom,
    ( sP117(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP117(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_263,axiom,
    ( sP118(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP118(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_264,axiom,
    ( sP119(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP119(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_265,axiom,
    ( sP120(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP120(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_266,axiom,
    ( sP121(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP121(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_267,axiom,
    ( sP122(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP122(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_268,axiom,
    ( sP123(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP123(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_269,axiom,
    ( sP124(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP124(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_270,axiom,
    ( sP125(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP125(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_271,axiom,
    ( sP126(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP126(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_272,axiom,
    ( sP127(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP127(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_273,axiom,
    ( sP128(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP128(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_274,axiom,
    ( sP129(Eq_y_0,Eq_y_1)
    | ~ sP129(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_275,axiom,
    ( sP130(Eq_y_0,Eq_y_1)
    | ~ sP130(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_276,axiom,
    ( sP131(Eq_y_0,Eq_y_1)
    | ~ sP131(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_277,axiom,
    ( sP132(Eq_y_0,Eq_y_1)
    | ~ sP132(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_278,axiom,
    ( sP133(Eq_y_0,Eq_y_1)
    | ~ sP133(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_279,axiom,
    ( sP134(Eq_y_0,Eq_y_1)
    | ~ sP134(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_280,axiom,
    ( sP135(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP135(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_281,axiom,
    ( sP136(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP136(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_282,axiom,
    ( sP137(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP137(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_283,axiom,
    ( sP138(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP138(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW473+6 : 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
% 0.11/0.52  % Computer : n020.cluster.edu
% 0.11/0.52  % Model    : x86_64 x86_64
% 0.11/0.52  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.52  % Memory   : 8046.5625MB
% 0.11/0.52  % OS       : Linux 6.8.0-71-generic
% 0.11/0.52  % CPULimit : 300
% 0.11/0.52  % WCLimit  : 300
% 0.11/0.52  % DateTime : Sun Sep 20 05:42:49 UTC 2026
% 0.11/0.52  % CPUTime  : 
% 57.50/57.93  % SZS status Theorem for theBenchmark
% 57.50/57.93  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------